Feature Extraction and its Use in Enhancing Image ...

Faculty of Engineering

Feature Extraction and its Use in Enhancing Image Performance and Fingerprint Classification

by

Mina Adel Thabet Bishay

A Thesis Submitted in partial fulfillment of the requirements for the degree of Master of Science

The Department of Electrical Engineering Assiut University, Assiut, Egypt March 2014

Abstract The aim of feature extraction in image processing is simplifying the amount of resources required to describe a large set of data accurately by transforming the input data into set of features. To select a set of appropriate numerical features from the interested objects for the purpose of classification has been among the fundamental problems in the pattern recognition system. One of the solutions, the utilization of moments for object characterization has received considerable attentions in recent years. Many applications in image processing are based on feature extraction. In this thesis, we present four contributions to improve image applications that are based on feature extraction. Firstly, new techniques are described to increase the efficiency of Pseudo Zernike moment (PZM) computation for small images. It is proposed to compute PZM for a decimated image, and use Bspline interpolation to interpolate between image pixels. This

significantly

improves

PZM

computations

due

it

is

smooth

and

robust

performance. Further improvements are also possible, by basing our computations on least

square

Bspline

decimated

images,

as

well

as

optimizing

some

of

PZM

coefficients. Secondly, the rotation invariant property of Pseudo Zernike moments is used in modifying

a

natural

preserving

watermarking

technique,

that

are

known

for

its

robustness against cropping, compression and noise attacks, to make it withstand rotation attacks. Thirdly, feature extraction is used to improve the fingerprint segmentation, one of the

main

steps

of

Automatic

Fingerprint

Identification

System.

An

accurate

segmentation algorithm is helpful in speeding up the computations. In this thesis, a novel segmentation method is presented that are mainly based on block range calculation

together

with

some

morphological

i

opening

and

closing

operations

to

extract

the

fingerprint

foreground.

The proposed

method

provides

accurate

high-

resolution segmentation results compared to other segmentation methods.

Finally, a new approach for fingerprint image enhancement is introduced to improve the extraction of features from poor quality fingerprints. The enhancement method is based on features extracted from the fingerprint such as the local ridge orientation and local frequency. We use two stage for enhancement in both the spatial domain and the frequency domain. The fingerprint image is enhanced in the spatial domain with a directional mean filter or an interpolation technique. Then, a frequency bandpass filter that is separable in the radial and angular frequency domains, is employed. The center frequency of the radial filter is accurately determined using a novel Radon-based technique. The second stage is repeated two or three times. The iteration method enhances gradually and significantly the low quality fingerprint images. We also measure the effectiveness of the enhancement algorithm and show that it can improve the sensitivity and recognition accuracy of existing feature extraction and matching algorithms.

ii

Dedicated To My Family & My Friends

iii

Acknowledgments Many people have provided advice, support, and encouragement to the author, during the research which led to this thesis. I would like to express my heartfelt appreciation to: My supervisor, Prof. Dr. Mamdouh F. Fahmy, for his generous support and intellectual guidance throughout my years as a graduate student; his insightful advice, clear vision, many suggestions, and endless efforts to be available for many educational discussions, were invaluable; Prof.

Dr.

Gamal

M.

Abd

Raheem,

whose

friendship

and

encouragement

were

invaluable; My parents and my brother who taught me the importance of education and shared the pains and happiness during the course of this work, their endless support, sacrifice, and understanding kept me going through it all; My friends who kept me thinking that there really was a light at the end of the tunnel;

iv

TABLE OF CONTENTS Page ABSTRACT………………………………………………………………………………....... i DEDICATION……………………………………………………………………………....... iii ACKNOWLEDGMENTS…………………………………………………………………..... iv TABLE OF CONTENTS…………………………………………………………………...... v LIST OF FIGURES………………………………………………………………………....... viii LIST OF TABLES ………………………………………………………………………….... xiii LIST OF ABBREVIATIONS ..................................................................................................... xiv CHAPTER 1: Image Identification Using the Moment Concept ....................................... ……………………………………………………….. 1.1 Introduction……………………………………………………………………. 1.2 Geometric Moments ……………………………………………….................

1 1 2

1.2.1 Properties of Geometric Moments …………………………………

3

1.2.2 Image Reconstruction from Geometric Moments .…………………

5

1.2.3 Moment Invariants ……..…………..………….…………….…….

6

1.2.4 Accuracy ..………………..………………..……. …………………

9

1.3 Legendre Moments …….……………………………………………………

9

1.3.1 Legendre Polynomials ………………….………………….………

9

1.3.2 Legendre Moments ………………….…………………….………

11

1.3.3 Image Reconstruction from Legendre Moments ....………..………

12

1.4 Zernike Moments ……………………………………………………………..

13

1.4.1 Zernike Polynomials ………………………………...……............

13

1.4.2 Zernike Moments ………………………………………….............

16

1.4.3 Rotational Properties of Zernike Moments ………………………

17

1.4.4 Image Reconstruction from Zernike Moments ……………………

19

1.4.5 Accuracy …………………………………………………………

20

1.5 Pseudo Zernike Moments ………..………..………..……………..………...... CHAPTER 2: Enhanced B-spline Based Zerinke Moment Evaluations ……..……... 2.1 Introduction .........................................................…...….….….….….….…..…..….… v

13 22 26 26

2.2 B-spline Interpolation …………………………………….…………………

26

2.2.1 Mathematical Background ………………………………………

27

2.2.2 Signal interpolation using B-spline polynomials ………………

28

2.2.3 B-spline calculation ………………………………………………

30

2.3 B-spline Based PZM Computation ………………………………………………

32

2.4 Least Square B-spline PZM Computation …………….………………………… …………………………………….

33

2.5 Optimization of PZM Coefficients …………..…………………………………

34

CHAPTER 3: NPT Watermarking Technique …..…..…..…..…..…..…..…..…..…..…..…..

36

3.1 Introduction……………………………………………………………………….. …………………………………………………... 3.2 Mathematical background …………………………………..………………… 4.1Watermark Embedding and Extraction ……………………………………… 3.3

36

3.4 Robustness to Attacks ……………………………………..…………………

40

4.2

3.4.1 Robustness to Cropping ……………………………………………

37 39

40

3.4.2 Robustness to Compression Attacks ……………………………

41

3.4.3 Robustness to Noise Attacks ……………………………………

41

3.4.4 Rotation Attacks …………………………………………………

43

3.5 Similarity between PZM of the Watermarked Image and Original Image …………

44

3.6 Rotation Invariant NPT Watermarking Scheme

45

……………………………..……………… CHAPTER 4: Introduction to Fingerprints

50

4.1 Introduction………………………………………………………………….. ……………………………………………………………………

50

4.2 Biometrics …………………………………………………………………… ……………………………. 4.2.1 The Verification Problem

50 52

4.2.2 Performance Evaluation ……………………………………… ……………………………….……………………

53

4.2.3 System Errors …………………………………………………

54

4.2.4 Caveat …………………………………………………………

55

4.3 Fingerprint as a Biometric ………………………………………………….

57

4.4 Fingerprint Representations and Matching Algorithms ……………………….

60 60

4.4.1 Image 4.4.2 Minutiae Representation ……………………………….………………………………………………………… ….…………………………………………………………

vi

61

CHAPTER 5: A Fingerprint Segmentation Technique Based on Morphological

65

Processing .......................................................................................……………………… 5.15.1 Introduction………………………………………………………………………..

65

5.25.2 Feature Extraction …………………………………………………………………

67

5.35.3The Proposed Segmentation Technique ………………………………………….…

70

5.4

5.3.1 Basic Morphological Operation ……......……………………………

71

5.5 5.3.2 Fingerprint Segmentation ...………………………………………… ……………

71

5.3.3 Contour Smoothing …………………………………………………

72

5.45.7Experimental Results ………………………………………………………………

74

CHAPTER 6: A Novel Scheme for Fingerprint Enhancement ...............…………………

79

6.1 Introduction………………………………………………………………………… 6.2 The Pre-Processing Step .................................………………………………………

79 810

6.3 The First Stage Enhancement : Spatial Filter ..............................................................

83

6.4 The Second Stage Enhancement: Frequency Bandpass Filter ………………............ 6.5 Experimental Results ..................................................………………………………

87

6.6 Application in Minutiae Extraction .........…………………………………….......…

95

5.6

CHAPTER 7: Conclusion ………………………………………………………………… REFERENCES …………………………………………………………………………….

93

97

99

List of Published Papers ……………………………………………………………… 106

vii

List of Figures Figure

Page

CHAPTER 1 7 1.1 An object which have been translated, scaled and rotated .............................................. 1.2 (a) Lena image. (b) Rotated Lena image. (c) Scaled Lena image ..................................

8

1.3 Comparing absolute distance of 10th order PZM for a rotated Cameraman image ........

18

1.4 (a) 8x8 image. (b) image includes unit circle .................................................................

21

1.5 (a) 8x8 image. (b) unit circle includes image .................................................................

22

1.6 Comparing absolute distance of 10th order PZM for a noisy Cameraman image ...........

24

1.7 PSNR performance when using complete 256x256 image and Bicubic interpolation method in PZM computations for: (a) Lena image. (b) Cameraman image ..........................

25

CHAPTER 2 2.1 Bspline generation using Haar functions ........................................................................

27

2.2 Flipping technique of non-real time computation ...........................................................

29

2.3 PSNR performance when using complete 256x256, Bspline, and Bicubic interpolation methods in PZM computations ........................................................................

33

2.4 Reconstructed Lena images using 80 pseudo Zernike Moments generated using Bspline and Bi-cubic interpolation ........................................................................................

33

2.5 PSNR performance when using complete 256x256, L S Bspline, Bspline and Bicubic interpolation methods in PZM computations ..........................................................................

34

2.6 Comparing PSNR performance when using optimization in PZM computations, with LS and Bspline interpolation ...........................................................................................

35

viii

CHAPTER 3 3.1 Transform domain basis. (a) Hartley. (b) DCT. (c) Hadamard ........................................

38

3.2 The main steps of the process of watermark embedding. ..............................................

39

3.3 Watermark Extraction. ...................................................................................................

40

3.4 Cropping performance. (a) Embedded watermarked image. (b) NPT watermarked image. (c) Cropped watermarked image. (d) Extracted watermarking logo .........................................

40

3.5 Compression performance of the 3 embedding schemes, bpp= 0.95 and 0.93, together with the extracted logos for top embedding using 0.8 bpp ...................................................

42

3.6 Comparison of NCORR of both top and bottom embedding cases in noisy environments for different SNR’s, for 2 different alpha values, 0.95 and 0.93 .................................................

42

3.7 Typical performance of Top embedding case with 0.95 : Left: AWGN case, NCORR=0.938 Right: Salt and pepper case with D=0.05, NCORR=0.9 .............................

43

3.8 Watermark Extraction after rotation attack. ...................................................................

43

3.9 Absolute distance of 10th order PZM between unrotated and rotated watermarked Cameraman image with other data box images ....................................................................

44

3.10 Watermark Extraction after de-rotation ........................................................................

45

3.11 Rotation and de-rotation of the host image. (a) Host image (Y). (b) Rotated host image (Yr). (c) De-rotated host image (Ŷ) .............................................................................

46

3.12 Determination of interpolation errors. (a) Host image (Y). (b) De-rotated host image (Ŷ). (c) Error image er ...........................................................................................................

46

3.13 Steps of Rotation error compensation. (a) Error image er. (b) De-rotated watermarked image. (c) Obtained image ..............................................................................

46

3.14 Watermark extraction after rotation error compensation. ............................................

47

3.15 (a) Watermarked transformed image. (b) Transmitted watermarked image after replacing the logo region by the original host image part.(c) Rotated watermarked image.(d) Watermarked image after rotation error compensation. (e) Extracted logo .........

48

ix

3.16 (a) Watermarked transformed image. (b) Transmitted watermarked image after replacing the logo region by the original host image part. (c) Rotated watermarked image.(d) Watermarked image after rotation error compensation. (e) Extracted logo ........

48

CHAPTER 4 4.1 Various biometric modalities: (a) Fingerprint. (b) speech. (c) face. (d) iris. (e) hand geometry ..........................................................................................................................

51

4.2 General architecture of a biometric ................................................................................

52

4.3 An illustration showing the intra user variation present in biometric signals ...............

53

4.4 Genuine and imposter distributions ................................................................................

55

4.5 An illustration of a general biometric system with points of threats identified ..............

56

4.6 Revenue by biometric traits as estimated by International Biometric Group in 2009. Fingerprint-based systems (both forensic and non-forensic applications) continue to be the leading biometric technology in terms of market share, commanding 66.7 % of biometric revenue ........................................................................................................... 4.7 Fingerprint Classes: (a) Tented Arch (b) Arch (c) Right Loop (d) Left Loop (e) Whorl 4.8 (a) Local Features: Minutiae (b) Global Features: Core and Delta .................................

58 59

59

4.9 General architecture of a fingerprint verification system ..............................................

59

4.10 The illustration shows the results of correlation between images of the same user(a) and different user(b). It can be seen the peak output of the correlation is high in case of genuine match and low for an imposter match ..........................................................

61

4.11 The figure shows the primary approach for matching minutiae. Each fingerprint is represented as a set of tuples each specifying the properties of minutiae (usually (x,y, )) .............................................................................................................................

62

4.12 The minutiae are matched by transforming one set of minutiae and determining the number of minutiae that fall within a bounded region of anther. ...................................

64

x

CHAPTER 5

5.1 Fingerprint images from different database. ......................................................................

66

5.2 Flowchart for the proposed segmentation method ............................................................

67

5.3 Foreground and background distributions in: (a) Range. (b) Entropy. (c) Gradient entropy ...............................................................................................................................

69

5.4 (a) Fingerprint image. (b) Binarized image without feature extraction. (c) The resultant segmented image of (b). (d) Binarized image with feature extraction. (e) The resultant segmented image of (d). ..................................................................................

70

5.5 The proposed fingerprint segmentation algorithm .........................................................

73

5.6 Segmentation results of different databases: (a) FVC2004_DB1_103_4, (b) FVC2004_DB2_101_2, (c) FVC2004_DB3_101_4, (d) FVC2002_DB1_101_4, (e) FVC2002_DB2_106_4, (f) FVC2000_DB3_107_6, (g) FVC2000_DB1_103_7, (h) FVC2000_DB2_103_6, (i) FVC2002_DB3_107_8, (j) FVC2004_DB4_107_7, (k) FVC2002_DB4_105_1, (l) FVC2000_DB4_110_1 ........................................................

76

CHAPTER 6 6.1 (a) Original image. (b) Histogram equalized image. (c) Normalized image. (d) Image filtered using Wiener filter ..............................................................................................

79

6.2 The steps of the first-stage enhancement method. (a, e) Original image. (b, f) Segmented image. (c, g) Normalized image. (d, h) Image filtered using DMF ..............

84

6.3 Demonstration of a rotated rectangle to match the local orientation. .............................

85

6.4 Orientation of Fingerprint Ridge Flow ...........................................................................

86 85

6.5 The steps of the first-stage enhancement method. (a) Original image. (b) Segmented image. (c) Normalized image. (d) The proposed broken ridge interpolation technique .

86

6.6 Performance of the proposed interpolation technique ....................................................

86

6.7 (a) Original image. (b) Normalized image. (c) Image filtered using DMF. (d) The interpolated image ..........................................................................................................

87

xi

6.8 A low quality 4_8.tif fingerprint image from FVC2004. ..............................................

88

6.9 Ridge-valley intensity variations over a local block [72] ...............................................

88

6.10 Radon transform behavior along the normal of the orientation direction .....................

89

6.11 (a) Original image. (b) 1st stage enhanced image. (c) 1st stage + 2nd stage enhanced image (before iteration step). (d) Our proposed two stage enhanced image ..................

92

6.12 (a),(f),(k) Original fingerprint images. (b),(g),(l) Hong enhanced image. (c),(h),(m) STFT enhanced image. (d),(i),(n) Yang enhanced image. (e),(j),(o) Our proposed enhanced image .................................................................................................................

xii

93

List of Tables Table

Page

CHAPTER 1

1.1 Comparison of seven invariant Hu moments calculated for images in Fig.(1.1) ............

8

1.2 Comparison of seven invariant Hu moments calculated for images in Fig.(1.2) ............

8

1.3 List of Legendre Polynomials up to 10th order ...............................................................

11

1.4 Listing of Zernike Polynomials up to 7th order ..............................................................

14

CHAPTER 5 5.1 Specifications of chosen fingerprints. ............................................................................

68

5.2 Scanners/technologies used for collecting the databases of FVC2004, FVC2002 & FVC2000 .......................................................................................................................

74

5.3 Classification error rates of FVC2004, FVC2002 & FVC2000 ................................

75

5.4 Average segmentation time for each DB in FVC2004, FVC2002, and FVC2000 .........

77

CHAPTER 6 87

6.1

Average time (second) of the 1st enhancement stage for each DB in FVC2004 ..........

6.2

Average TMR (%), FMR (%), DMR (%), AND EMR (%) for different enhancement 96 algorithms .......................................................................................................................

6.3

Average enhancement time (second) for each DB in FVC2004 ................................. xiii

96

LIST OF ABBREVIATIONS HCI

Human Computer Interaction

FEM

Feature Extraction Method

ZM

Zernike Moments

PZM

Pseudo Zernike Moments

PSNR

Peak Signal to Noise Ratio

NPT

Natural Preserving Transform

DCT

Discrete Cosine Transform

bpp

bits per pixel

NCORR

Normalized Correlation

AWGN

Additive White Gaussian Noise

FTE

Failure to enroll

FTA

Failure to authenticate

FMR

False Match Rate

FNMR

False Non Match Rate

CMV

coherence, mean and variance

SE

Structuring Element

pdf

probability density function

FVC

Fingerprint Verification Competition

fpts

fingerprints

AFIS

Automatic Fingerprint Identification System

DMF

Directional Mean Filter

FFT

Fast Fourier Transform

TM

True minutiae

PM

Paired minutiae

FM

False minutiae

DM

Dropped minutiae

EM

Exchanged minutiae

TMR

True Minutiae Ratio

FMR

False Minutiae Ratio

DMR

Dropped Minutiae Ratio

xiv

EMR

Exchanged Minutiae Ratio

Err

classification error

xv

Chapter 1

Image Identification Using the Moment Concept

CHAPTER 1 Image Identification Using the Moment Concept 1.1 Introduction Recently, there has been an increasing interest on modern machine vision systems for industrial and commercial purposes. More and more products are introduced in the market, which are making use of visual information captured by digital cameras. For example, as in detecting and/or recognizing a face in an unconstrained environment for security purposes, for analyzing the emotional states of a human by processing his facial expressions, or for providing a vision based interface in the context of the Human Computer Interaction (HCI), etc. In almost all the modern machine vision systems there is

a

common

processing

procedure

called

feature

extraction,

dealing

with

the

appropriate representation of the visual information. This task has two main objectives simultaneously: the compact description of the useful information by a set of numbers (features), while keeping the dimension of the feature as low as possible. Image moments constitute an important Feature Extraction Method (FEM) which generates high discriminative features, able to capture the particular characteristics of the described pattern while being able to distinguish it from similar or totally different objects. Their ability to fully describe an image by encoding its contents in a compact way makes them suitable for many fields in digital image processing, such as image analysis, image watermarking and pattern recognition. In order to use the moments to classify visual objects, they have to ensure high recognition rates for all possible object’s orientations. This condition requires that the class of moments used should be invariant under the basic geometric transformations of rotation, scaling and translation.

.

. 1

Chapter 1


Among the several moment families introduced in the past, the geometric and orthogonal moments. Orthogonal moments are the most popular moments. They are widely used in many applications, due to their orthogonality property. As a result, the orthogonal moments have minimum information redundancy meaning that different moment orders describe different parts of the image. In this chapter, the main theoretical properties of the geometric, and the orthogonal moments

like

Legendre,

Zernike,

and

Pseudo

Zernike moments

as

well

as

the

reconstruction of an image from these moments are described. It is assumed that an image can be represented by a real valued measurable function f(x, y).

1.2 Geometric Moments The two-dimensional geometric moment of order (p+q) of a function f(x, y) is defined as:

(1.1) where p,q = 0,1,2,....,  . Note that the monomial product xpyq is the basis function for this moment definition. Thus, a set of n moments of all Mpq's for p+q

, i.e., the set

contains (n+1)(n+2)/2 elements.

The use of moments for image analysis and pattern recognition was inspired by Hu [1] and Alt [2]. Hu stated that if f(x, y) is piecewise continuous and has nonzero values only in a finite region of the (x, y) plane, then the moment sequence Mpq is uniquely determined by f(x, y) and conversely f(x, y) is uniquely determined by Mpq, (this will be proved shortly). Considering the fact that an image segment has finite area, or in the worst case is piecewise continuous, moments of all orders exist and a complete moment set can be computed and used uniquely to describe the information contained in the image. However, to obtain all the information contained in an image, this requires an infinite number of moment values. Therefore, selecting a meaningful subset of the

.

. 2

Chapter 1


moment values that contain sufficient information to characterize the image uniquely for a specific application becomes very important.

1.2.1 Properties of Geometric Moments The lower order moments

represent some well

known fundamental

geometric

properties of the underlying image functions. Central Moments The central moments of f(x, y) are defined as

(1.2)

where ẋ and ẏ are defined in (1.7). One can show that, the central moments µpq defined in Eq. (1.2) are invariant under the translation of coordinates [1]:

(1.3) where α and

are constants.

Mass and Area The definition of the zeroth order moment M00 of the function f(x, y) is given by:

(1.4)

00

represents the total mass of the given function or image f(x, y). When computed for a binary image, the zeroth moment (1.4) represents the total area of the image. Centre of Mass The two first order moments, .

. 3

Chapter 1


10

(1.5)

01

(1.6)

and

represent the centre of mass of the image f(x, y). The centre of mass is the point where all the mass of the image could be concentrated without changing the first moment of the image about any axis. In the two-dimensional case, in terms of moment values, the coordinates of the centre of mass are

,

(1.7)

As a usual practice, the centre of mass is chosen to represent the position of an image in the field of view. The equations in (1.7) define a unique location of the image f(x, y) that can be used as a reference point to describe the position of the image. Orientations The second order moments {M02 , M11 , M20 } known as the moments of intertia. These moments may be used to determine an important image feature, e.g. orientation. In general, the orientation of an image describes how the image lies in the field of view, or the directions of the principal axes. In terms of moments, the orientation of the principal axes , are given by [3]: (1.8)

In (1.8),

is the angle of the principal axis nearest to the x axis and is in the range

.

.

. 4

Chapter 1


1.2.2 Image Reconstruction from Geometric Moments In this section, we want to verify how much information is contained in moments. This issue can be addressed by analyzing the reconstruction power of the moments. A problem which is raised here can be stated as follows, if only a finite set of moments of an image is given, how well can we reconstruct the image? We start the investigation by discussing the inverse moment problem. Consider the characteristic function [4] for the image function f(x, y) : (1.9) Provided that f(x, y) is piecewise continuous and the integration limits are finite, is a continuous function and may be expanded as a power series in u and v. Therefore,

(1.10)

where the interchange of order of summation and integration is permissible, and the moment Mkl is the geometric moment of order (k+l) of the image function f(x, y). We see from (1.10) that the moment Mkl is the expansion coefficient to the ukvl term in the power series expansion of the characteristic function of the image function f(x, y). Then, we consider the inverse form of the characteristic function

. From

(1.10) and the two-dimensional inversion formula for the Fourier transform, it follows that:

.

. 5

Chapter 1


(1.11) However,

the

order

of

summation

and

the

integration

in

(1.11)

interchanged. Thus we conclude that the power series expansion for

cannot

be

cannot be

integrated term by term. Particularly, if only a finite set of moments is given, we cannot use a truncated series in (1.11) to learn about the original image function

.

The difficulty encountered in (1.11) could have been solved if the basis set { ukvl } were orthogonal. Unfortunately, with the Weierstrass approximation theorem [5], the basis set { ukvl }, while complete, is not orthogonal. To solve this problem, we need a set of basis functions which are orthogonal over a finite interval. Based on this requirement, the Legendre or the Zernike polynomials would be the appropriate set.

1.2.3 Moment Invariants The earliest significant work employing moments for image processing and pattern recognition was performed by Hu [1] and Alt [2]. Based on the theory of algebraic invariant, Hu [1,6] derived relative and absolute combinations of moments that are invariant with respect to scale, position, and orientation. The method of moment invariants is derived from algebraic invariants applied to the moment generating function under a rotation transformation. The set of absolute moment invariants consists of a set of nonlinear combinations of central moments that remain invariant under rotation. Hu defines the following seven functions, computed from central moments through order three, that are invariant with respect to object scale, translation and rotation: (1.12)

(1.13)

.

. 6

Chapter 1

Image Identification Using the Moment Concept (1.14) (1.15)

(1.16)

(1.17)

(1.18) The functions m1 through m6 are invariant with respect to rotation and reflection while m7 changes sign under reflection. The definition of the geometric moments (1.1) has the form of the projection of the image function f(x, y) onto the monomial xpyq. However, with the Weierstrass approximation theorem [5], the basis set { xpyq }, while complete, is not orthogonal. Fig. (1.1, 1.2) shows an object which have been translated, scaled and rotated with respect to the first. The values of the seven invariant moments are calculated according to Eq. (1.12-1.18) for all three shapes. As is evident in table (1.1, 1.2), they are equal to within the computational precision allowed by a discrete, digital implementation of the Eq. (1.12-1.18).

(a)

(b)

(c)

Figure 1.1: An object which have been translated, scaled and rotated. .

. 7

Chapter 1


Table 1.1: Comparison of the seven invariant Hu moments calculated for images in Fig.(1.1). Hu's moments

Fig. (1.1)a

Fig. (1.1)b

Fig. (1.1)c

1

0.713

0.732

0.709

2

1.668

1.721

1.658

3

3.716

3.706

3.678

4

4.491

4.502

4.439

5

8.594

8.607

8.499

6

5.329

5.368

5.273

7

12.573

12.550

12.575

(a)

(b)

(c)

Figure 1.2: (a) Lena image. (b) Rotated Lena image. (c) Scaled Lena image.

Table 1.2: Comparison of seven the invariant Hu moments calculated for images in Fig.(1.2). Hu's moments

Fig. (1.2)a

Fig. (1.2)b

Fig. (1.2)c

1

0.864

0.902

0.864

2

6.974

6.822

6.938

3

9.574

8.498

9.457

4

7.177

7.432

7.191

5

16.109

17.544

16.206

6

11.313

11.304

11.297

7

15.751

15.410

15.660

.

. 8

Chapter 1


1.2.4 Accuracy If an analog original image function f(x, y) is digitized into its discrete version f(xi, yj) with an M x N array of pixels, the double integration of (1.1) may be approximated by double summations. In fact, in digital image processing, one can observe f(x, y) only at discrete pixels, i.e., instead of { f(x, y) , (x,y)

} , { f(xi, yj) ; 1

i

M ,1

j

N

} is used. It has been a common prescription to replace Mpq in (1.1) with its digital version: (1.19) where x and y are sampling intervals in the x and y directions.

However, when the moment order increases, (1.19) cannot produce accurate results as the numerical computation error propagates and leads to severe inefficiency in image identification [7]. Extended Simpson's rule can be applied to reduce these numerical errors, however, the associated numerical errors lead to unacceptable reconstructed image quality.

1.3 Legendre Moments Legendre moments are considered one of the orthogonal moments. It is based on using Legendre polynomials. To describe these moments, we firstly describe Legendre polynomials.

1.3.1 Legendre Polynomials The nth order Legendre polynomial may be expressed using Rodrigue's formula: Pn (x) =

(1.20)

The Legendre polynomials have the following generating function [7]: .

. 9

Chapter 1

Image Identification Using the Moment Concept Ps (x) , where r < 1

(1.21)

From the generating function, the recurrent formula of the Legendre polynomials can be acquired straightforwardly: Ps (x) )

=

(x - r)

Ps (x)

Ps (x) =

Ps (x)

(1.22)

We can multiply both sides of (1.22) term by term, and produce the following summations. From this point, s will assume an upper limit of infinity for each summation:

(1.23) To equate terms with equal powers of r. We need to be careful to choose the proper value of s in each summation so that each summation produces the same exponent for h. For example, suppose we want to equate all

terms; to produce

terms in each

summation, we need to set s=3 in the first sum; s=2 in the second, s=4 in the third sum (the first sum on the RHS); s=3 in the fourth sum, and s=2 in the final sum. Using these values in (1.23), we get: (1.24)

We can use eq. (1.24) to derive our final recursion relation: x Pk (x)- Pk -1 (x)= (k + 1) Pk +1 (x) - 2xk Pk (x)+(k - 1) Pk -1 (x) or, the recurrent formula is abbreviated to: .

. 10

Chapter 1

Image Identification Using the Moment Concept Pn +1 (x) =

xPn (x) -

xPn-1 (x)

(1.25)

The first few Legendre polynomials are listed in table (1.3). Table 1.3: List of Legendre Polynomials up to 10th order. n 0 1

1

2 3 4 5 6 7 8 9 10

The Legendre polynomials {Pm (x)} [5] are a complete orthogonal basis set on the interval [-1,1] : (1.26)

mn

where

mn

is the Kronecker symbol.

1.3.2 Legendre Moments The (m+n)th order of Legendre moment of f(x, y) defined on the square [-1,1]

.

[-1,1] is:

. 11

Chapter 1

Image Identification Using the Moment Concept mn =

f(x, y) dx dy

(1.27)

where m, n = 0,1,2,..... . Using (1.1), (1.20), and (1.27), we have:

mn =

f(x, y) dx dy

f(x, y) dx dy

f(x, y) dx dy

Therefore, the Legendre moments and geometric moments are related by the following relation: (1.28)

mn

The above relationship indicates that a given Legendre moment depends only on geometric moments of the same order and lower.

1.3.3 Image Reconstruction from Legendre Moments As mentioned before, the Legendre polynomials {Pm(x)} are a complete orthogonal basis set on the interval [-1,1]. By the orthogonality principle, and considering that f(x, y) is piecewise continuous over the image plane, we can write the image function

f(x, y)

as an infinite series expansion using Legendre moments: (1.29)

In practice, one has to truncate the infinite series in (1.29). If only Legendre moments of order

Mmax are given, the function f(x, y) can be approximated by a

truncated series as follows: (1.30) .

. 12

Chapter 1 Furthermore,

Image Identification Using the Moment Concept must be replaced by their approximations

, which result

from expressing the double integration by a double discrete summation in eq. (1.27) That yield the following reconstruction scheme: (1.31) This is actually the basic equation used in the image reconstruction via the Legendre moments. Therefore, as Legendre moments depend on geometric moments, the same source of computation errors still exist. Besides, it is variant under rotation. This limits its use in image identification using the moment concept.

1.4 Zernike Moments The usage of Zernike polynomials in optics dates back to the early 20th century, while the applications of orthogonal moments based on Zernike polynomials for image processing were pioneered by Teague [8] in 1980. Zernike moments are considered one of the orthogonal moments. As we will show shortly, it is rotational invariant. Therefore, it is suitable for being used in image classification.

1.4.1 Zernike Polynomials A set of orthogonal functions with simple rotation properties which forms a complete orthogonal set over the interior of the unit circle was introduced by Zernike [9]. The form of these polynomials is: Vn,m ( x, y) Vn,m (r cos , r sin  )  Rn,m (r ) e jm

(1.32)

where n is either a positive integer or zero, and m takes positive and negative integers subject to constraints n - |m| = even, |m| origin to the pixel at (x, y), and

n ,

is the length of the vector from the

is the angle between vector

and the x-axis in the

counterclockwise direction.

.

. 13

Chapter 1


The Radial polynomial Rnm( ) is defined as: n m

Rn ,m (r ) 

  1 2

n  k !

k

k 0

n m  n m  k!  k !  k !  2  2 

r n2 k

(1.33)

with Rn,-m( ) = Rn,m( ). Zernike Polynomials up to the 7th order (36 terms) are listed in table (1.4). Table 1.4: List of Zernike Polynomials up to 7th order. j= index

n= order

m= repetition

0

0

0

1

1

-1

2 r sin

2

1

1

2 r cos

3

2

-2

4

2

0

(2r2-1)

5

2

2

r2 cos 2

6

3

-3

r3 sin 3

7

3

-1

(3r3-2r) sin

8

3

1

(3r3-2r) cos

9

3

3

r3 cos 3

10

4

-4

r4 sin 4

11

4

-2

(4r4-3r2) sin 2

12

4

0

(6r4-6r2+1)

13

4

2

(4r4-3r2) cos 2

14

4

4

r4 cos 4

1

r2 sin 2

.

. 14

Chapter 1

Image Identification Using the Moment Concept 15

5

-5

r5 sin 5

16

5

-3

(5r5-4r3) sin 3

17

5

-1

(10r5-12r3+3r) sin

18

5

1

(10r5-12r3+3r) cos

19

5

3

(5r5-4r3) cos 3

20

5

5

r5 cos 5

21

6

-6

r6 sin 6

22

6

-4

(6r6-5r4) sin 4

23

6

-2

(15r6-20r4+6r2) sin 2

24

6

0

(20r6-30r4+12r2-1)

25

6

2

(15r6-20r4+6r2) cos 2

26

6

4

(6r6-5r4) cos 4

27

6

6

r6 cos 6

28

7

-7

4 r7 sin 7

29

7

-5

4 (7r7-6r5) sin 5

30

7

-3

4 (21r7-30r5+10r3) sin 3

31

7

-1

4 (35r7-60r5+30r3-4r) sin

32

7

1

4 (35r7-60r5+30r3-4r) cos

33

7

3

4 (21r7-30r5+10r3) cos 3

34

7

5

4 (7r7-6r5) cos 5

35

7

7

4 r7 cos 7

The Zernike polynomials (1.32) are a complete set of complex-valued functions orthogonal on the unit disk

 Vn ,m ( x , y )  V p ,q ( x , y ) * dxdy x2  y 2  1

.



 n 1

 n , p  m ,q

(1.34) .

15

Chapter 1


or, in polar coordinates 2 1

*



 Vn ,m ( r , ) V p ,q ( r , )  r dr d  n 1  n , p  m ,q 0

(1.35)

0

where the asterisk denotes the complex conjugate. As is seen from (1.32) and (1.35), the real-valued radial polynomials {Rn,m( )} satisfy the following relation: Rnl( ) Rml( ) r dr =

(1.36)

nm

The radial polynomials Rnm( ) have the following generating function [7]:

Rm+2s,m

)

(1.37)

When m = 0, it is interesting to see that the equation (1.37) reduces to the following equation: Ps

(1.38)

and becomes the generating function for the Legendre polynomials of argument (12 ), so that R2n,0

) = Pn

(1.39)

1.4.2 Zernike Moments The complex Zernike moments of order n with repetition m for an image function f(x, y) are defined as: An , m 

n 1



 f ( x , y )  Vn ,m ( x, y ) * dx dy x 2  y 2 1

(1.40)

or, in polar coordinates: .

. 16

Chapter 1

Image Identification Using the Moment Concept n 1

An ,m  

2 1

  f ( r , ) Rn ,m ( r , ) e 0

 jm 

rdr d

(1.41)

0

where the real-valued radial polynomial Rnm( ) is defined in (1.33). Due to the conditions n - |m| = even and |m|

n for the Zernike polynomials (1.32)

the set of Zernike polynomials contains (n+1)(n+2)/2 linearly independent polynomials if the given maximum degree is n. Since

A 

*

n,m

 An,  m , then | An ,m | = | An,  m |,

therefore, one only needs to consider | An ,m | with m ≥ 0 .

1.4.3 Rotational Properties of Zernike Moments Under a rotation transformation, the angle of rotation of the Zernike moments is simply a phase factor. Therefore, the magnitude of Zernike moments are invariant under image rotation. If the original image and the rotated image in the same polar coordinates are denoted by f( ,

) and

( ,

) respectively, the relationship between

them is: ( , ) =f( , where

)

(1.42)

is the angle of rotation of the original image. Using (1.42), the Zernike

moment of the rotated image is:

r

An ,m 



n 1



n 1



2 1



f ( r ,  ) Rn ,m ( r )  e

(  jm (   ))

rdr d

0 0

2 1

  f ( r ,  ) Rn ,m ( r )  e

(  jm (   ))

e

 jm 

rdr d

0 0

Therefore, the relationship between A

r

n,m

and An , m is

r

An ,m  An ,m e .

 jm 

(1.43) .

17

Chapter 1


Eq. (1.43) indicates that the Zernike moments have simple rotational transformation properties. The magnitudes of the Zernike moments of a rotated image function remain identical to the original image function. Thus, the magnitude of the Zernike moment |Anm| can be employed as a rotation invariant feature of the fundamental image function. To verify the rotational invariant property of the Zernike Moments ZM, we consider a specific image, and rotate it by an angle

. The classification algorithm can be

described as follows: 1. The ZM are computed for this image, as well as those in the image data box including the original un-rotated image. 2.

Evaluate the absolute error

k

between the ZM of the rotated unknown image

(k ) , and the kth image of the data box, i.e. An,m , k 1, 2 ,.., M where M is the number

of data box images, i.e. N

n

k   

n 0 m0

(r )

(k )

An, m  An, m

Where N is the order of ZM used. In this experiment, the test image used is a Cameraman image rotated by an angle . In this experiment, the image data box size is 5, and moments of order 10 were used. Fig. (1.3), compares the absolute distance between the ZM of the rotated Cameraman image and the ZM of an image data box including the un-rotated Cameraman image. Absolute distance performance 2.5

Absolute distance

2

1.5

1

0.5

0 Boat

Lena

cameraman Image

Baboon

Barbara

Figure 1.3: Comparing absolute distance of 10th order ZM for a rotated Cameraman image. .

. 18

Chapter 1


1.4.4 Image Reconstruction from Zernike Moments Subject to the discussion of orthogonal functions for the Legendre moments, the image function f(x, y) can be expanded in terms of the Zernike polynomials over the unit disk as follows: (1.44) where m takes on positive and negative integers subject to the conditions n - |m| = even, and |m|

n.

If terms only up to the maximum Zernike moment Nmax are taken, then the truncated expansion is the approximation to

: (1.45)

where

and

are the Zernike moment numerically computed from f(x,

y) and the reconstructed image from f(x, y) with the maximum Zernike moments Nmax. Note that,

, (1.44) can be expanded as:

(1.46) and considering that: .

. 19

Chapter 1


and

Then, (1.46) becomes:

,0 +

,0

0 (1.47)

The formula (1.47) is the basic equation employed in image reconstruction via the Zernike moments.

1.4.5 Accuracy There are two kinds of errors in the computation of the Zernike moments Anm, which are the geometric and the approximation errors. Geometric Error When computing the Zernike moments, if the centre of a pixel falls inside the border of unit disk

, this pixel will be used in the computation, otherwise

.

. 20

Chapter 1


the pixel will be discarded. Therefore, the area covered by the moment computation is not exactly the area of the unit disk. Fig. (1.4) shows the original image and the different areas covered by a unit disk with all pixels whose centre fall inside the unit disk are in black.

(a)

(b)

Figure 1.4: (a) 8x8 image. (b) image includes unit circle. In the case of Zernike moments, the unit disk is located in a 2 units

2 units square

which is composed of n n pixels. Therefore, the area of the unit disk is

. If A(n)

represents the number of pixels whose centre fall inside the unit disk, the summation of the areas of all these pixels is: (1.48) Now, the geometric error between the unit disk and the summation of all the pixels used in the Zernike moment computation is: (1.49) This geometric error can be reduced to zero, by including the whole image inside the unit disc [10]. Fig. (1.5), illustrates this concept.

.

. 21

Chapter 1


(a)

(b)

Figure 1.5: (a) 8x8 image. (b) unit circle includes image. Approximation Error There is another significant computational error arising from expressing the double integration by a double discrete summation. As discussed previously, the Zernike moments of order n with m repetitions of an image function f(x, y) are:



An ,m

n 1



2 1

  f ( r , ) Rn ,m ( r , ) e

 jm 

rdr d

0 0

After replacing the double integration by double summation, the Zernike moments are given as follows:

An ,m 

n 1



N 1

N 1

  j 0

i 0 xi2  y 2j  1

*

f ( x i , y j )Vn m ( x i , y j )  x i  y j

(1.50)

where (xi , yj) is the (i, j) pixel when mapped into the unit disc by a mapping transform.

1.5 Pseudo Zernike Moments If we eliminate the condition n - |m| = even from the Zernike polynomials defined in (1.33), {Vnm} becomes the set of pseudo Zernike polynomials. The set of pseudo Zernike polynomials was derived by Bhatia and Wolf [11] and has properties analogous to those of Zernike polynomials.

.

. 22

Chapter 1


For the pseudo Zernike polynomials, the real-valued radial polynomial Rnm( ) is defined as:

Rn,m (r ) 

where n = 0,1,2,...,

2n  1  k !

n |m|

  1 k!n  m  k !n  m  1  k ! r k

nk

(1.51)

k 0

and m takes on positive and negative integers subject to |m|

n

only. Unlike the set of Zernike polynomials, this set of pseudo Zernike polynomials contains (n+1)2 linearly independent polynomials rather than (n+1)(n+2)/2 if the given maximum order is n. The definition of the Pseudo Zernike Moments (PZM) is the same as that of the Zernike moments in (1.40) and (1.41) except that the radial polynomials {Rnm( )} in (1.51) are used. To speeds up the computations, it is proposed in [12], to use a P-recursive method for the calculation of radial polynomials

of PZMs.

The radial polynomials

are

recursively computed as: (1.52)

(1.53)

(1.54) (1.55)

(1.56)

(1.57) The

recurrence

eq.

of

(1.52-1.57)

facilitate

the

computation

of

the

radian

polynomials and subsequently reduce the numerical computation error associated in .

. 23

Chapter 1


PZM computation. PZM can be made scaling and translation invariant after certain geometric transformations. It has been reported in [13,14] that pseudo Zernike moments are less sensitive to noise. Therefore, PZM are preferred than the commonly used Zernike moments. To test the ability of Pseudo Zernike moments to classify images even in the presence of noise, a Cameraman image is corrupted by zero mean Gaussian noise of variance 0.05. Then, PZM of order 10 were used for classification. Fig. (1.6), compares the absolute distance between the PZM of the noisy Cameraman image and the PZM of an image data box including the noiseless Cameraman image. This figure indicates the ability of PZM to identify the correct host image even in presence of noise. Absolute distance performance 2.5

Absolute distance

2

1.5

1

0.5

0 Boat

Lena

cameraman Image

Baboon

Barbara

Figure 1.6: Comparing absolute distance of 10th order PZM for a noisy Cameraman image. Since the set of pseudo Zernike orthogonal polynomials is analogous to that of Zernike polynomials, most of the previous discussion for the Zernike moments can be adapted to the case of pseudo Zernike moments. In order to save memory space and allow for storing many images for classification and feature extraction, it is suggested to use a small sized image (64x64 pixels). This is achieved

by using

a

decimated

version

of

the

original

image.

To

reduce

the

approximation errors, the inter pixel distance has to be reduced and PZM must be computed for the interpolated version of the decimated image. In [12], Bi-cubic interpolation is used to reconstruct a 256x256 image. To overcome the geometric .

. 24

Chapter 1 errors,


PZM

computations

have

been

performed

by

mapping

the

image

to

lie

completely inside the unit disc. The Peak Signal to Noise Ratio (PSNR) of the interpolated image is computed as:

PSNR=10 Log ( Where

is the original image and

)

(1.58)

is the reconstructed image.

Fig. (1.7)a compares the PSNR of the reconstructed image from the PZM of original Lena image, with the PSNR of the reconstructed image from PZM of a small image interpolated using Bi-cubic interpolation. Fig. (1.7)b shows the same comparison for a Cameraman image. This results indicates that the quality of the reconstructed images from Bi-cubic interpolation using PZM has to be improved. PSNR of Original and reconstructed Cameraman Image

PSNR of Original and reconstructed Lena Image 22

24 23 22

Original Bicubic

Original Bicubic

21 20

20

PSNR in dBs

PSNR in dBs

21

19 18

19 18 17

17 16

16 15

15 14 10

20

30

40 No. of Moments

50

60

70

(a)

14 10

20

30

40 No. of Moments

50

60

70

(b)

Figure 1.7: PSNR performance when using complete 256x256 image and Bi-cubic interpolation method in PZM computations for: (a) Lena image. (b) Cameraman image.

.

. 25

Chapter 2

Enhanced B-spline Based Zernike Moment Evaluations

CHAPTER 2 Enhanced B-spline Based Zernike Moment Evaluations 2.1 Introduction Based on the analysis given on chapter 1, it is clear that the quality of the images reconstructed using Pseudo Zernike Moments (PZM) has to be improved. This is due to the

computational

errors

associated

with

PZM

computation

especially

when

the

moment order increases. In order to reduce the effect of these errors and make PZM suitable for image processing applications, it is proposed to compute PZM for a decimated image, and use B-spline interpolation to interpolate between image pixels. This

significantly improves

the

performance,

due

to

the

superior

low

frequency

concentration feature of B-spline polynomials and their robust performance. Further improvements are also possible, by basing our computations on least squares B-spline decimated images, as well as optimizing some of PZM coefficients. Note that, PZM computations have been performed by mapping the image to lie completely inside the unit disc to eliminate the geometric error. In the next section, a brief description of Bspline polynomials is given.

2.2 B-spline Interpolation B-splines have been long introduced and analyzed by [15-18], which caught interest of many engineering applications and signal processing experts as in [17,18]. B-splines are flexible and providing a large degree of differentiability. By changing the B-spline function order we move from a linear representation to a high-order bandlimited representation. polynomial

In

[19,20],

equations.

In

B-splines [21],

were

B-splines

utilized

for

were

used

signal for

reconstruction image

zooming

using and

interpolation. .

. 26

Chapter 2


2.2.1 Mathematical Background The mth order B-spline function Bm(t), satisfies the following basic properties: 1. Bm(t) is of finite support and equals zeros at t ≤ 0 and t ≥ m. Between the knots t = 1, 2, . . . ,m − 1, it is represented by a polynomials of order (m − 1) in t. It satisfies the recurrence relation:

(2.1) 2. Bm(t) is constructed as the convolution of: (2.2) m -times where

the unit step Haar function. Fig. (2.1) illustrates this concept. 1st Order Bspline

2nd Order Bspline

3rd Order Bspline

4th Order Cubic Bspline

Figure 2.1: Bspline generation using Haar functions. .

. 27

Chapter 2


3. The Fourier transform

is given by: (2.3)

This feature indicates the superior low frequency concentration property. 4.

is symmetric around

: (2.4)

The discrete B-spline basis Bm(n) is obtained by sampling Bm(t) at its knots t = 0, 1,...,m. The Lth interpolated discrete B-spline basis

is obtained by sub-sampling

the sampling interval into L equal intervals [22] i.e.

.

2.2.2 Signal interpolation using B-spline polynomials As shown in [22], for a discrete signal g(k) of length N, that is interpolated using an mth order discrete B-spline Bm(n), we would have: (2.5) where c(l)'s are the B-spline decomposition coefficients for the g(k) signal. The limits in (2.5) are due to the nonzero values of Bm(n), this means that a batch of length N can be expanded by B-spline polynomial having an utmost N+m−2 coefficients. To compute the c' s we have to evaluate the C(z) [23], as follows: (2.6) Hence, the interpolating coefficients c(l) can be viewed as the output of the IIR filter , when driven by the sequence g(k). However, online computations of the c's are not possible, as Bm(z) has roots outside the unit circle, as well as inside the unit circle (as a result of mirror symmetric around

). Solution of this problem can be achieved in

non-real time as follows: consider the digital system of Fig. (2.2), as .

. 28

Chapter 2

Enhanced B-spline Based Zernike Moment Evaluations , and if H(z) has all its poles outside the unit circle, then

is

recursively computable. To evaluate y(n), we apply the following flipping technique in computing y(n):

, to get

1. Flip the batch of the sequence 2. Filter 3. Flip

by the now-stable system

.

back to get

g(n)

X(z)

.

to yield the output

c(n)

Y(z)

X(

Y(

)

x(n)

Flip back right to left

Flip left to right

)

y(n)

Figure 2.2: Flipping technique of non-real time computation.

This idea is now exploited in the computations of c(l), as follows: 1. Factorize

as are

the

stable

and

unstable

parts

of

Bm(z),

respectively. 2. Filter the sequence g(k) by all-pole filter Hs(z), to get y(k), k = 0, 1, . . . , N − 1. 3.

As

, apply the flipping technique, to get c(l). Select (N + m − 2)

consecutive coefficients of this output. .

. 29

Chapter 2


2.2.3 B-spline calculation As shown in the previous sections, a discrete signal g(k) of length N, that is interpolated using an mth order discrete B-spline Bm(n), we would have N+m−2 resulting samples, which means it will generate extra samples (m samples for N samples interpolated with a B-spline of order m). In order to make the number of c's of equation (2.5) equal to the length of batch (instead of N+m-2). It is proposed in [20] to compute this reduced number of coefficients as a solution of the following linear equation:

g (k ) 

N  m 1 2



l  m 2

c(l ) Bm (k  l )

(2.7)

(2.8)

Then, only N coefficients are needed. The c' s are solution of the linear system:

BC=g,

g=[g(0) g(1) .... g(N-1)] t

(2.9)

The solution of this system is much simpler. In case of cubic B-spline, the matrix B is reduced to a Tri-diagonal matrix, whose solution is straightforward and can be implemented online.

.

. 30

Chapter 2


In case of L interpolation, one can show that, the interpolation of L−1 new points between every two knots is given by: (2.10)

(2.11)

where j is the new interpolation of the input k samples. As far as signal compression is concerned, if a batch of N samples of g(n) is decimated by L, where N is multiple of L, then the optimum B-spline coefficients ĉ, must be chosen to minimize the norm of the error signal: (2.11)

(2.12)

Now, if it is desired to minimize the norm of the error signal between the exact function and interpolated

, one has to choose the c's that minimize this error. It has been

shown in [23] that the optimum c's are obtained as a solution of the following set of linear equations:

ĉ(k) =

where r = −

,−

+1 , ...,

. As B-spline interpolated basis is known

(2.13)

,

the solution can be achieved. In this case, the decimation is based on least square Bspline. Both of the interpolation and decimation techniques can be applied on images by working on rows and then columns, or vice versa.

.

. 31

Chapter 2


2.3 B-spline Based PZM Computation In [12], to save memory space and allow for storing many images for classification and feature extraction, it is suggested to use a small sized image. This is achieved by using a decimated version of the original image. As discussed in the previous chapter, the source of computational errors in computing PZM can be reduced by using Bi-cubic interpolation.

In this section, we propose to use cubic B-spline interpolation, known for its superior

low

frequency

concentration

and

robust

performance.

To

illustrate

the

proposed technique, consider a 256x256 image. Construct its decimated 64x64 image. Then, this small-sized image is interpolated by 4 using B-spline interpolation. PZM are computed for the interpolated image. The image is then reconstructed using the computed PZM coefficients, as given by Eq. (1.44). The quality of the reconstructed image can be further improved without exceeding the allocated memory size. Fig. (2.3), compares the PSNR performance of images constructed using the PZM coefficients computed for the complete 256x256 image, with those constructed for its 64x64 decimated images that is interpolated using B-spline interpolation for different number of moments. Cameraman and Lena images are used for testing. we can conclude that the B-spline interpolation yields a significant image quality improvement over the classically

used

Bi-cubic

interpolation.

Fig.

(2.4)

compares

the

quality

of

the

reconstructed Lena images when using Bi-cubic and B-spline interpolation with PZM of order 80.

.

. 32

Chapter 2

Enhanced B-spline Based Zernike Moment Evaluations PSNR Performsnce of Lena Image

PSNR Performsnce of Cameraman Image

24

22

Original Bspline Bicubic

23 22

20

21 20

PSNR in dBs

PSNR in dBs

Original Bspline Bicubic

21

19 18

19 18 17

17 16

16 15

15 14 10

20

30

40 No. of Moments

50

60

70

14 10

20

30

40 No. of Moments

50

60

70

Figure 2.3: PSNR performance when using complete 256x256, B-spline, and Bicubic interpolation methods in PZM computations.

Bicubic Case [12]: 80 Moments

Bspline Case: 80 Moments

Figure 2.4: Reconstructed Lena images using 80 pseudo Zernike Moments generated using B-spline and Bi-cubic interpolation.

2.4 Least Square B-spline PZM Computation By basing PZM computations on the least squares decimated image, rather than the ordinary decimated one. Further improvements are achieved. Fig. (2.5), compares the PSNR performance of images constructed using the PZM coefficients computed for the complete 256x256 image, with those constructed for its 64x64 decimated images using the proposed Least Squares B-spline, B-spline interpolation techniques and the Bi-cubic interpolation, for both Cameraman and Lena images when computed using different .

. 33

Chapter 2 number

Enhanced B-spline Based Zernike Moment Evaluations of

moments.

This

experiment

indicates

that

the

Least

Square

Bspline

interpolation yields a significant image quality improvement over the used Bi-cubic and B-spline interpolation, and competes very well with the 256x256 un-decimated case.

PSNR Performsnce of Lena Image

PSNR Performsnce of Cameraman Image

24

22

Original Least square Bspline Bspline Bicubic

23 22

21 20

Original Least square Bspline Bspline Bicubic

20

PSNR in dBs

PSNR in dBs

21

19 18

19 18 17

17 16

16 15

15 14 10

20

30

40 No. of Moments

50

60

70

14 10

20

30

40 No. of Moments

50

60

70

Figure 2.5: PSNR performance when using complete 256x256, Least Square B-spline, B-spline, and Bi-cubic interpolation methods in PZM computations.

2.5 Optimization of PZM Coefficients To further enhance performance, it is proposed to optimize the computed PZM coefficients such that the error norm between the original and reconstructed image is minimum. Besides, in order to save computations, only the Ak0, k=0,1,..M, enters an unconstrained optimization process, while M is the maximum order of the moments used. Fig. (2.6), compares the PSNR performance of the proposed optimized technique, over the Least Square B-spline and B-spline methods. This figure indicates that the optimization of

PZM coefficients offers sum improvement over the Least Squares

method.

.

. 34

Chapter 2

Enhanced B-spline Based Zernike Moment Evaluations * Lena *

* Cameraman *

21

20

20

19

19

PSNR in dBs.

PSNR in dBs.

18 18

17

17

16 16

15

14 10

15

Bspln. LS Bspln Optim. 20 30 No. of Moments

40

14 10

Bspln. LS Bspln Optim. 20 30 No. of Moments

40

Figure 2.6: Comparing PSNR performance when using optimization in PZM computations, with Least Square B-spline and B-spline interpolation.

.

. 35

Chapter 3

NPT Watermarking Technique

CHAPTER 3 NPT Watermarking Technique 3.1 Introduction With the widespread use of the Internet and the rapid and massive development of multimedia, there is an

impending need for efficient and powerfully effective

copyright protection techniques. A variety of image

watermarking methods have

been proposed [24-32], where most of them are based on the spatial domain [24,25] or the

transform domain [26,27]. However, in recent years [28,29], several image

watermarking techniques based on the transform domain has been appeared. Digital watermarking schemes are typically classified into three categories. Private watermarking which requires the prior secret

keys at

the

knowledge

of

the

original

information

and

receiver. Semi-private or semi-blind watermarking where the

watermark information and secret keys must be available at the receiver. And Public or

blind watermarking where the receiver must only know the secret keys [28]. The

robustness of private watermarking

schemes is high to endure signal processing

attacks. However, they are not feasible in real applications, such as protection

where

the

original

detection. On the other

information

may not

be

available

for

DVD copy watermark

hand, semi-blind and blind watermarking schemes are more

feasible in that situation [30]. However, they have lower

robustness than the private

watermarking schemes [31]. In general, the requirements of a watermarking system fall

into three categories: robustness, visibility, and capacity. Robustness refers to

the fact that the watermark must

survive against attacks from potential pirates.

Visibility refers to the requirement that the watermark be Capacity refers Embedding a

to

the

amount

of

information

that

the

imperceptible to the eye. watermark

must

carry.

watermark logo typically amounts to a tradeoff occurring between

.

. 36

Chapter 3


robustness, visibility, and capacity. In [28,33], a watermarking scheme has been presented. It is based on making use of the Natural Preserving Transform, NPT. The NPT is a special orthogonal transform class that has been used to code and reconstruct missing signal portions [34]. Unlike previous watermarking schemes that use binary logos, NPT amounts to evenly distributing the watermarking gray scale logo or text, all over the host image. The method assumes the prior knowledge of the host image, for watermark extraction. In fact, apart from its simplicity, the method is virtually insensitive to cropping attacks and performs well in case of compression and noise attacks. The main drawback of this watermarking technique is the sensitivity to rotation attacks. In this thesis, a method is proposed based on Pseudo Zernike moments to make the watermarking scheme overcomes the rotation attacks. The proposed approach also delivers an extracted watermark that can be visually seen by the user, which gives the application more user confidence and trust.

3.2 Mathematical background The NPT was first used as a new orthogonal transform that holds some unusual properties that can be used for

encoding and reconstructing lost data from images. The

NPT transform of an image S of size N×N is given by: (3.1) where

is the transformation kernel defined as [35,36]:

   I N  (1   ) H ,  1 IN is Nth order identity matrix, 0 Hadamard,

Discrete

Cosine

Transform

(3.2)

1, and HN is any orthogonal transform, like DCT,

Hartley or

any

other orthogonal

transform. Throughout this thesis, we use the 2-D Hartley transform, defined by:

(3.3)

.

. 37

Chapter 3 We


note

here

that

the

Hartley

symmetry performance, as it evenly

transform

was

utilized

due

to

its

circular

distributes the energy of the original image in

the 4 corners of the orthogonally projected transform image. Hence, the Hartley transform achieves a tradeoff point between the energy concentration feature and spreading feature. Fig. (3.1) illustrates this idea by showing the energy concentration for different well known orthogonal transforms such as Hartley, DCT, and Hadamard.

(a)

(b)

(c)

Figure 3.1: Transform domain basis. (a) Hartley. (b) DCT. (c) Hadamard. The value of in eq. (3.2), gives a balance between the original domain and the transform domain sample basis. Clearly, when 1, the transformed image is the original image, whereas when 0, it will be its orthogonal projection. Hence, the NPT transform is capable of concentrating energy of the image while still preserving its original samples values on a tradeoff basis. This makes the NPT transform domain image has both almost original pixel values (that can’t be visually distinguished from the original image) and mostly capable of retrieving the original image from a small part of the transformed image (provided that this small part has enough energy   . 1 

 concentration in it). The transformed image has PSNR of the order 20 log10 

The original image can be retrieved from the transformed image Str, using the following relation:

S   1 ( ) Str  t ( )

(3.4)

If H is symmetric, as in Hartley or Hadamad matrices, one can show that .

. 38

Chapter 3


   1  2  1  . Otherwise, the matrix  can be computed as: 

 1  

 1 

2 3  1  1  1   1  I  H  H   H   ....           

This means that it can be evaluated to any desired accuracy as

1



(3.5)

H 1 .

3.3 Watermark Embedding and Extraction Watermark embedding is achieved by replacing a part of the host image by the watermarking

logo.

Then,

the

NPT

transformed

image

Str

is

constructed.

After

registering its effects, the watermarking logo is replaced by the original host image that occupies the watermarking area, to make the watermarked image looks similar to the host image. Complete details of the process of watermark embedding are given in [37,38]. Furthermore, the main steps of the process of watermark embedding are shown in Fig. (3.2).

Figure 3.2: The main steps of the process of watermark embedding The watermark extraction from the received image is given in [37,38] and proceeds as follows: 1. Determine the logo size by correlating the watermarked image Awm to the host image S. 2. Form

.

3. The watermark w is the least squares solution of the system. Fig. (3.3) shows the extracted watermark after applying the watermark extraction steps. .

. 39

Chapter 3


Figure 3.3: Watermark Extraction steps.

3.4 Robustness to Attacks The

NPT

watermarking

extraction

algorithm

has

been

tested

against

cropping,

compression, noise, and rotation attacks. The following simulation results, show its robustness to these attacks.

3.4.1 Robustness to Cropping The main feature of the NPT watermarking scheme, is the even distribution of the watermark all over the host image. So, as long as the size of the cropped watermarked image is greater than the size of the embedded logo, cropping has no effects on the extracted logo and one can extract the logo exactly, as the number of linear equations needed to determine the logo is greater than or equal to the number of unknowns [38]. To verify this feature, an example have been considered. In the first, we consider half cropping the watermarked Lena image Awm. The cropped part is filled with white pixels. Fig. (3.4), shows the watermarked cropped image together with the extracted logo.

(a)

(b)

.

. 40

Chapter 3


(c) Figure

3.4:

Cropping

performance.

(d) (a)

Embedded

watermarked

image.

(b)

NPT

watermarked image. (c) Cropped watermarked image. (d) Extracted watermarking logo.

3.4.2 Robustness to Compression Attacks To verify that the watermarking logo can be easily identified even in presence of compression, the watermarked image Awm is compressed using SPIHT coder/decoder [39] algorithm implemented with different number of bits per pixel (bpp). Fig. (3.5), compares the performance of Normalized Correlation (NCORR) of the extracted logos versus compression, (bpp) for three embedding techniques (bottom, top, and optimum embedding) [38], evaluated for different values of

. Note is a in the figure.

3.4.3 Robustness to Noise Attacks In this simulation, the watermarked image Awm is contaminated with zero mean Additive White Gaussian Noise (AWGN) as well as salt and pepper noise. The simulation is performed for 10 independent noises, with different seeds and the extracted logos are averaged over these 10 simulations [38]. Fig. (3.6) compares the normalized correlation of both top and bottom embedding, when the watermarked image is mixed with AWGN with different powers. Fig. (3.7) shows the watermarked images as well as the extracted logos when corrupted for the cases of AWGN yielding SNR=15 dB, and salt and pepper noise with noise density D=0.05, note is a in the figure.

.

. 41

Chapter 3


Figure 3.5: Compression performance of the 3 embedding schemes, bpp= 0.95 and 0.93, together with the extracted logos for top embedding using 0.8 bpp.

Figure 3.6: comparison of NCORR of both top and bottom embedding cases in noisy environments for different SNR’s, for 2 different alpha values, 0.95 and 0.93. .

. 42

Chapter 3


Figure 3.7: Typical performance of Top embedding case with 0.95. Left: AWGN case, NCORR= 0.938. Right: Salt and pepper case with D=0.05, NCORR=0.9.

3.4.4 Rotation Attacks From the previous sections, we show that the watermarking technique is robust to cropping, compression and noise attacks but if the watermarked image is rotated, we will be unable to retrieve the watermarking logo as shown in Fig. (3.8).

Figure 3.8: Watermark Extraction after rotation attack.

.

. 43

Chapter 3


Pseudo Zernike moments is known to be rotation invariant. So, it is proposed to use PZM to make the watermarking technique robust to rotation attacks.

3.5 Similarity between PZM of the Watermarked Image and Original Image Now, as the transformed image has PSNR of the order

   20 log10   1 

dB, it is

expected that the PZM of the watermarked image has a close resemblance to the PZM of the original host image. To verify this feature, we consider embedding Assiut University logo, (size 87x60), in the north-west corner of a 256x256 Cameraman image, using =0.985. Pseudo Zernike Moments of 10th order have been used for analyzing the watermarked image, as well as a data box containing N=10 different images. Fig. (3.9), shows the absolute distance which is defined as follows: N

n

( w)

k   

n 0 m 0

(k )

(3.6)

An ,m  An ,m

( w)

where

An ,m

is the watermarked PZM.

Fig. (3.9), also shows the effects of rotating the watermarked image by angle  / 6 . We conclude that, the original host

image can be easily identified, given the

watermarked image, whether rotated or not. Absolute distance performance 3.5 Unrotated Rotated

3

Absolute distance

2.5

2

1.5

1

0.5

0 Odie

Lena

Boat

Fruits Cameraman Clown Image

Build

Baboon

Barbara

Rice

Figure 3.9: Absolute distance of 10th order PZM between un-rotated and rotated watermarked Cameraman image with other data box images. .

. 44

Chapter 3


3.6 Rotation Invariant NPT Watermarking Scheme After showing the similarity between PZM of the host image and the rotated watermarked image. The watermarking logo is extracted. To extract the watermarking logo, the PZM of the rotated watermarked image is firstly obtained. Then, they are used to determine the rotation angle of the watermarked image using Eq. (1.44). Subsequently, we de-rotate the watermarked image and apply the watermark extraction steps. However, the interpolation errors associated by rotation algorithm inter hamper the recovery of the watermarking logo. Fig. (3.10) shows the effect of watermark extraction for a de-rotated watermarked image.

Figure 3.10: Watermark Extraction after de-rotation. To compensate the effect of these errors, the following procedure is adopted: 1. After determining the exact rotation angle. Rotate the host image Y by this angle to get Yr. Then, de-rotate Yr by the same angle to get Ŷ. Fig. (3.11) illustrates the rotation and the de-rotation of host image. 2. Theoretically,

Y  Yˆ

should be zero. However, it

is

present

due to

rotational interpolation errors. Denote this error by er  Y  Yˆ . This error is shown in Fig. (3.12). 3. Add this error er to the de-rotated watermarked image, as shown in Fig. (3.13). 4. Finally, extract the watermarking logo as described in [37,38]. The extracted watermarking logo is shown in Fig. (3.14). .

. 45

Chapter 3


(a)

(b)

(c)

Figure 3.11: Rotation and de-rotation of the host image. (a) Host image (Y). (b) Rotated host image (Yr). (c) De-rotated host image (Ŷ).

(a)

(b)

(c)

Figure 3.12: Determination of interpolation errors. (a) Host image (Y). (b) De-rotated host image (Ŷ). (c) Error image er .

(a)

(b)

(c)

Figure 3.13: Steps of Rotation error compensation. (a) Error image er. (b) De-rotated watermarked image. (c) Obtained image.

.

. 46

Chapter 3


Figure 3.14: Watermark extraction after rotation error compensation. The main steps of watermark extraction can be summarized as follows: 1. Obtain the PZM of the rotated watermarked image. 2. Determine the host image having the minimum Subsequently, determine the rotation angle



k

distance using Eq. (3.6).

( w) (k ) between An,m , An,m

using Eq.

(1.44). 3. Rotate the watermarked image by   , to compensate the rotation effects. Add the error matrix described above to the de-rotated watermarked matrix. 4. Apply the watermark extraction procedure of [37,38] to retrieve the watermark. As a simulation example, the Assiut University logo is embedded in the north-west corner of the Lena and Boat images, using   0.985 . After NPT transformation, and reinserting the original north-west section of the host images, the watermarked images is rotated by different angles. Pseudo Zernike Moments of 10th order were used for image classification and rotation angle compensation. Next, the logo is extracted from the de-rotated watermarked images, following the procedure just described. Fig.(3.15, 3.16), show the watermarked image before and after rotation, as well as the extracted logo.

.

. 47

Chapter 3


(a)

(b)

(d)

(c)

(e)

Figure 3.15: (a) Watermarked transformed image. (b) Transmitted watermarked image after replacing the logo region by the original host image part. (c) Rotated watermarked image.(d) Watermarked image after rotation error compensation. (e) Extracted logo.

Watermarked Image A w

(a)

Watermarked Image Aw m

(b)

.

(c) .

48

Chapter 3


(d)

(e)

Figure 3.16: (a) Watermarked transformed image. (b) Transmitted watermarked image after replacing the logo region by the original host image part. (c) Rotated watermarked image.(d) Watermarked image after rotation error compensation. (e) Extracted logo.

.

. 49

Chapter 4

Introduction to Fingerprints

CHAPTER 4 Introduction to Fingerprints 4.1 Introduction In an increasingly digital world, reliable personal authentication has become an important

human

computer

interface

activity.

National

security,

e-commerce,

and

access to computer networks are some examples where establishing a person’s identity is vital. Existing security measures rely on knowledge-based approaches like passwords or token-based approaches such as swipe cards and passports to control access to physical and virtual spaces. Such methods are not very secure. Tokens such as badges and access cards may be shared or stolen. Passwords and PIN numbers may be stolen electronically [42]. Biometrics such as fingerprint, face, and voice offers means of reliable personal authentication that can address these problems and is gaining citizen and government acceptance.

4.2 Biometrics Biometrics are the science of verifying the identity of an individual through physiological

measurements

or

behavioral

traits.

Since

biometric

identifiers

are

associated permanently with the user, they are more reliable than token or knowledge based authentication methods. Biometrics offers several advantages over

traditional

security measures [81]. The various biometric modalities are shown in fig. (4.1) can be broadly categorized as: • Physical biometrics: These involve some form of physical measurement such as face, fingerprints, iris-scans, hand geometry, etc.

.

. 50

Chapter 4


• Behavioral biometrics: These are usually temporal in nature and involves measuring the way in which a user performs certain tasks. This includes modalities such as speech, signature, etc. • Chemical biometrics: This is still a nascent field and involves measuring chemical cues such as odor and the chemical composition of human perspiration.

(a)

(b)

(c)

(d)

(e)

Figure 4.1: Various biometric modalities: (a) Fingerprint. (b) speech. (c) face. (d) iris. (e) hand geometry. Depending on the application, biometrics can be used for identification or for verification. In verification, the biometric is used to validate the claim made by the individual. The biometric of the user is compared with the biometric of the claimed individual in the database. The claim is rejected or accepted based on the match. In identification, the system recognizes an individual by comparing his biometrics with every record in the database. In general, biometric verification consists of two stages .

. 51

Chapter 4


(Fig. 4.2) (i) Enrollment and (ii) Authentication. During enrollment, the biometrics of the user is captured and the extracted features are stored in the database. During authentication, the biometrics of the user is captured again and the extracted features are compared with the ones already existing in the database to determine a match [81].

Figure 4.2: General architecture of a biometric system.

4.2.1 The Verification Problem Here, we consider the problem of biometric verification in a more formal manner. In a verification problem, the biometric signal from the user is compared against a single enrolled template. This template is chosen based on the claimed identity of the user. Each user i is represented by a biometric Bi. It is assumed that there is a one-to-one correspondence between the biometric Bi and the identity i of the individual. The feature extraction phase results in a machine representation (template) Ti of the biometric. During verification, the user claims an identity j and provides a biometric signal Bj. The feature extractor now derives the corresponding machine representation Tj. The recognition consists of computing a similarity score S(Ti,Tj). The claimed identity is assumed to be true if the S(Ti,Tj) > Th for some threshold Th. The choice of the threshold also determines the trade-off between user convenience and system security as will be seen in the ensuing section.

.

. 52

Chapter 4


Figure 4.3: An illustration showing the variation present in biometric signals.

4.2.2 Performance Evaluation Unlike

passwords

and

cryptographic

keys,

biometric

templates

have

high

uncertainty. There is considerable variation between biometric samples of the same user taken at different instances of time (Fig. 4.3). Therefore, the match is always done probabilistically. The inexact matching leads to two forms of errors: •

False Match: An impostor may sometime be accepted as a genuine user, if the similarity with his template falls within the intra-user variation of the genuine user.

•

False Non Match: When the acquired biometric signal is of poor quality, even a genuine user may be rejected during authentication. This form of error is labeled as a 'false reject'.

The system may also have other less frequent forms of errors such as •

Failure to enroll (FTE): It is estimated that nearly 4% of the population have illegible fingerprints. This consists of senior population, laborers who use their hands a lot and injured individuals. Due to the poor ridge structure present in such individuals, such users cannot be enrolled into the database and therefore cannot be subsequently authenticated. Such individuals are termed as 'goats' [40]. A biometric system should have exception handling mechanism in place to deal with such scenarios.

•

Failure to authenticate (FTA): This error occurs when the system is unable to extract features during verification even though the biometric was legible during

.

. 53

Chapter 4


enrollment. In case of fingerprints, this may be caused due to excessive sweating, recent injury, etc. In case of speech, this may be caused to due cold, sore throat, etc. It should be noted that this error is distinct from False Reject where the rejection occurs during the matching phase. In FTA, the rejection occurs in the feature extraction stage itself.

4.2.3 System Errors A biometric matcher takes two templates T and T' and outputs a score S=S(T,T') which is a measure of similarity between the two templates. The two templates are identical if S(T,T')=1 and are completely different if S(T,T')=0. Therefore, the similarity can be related to matching probability in some monotonic fashion. An alternative way to compute the match probability is to compute the matching distance D(T,T'). In this case, identical templates will have D(T,T')=0 and dissimilar templates should ideally have D(T,T’)= . Usually a matcher outputs the similarity score S(T,T')

[0, 1].

Given two biometric samples, we construct two hypothesis: •

The null hypothesis H0: The two samples match.

•

The alternate hypothesis H1: The two samples don't match.

The matching decides whether H0 is true or H1 is true. The decision of the matcher is based on some fixed threshold Th: Decide H0: if S(T,T') > Th

(4.1)

Decide H1: if S(T,T') ≤ Th

(4.2)

Due to variability in the biometric signal, the scores S(T,T') for the same person is not always unity and the score S(T,T') for different person is not exactly zero. In general the scores from matching genuine pairs are usually 'high' and the results from matching impostor pairs are usually 'low' (Fig. 4.4). Given that pg and pi represent the distribution of genuine and impostor scores respectively, the False Match Rate (FMR) and False Non Match Rate (FNMR) at threshold T is given by .

. 54

Chapter 4

Introduction to Fingerprints (4.3)

(4.4)

Figure 4.4: Genuine and imposter distributions.

4.2.4 Caveat Although biometrics offers reliable means of authentication, they are also subject to their own set of unique security problems [41]. Similar to computer networks, a biometric system can be prone to denial of service attack, Trojan horse attack and other forms of vulnerabilities. The architecture of a general biometric system consists of several stages (Fig. 4.5). An input device (A) is used to acquire and digitize the biometric signal such as face or fingerprint. A feature extraction module (B) extracts the distinguishing characteristics from the raw digital data (e.g. minutiae extraction from a fingerprint image). These distinguishing features are used to construct an invariant representation or a template. During enrollment the template generated is stored in the database (D) and is retrieved by the matching module (C) during authentication. The matcher arrives at a decision based on similarity of the two templates and also taking into account the signal quality and other variables. Within this framework we can identify eight locations where security attacks may occur [81]. .

. 55

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(1) Fake biometric attack: In this mode of attack, a replica of a biometric feature is presented instead of the original. Examples include: gummy fingers, voice recordings, photograph of the face, etc. (2) Denial of service attack: The sensor may be tampered or destroyed completely in a bid to prevent others from authenticating themselves. (3) Electronic replay attack: A biometric signal may be captured from an insecure link during transmission and then resubmitted repeatedly thereby circumventing the sensor. (4,6) Trojan horse attack: The feature extraction process may be overridden so that it always reproduces the template and the score chosen by the attacker. (5,7) Snooping and tampering: The link between the feature extraction module and the matcher or the link between the matcher and the database may be intercepted and the genuine template may be replaced with a counterfeit template. This template may have been recorded earlier and may not correspond to the current biometric signal. (8) Back end attack: In this mode of attack, the security of the central database is compromised and the genuine templates are replaced with counterfeit ones.

Figure 4.5: An illustration of a general biometric system with points of threats identified.

.

. 56

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4.3 Fingerprint as a Biometric Fingerprints were accepted formally as valid personal identifier in the early twentieth. Fingerprint recognition is one of the most mature biometric technologies and is suitable for a large number of recognition applications [42]. This is also reflected in the revenues generated by various biometric technologies (see Fig. 4.6). Fingerprints have several advantages over other biometrics [42], such as the following: 1. High universality: A large majority of the human population has legible fingerprints and can therefore be easily authenticated. This exceeds the extent of the population who possess passports, ID cards or any other form of tokens. 2. High distinctiveness: twins who share the same DNA have been shown to have different fingerprints, since the ridge structure on the finger is not encoded in the genes of an individual. Thus, fingerprints represent a stronger authentication mechanism than DNA. Furthermore, there has been no evidence of identical fingerprints in more than a century of forensic practice. 3. High permanence: The ridge patterns on the surface of the finger are formed in the womb and remain invariant until death except in the case of severe burns or deep physical injuries. 4. Easy collectability: The process of collecting fingerprints has become very easy with the advent of online sensors. 5. High performance: Fingerprints remain one of the most accurate biometric modalities available. 6. Wide acceptability: While a minority of the user population is reluctant to give their fingerprints due to the association with criminal and forensic fingerprint databases, it is by far the most widely used modality for biometric authentication. The fingerprint surface is made up of a system of ridges and valleys that serve as friction surface when we are gripping the objects. The surface exhibits very rich structural information when examined as an image. The fingerprint images can be represented by both global as well as local features.

.

. 57

Chapter 4

Introduction to Fingerprints Biometric Revenues by Technology, 2009

Iris 5.1 %

Voice 3%

Others 13.8 % Fingerprint 66.7 %

Face 11.4 %

Figure 4.6: Revenue by biometric traits as estimated by International Biometric Group in 2009. Fingerprint based systems (both forensic and non-forensic applications) continue to be the leading biometric technology in terms of market share, commanding 66.7 % of biometric revenue. The global features include the ridge orientation, ridge spacing and singular points such as core and delta. Singular points act as control points around which the ridge lines are “wrapped”. The singular points are very useful from the classification perspective (See Fig.

4.7).

However,

verification

usually

relies

exclusively

on

minutiae

features.

Minutiae are local features marked by ridge discontinuities. There are about 18 distinct types of minutiae features that include ridge endings, bifurcations, crossovers and islands. Among these, ridge endings and bifurcation are the commonly used features (See Fig. 4.8). A ridge ending occurs when the ridge flow abruptly terminates and a ridge bifurcation is marked by a fork in the ridge flow. Most matching algorithms do not even differentiate between these two types since they can easily get exchanged under different pressures during acquisition. Global features do not have sufficient discriminative power on their own and are therefore used for classification before the extraction of the local minutiae features.

.

. 58

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Figure 4.7: Fingerprint Classes: (a) Tented Arch (b) Arch (c) Right Loop (d) Left Loop (e) Whorl.

Figure 4.8: (a) Local Features: Minutiae (b) Global Features: Core and Delta.

Figure 4.9: General architecture of a fingerprint verification system.

.

. 59

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The various stages of a typical fingerprint recognition system is shown in Fig. (4.9). The fingerprint image is acquired using off-line methods such as creating an inked impression on paper or through a live capture device consisting of an optical, capacitive or thermal sensor [42]. The first stage is image segmentation to separate a fingerprint area from the image background. Accurate segmentation of a fingerprint will greatly reduce the computation time of the following processing steps, and discard many spurious minutiae. Then, the fingerprint image enhancement algorithms are specifically designed. Since, the fingerprint images that are obtained are of poor quality due to various reasons such as cracks, scars, dry skin, or poor ridges. The enhancement of image prior to feature extraction increases the consistency. Finally, the minutiae features are extracted from the image and are subsequently used for matching. Although research in fingerprint verification has been pursued for several decades. Now, there are several open research challenges still remaining such as fingerprint segmentation, and fingerprint

enhancement.

In

the

next

chapters,

new

techniques

for

fingerprint

segmentation and enhancement are proposed. The proposed methods competes very well with the existing techniques.

4.4 Fingerprint Representations and Matching Algorithms Fingerprint matching may be broadly classified into the following categories based on their representation.

4.4.1 Image In this representation, the image itself is used as a template. Matching is performed by correlation [43-44]. The correlation between two images I1(x, y), I2(x, y) is given by in the spatial domain

(4.5)

in the Fourier domain

(4.6)

The correlator matches by searching for the peak magnitude value in the correlation image (See Fig. 4.10). The position of the peak indicates the translation between the images and the strength of the peak indicates the similarity between the images. The .

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matching is global and requires an accurate registration of the fingerprint image, since correlation is not invariant to rotation. Furthermore, the accuracy of correlation based techniques also degrade with non-linear distortion of the fingerprint. Bazen [45] select 'interesting' regions in the fingerprint image to perform this correlation since plain ridges do not carry any information except their orientation and ridge frequency. The 'interesting' regions include regions around the minutiae, regions of high curvature and regions around the singular points such as core and delta.

Figure 4.10: The illustration shows the results of correlation between images of the same user(a) and different user(b). It can be seen the peak output of the correlation is high in case of genuine match and low for an imposter match.

4.4.2 Minutiae Representation The purpose of the matching algorithm is to compare two fingerprint images and returns a similarity score that corresponds to the probability of match between the two prints. Minutiae features are the most popular of all the existing representation and also form the basis of the visual matching process used by human experts.

.

. 61

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Minutiae represent local discontinuities and mark position where the ridge comes to an end or bifurcates into two. These form the most frequent types of minutiae, although a total of 18 minutiae types have been identified [42]. Each minutiae is described by its position (x, y) and its orientation θ as shown in Fig. 4.11. Given a pair of fingerprints and their corresponding minutiae features to be matched, features may be represented as an unordered set given by: (4.7)

(4.8) It is to be noted that both the point sets are unordered and have different number of points (M and N respectively). Furthermore, we do not know the correspondences between the point sets. This can be treated as a point pattern matching problem. Here the objective is to find a point

in I2 that exclusively corresponds to each point mi in

I1. However, we need to consider the following situations while obtaining the point correspondences: 1. The point mi in I1 may not have any point corresponding to it in I2. This may happen when mi is a spurious minutia generated by the feature extractor.

Figure 4.11: The figure shows the primary approach for matching minutiae. Each fingerprint is represented as a set of tuples each specifying the properties of minutiae (usually (x,y, )). .

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2. Conversely, The point

in I2 may not be associated with any point in I1. This

may happen when the point corresponding to

was not captured by the sensor

or was missed by the feature extractor.

Usually points in I2 is related to points in I1 through a geometric transformation T(). Therefore, the technique used by most minutiae matching algorithms is to recover the transformation function T( ) that maps the two point sets as shown in (Fig. 4.12). The resulting point set I2 is given by (4.9)

(4.10)

(4.11)

The minutiae pair mi and

are considered to be a match only if:

(4.12)

(4.13)

Here, r0 and θ0 denote the tolerance window. The matcher can make one of the following assumptions on the nature of the transformation T: Rigid Transformation [46], Affine Transformation [81], and Nonlinear Transformation [47-50].

.

. 63

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Figure 4.12: The minutiae are matched by transforming one set of minutiae and determining the number of minutiae that fall within a bounded region of anther.

.

. 64

Chapter 5

A Fingerprint Segmentation Technique Based on Morphological Processing

CHAPTER 5 A Fingerprint Segmentation Technique Based on Morphological Processing 5.1 Introduction Fingerprint

recognition

techniques

are

widely

applied

in

personal

identification

systems. A captured fingerprint is usually composed of two components, foreground and background. The foreground originates from the contact of the fingertip with the sensor. It is a typical flow-like pattern, which consists of ridges and valleys, as shown in Fig. 5.1. The dark straits form ridges, while the bright ones form valleys. The process of separating the foreground area (which contains ridges and valleys) from the background area is known as segmentation. Accurate segmentation of a fingerprint will greatly reduce the computation time of the following processing steps, and discard many spurious minutiae. It is worth mentioning that, fingerprint acquisition is affected by several factors, such as pressure, the types of sensors, finger tip condition. With the development of hardware techniques, many types of fingerprint sensors have become available in the market. Unfortunately, the variety of hardware types demands higher robustness to noise and adaptability of the Automatic Fingerprint Identification System (AFIS). Fig. 5.1 shows some sample images collected from different

sensors.

Fingerprints

collected

by

different

sensors

display

different

background noise. The different noise produced by different kinds of sensor increases the complexity and difficulty of a fingerprint segmentation algorithm. To develop a fingerprint

segmentation

method

for

each

new

sensor

is

impractical

and

also

unnecessary.

.

. 65

Chapter 5


Figure 5.1: Fingerprint images from different database. Several approaches to fingerprint segmentation are known from the literature. In [51], an optimal linear classifier is trained based on three pixel features, namely coherence, mean and variance (CMV). Then, a post processing step is applied to obtain compact clusters and reduce classification errors. In [52], an optimal linear classifier is trained based on block clusters degree, the image intensity mean, and the block variance. In [53], a segmentation technique based on Gaussian-Hermite moments, is proposed. In [54], a quadric surface model is used based on pixel-wise CMV features. In [55], an adaboost classifier is trained based on seven features. In [56], a k-means algorithm is used to cluster foreground and background blocks where the fingerprint block is represented by a 3-dimensional feature vector consisting of block-wise CMV. In [57], a decision-tree-based feature-usability evaluation method is presented, which utilizes a C4.5 decision tree algorithm to evaluate and pick the best suitable feature or feature set for fingerprint segmentation from a typical candidate feature set. .

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Although, there are a lot of researches on fingerprint segmentation, they either depend on empirical thresholds chosen by experts or a learned model trained by samples generated from manually segmented fingerprints. It is manpower and time consuming. Furthermore, some researches experiment their methods on a certain sensor without other sensors. Researchers always try their best to tune their fingerprint segmentation

methods

to

be

universal

to

all

unseen

fingerprints.

However,

one

fingerprint may have a significantly distinct distribution from another in the feature space because fingerprint acquisition is affected by several factors, such as pressure, the types of sensors, and the finger tip condition. As a result, the delicate thresholds and the well trained models may not be suitable to the new input fingerprint from a new finger or a new person [54]. In this thesis, a novel fingerprint segmentation algorithm is presented, which is suitable for different sensors and doesn't need empirical thresholds or a well trained model. Segmentation is achieved through three main steps as shown in Fig. 5.2. In the first step, the grayscale fingerprint image is decomposed into a set of non overlapping blocks of a specific size (normally 3x3), and the range over these blocks is computed. The resulting range image is converted to a binary one using adaptive thresholding to adequate the next step. Then, some morphological opening and closing operations are applied to extract the fingerprint foreground. Finally, The segmented contour can be further smoothed by applying complex Fourier series expansion. The performance of the proposed scheme is tested by computing the classification error rate. Experimental results using the databases of FVC2004, FVC2002, and FVC2000, have shown that the proposed algorithm apart from its computational simplicity, it has lower classification error when compared to other segmentation methods.

Figure 5.2: Flowchart for the proposed segmentation method.

.

. 67

Chapter 5


5.2 Feature Extraction In literature, several approaches have been described to perform fingerprint image segmentation, [51-57]. They are mainly based on fingerprint feature extraction. Among these features that can help in fingerprint segmentation are: the coherence of a block [56], which measures the gradients that are pointing in the same direction. Block mean as well as block variance are also two important fingerprint features. On the other hand, Entropy [55], as well as the entropy of a gradient, which measures the average information over the specified block. It is well known that the foreground contains higher entropy than the background. In this thesis, it is proposed to use the range information to describe the roughness of a foreground, and subsequently use it in fingerprint segmentation. The range value R for each output pixel is defined as (maximum value − minimum value) over the W W block. As an illustration, we randomly select fingerprint samples from the public fingerprint verification competition databases (FVC2000, FVC2002, and FVC2004). As each competition contains four distinct databases collected with four different sensors, namely DB1, DB2, DB3, and DB4, we randomly choose a fingerprint image from each database; as shown in table 5.1. Table 5.1: Specifications of chosen fingerprints

FVC2004

FVC2002

FVC2000

Database DB1 DB2 DB3 DB4 DB1 DB2 DB3 DB4 DB1 DB2 DB3 DB4

.

Image 101_7 107_8 101_5 103_1 102_8 103_8 102_7 102_2 104_4 104_3 107_6 107_3

Size 640x480 328x364 300x480 288x384 296 x560 388 x374 300 x300 288 x384 300x300 256x364 448x478 240x320 .

68

Chapter 5


Each fingerprint in each class (a total of 12 fingerprint), is manually segmented. Then, each is decomposed into 3x3 non overlapping blocks. The Entropy, GradientEntropy and range functions, are computed for all these blocks. Fig. 5.3, shows the background and foreground probability density function (pdf) distribution for each of these features. This figure indicates that the range feature has superior performance over the Entropy and Entropy-Gradient features, and explains why the range image is used as a feature in our proposed segmentation method. 0.7

0.45

Foreground background

0.6

Foreground background

0.4 0.35

0.5

0.4

Probability

Probability

0.3

0.3

0.25 0.2 0.15

0.2 0.1

0.1

0

0.05

0

50

100

150 Range

200

250

0

300

0

1

2

3

4 Entropy

(a)

5

6

7

8

(b) 0.5 Foreground background

0.45 0.4

Probability

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

1

2

3 Gradient Entropy

4

5

6

(c) Figure 5.3: Foreground and background distributions in: (a) Range. (b) Entropy. (c) Gradient entropy. After calculating the range over blocks of size W×W, adaptive thresholding is used to binarize the image. Fig. 5.4 shows that, using range as a feature gives better segmentation results in low quality images than using thresholding immediately. Since, it

assists

in

highlighting

regions

with

low

quality.

Consequently,

improves

the

performance of the subsequent morphological operations. .

. 69

Chapter 5


(a)

(b)

(c)

(d)

(e)

Figure 5.4: (a) Fingerprint image. (b) Binarized image without feature extraction. (c) The resultant segmented image of (b). (d) Binarized image with feature extraction. (e) The resultant segmented image of (d).

5.3 The Proposed Segmentation Technique The

proposed

segmentation

technique

is

based

on

applying

Morphological

processing operations on an adaptive thresholded range image of the given gray scale fingerprint image. In image processing, morphological operations are used to identify and extract meaningful image descriptors based on properties of form or shape within the image. This makes its application in fingerprint segmentation, very appealing. First, a brief review of the basic morphological operations is explained, while the second part discusses how we use these morphological operations for fingerprint segmentation. Finally, contour smoothing is discussed in the third section.

.

. 70

Chapter 5


5.3.1 Basic Morphological Operations Morphological operations are mainly applied to binary images, although grayscale application is also possible. It is a nonlinear shape-oriented technique that uses a small 3-D template known as Structuring Element (SE). The SE is positioned at all possible locations

in

the

neighborhoods

image's

pixels

surface

[58].

The

and

two

it

most

is

compared

important

with

the

morphological

corresponding operators

are

dilation and erosion. The mechanics of erosion and dilation are similar to convolution in filtering operations. Erosion has the effect of removing isolated foregrounds, while dilation has the effect of broadening or thickening narrow regions. In erosion, the centre pixel of the SE is placed on each foreground pixel (value 1). If any of the neighborhood pixels are background pixels (value 0), then the foreground pixel is switched to background. Formally, the erosion of image A by structuring element B is denoted as AӨB. On the other hand, dilation is the process of placing the centre pixel of the structuring element on each background pixel. If any of the neighborhood pixels are foreground pixels (value 1), then the background pixel is switched to foreground. The dilation of image A by structuring element B is denoted A⊕B. Thus, it is clear that erosion reduces binary image size, while dilation increases it. Another two important compound operations are opening and closing. Opening is the process of erosion followed by dilation using the same SE, whereas closing is the process of dilation followed by erosion. Thus, opening has the effect of removing isolated foreground, while closing has the effect of removing holes and changing small regions of background into foreground. The opening and closing operations of A by structuring element B, are mathematically denoted by A◦B and A•B respectively.

5.3.2 Fingerprint Segmentation In

this

section,

we

introduce

our

proposed

morphological-based

segmentation

technique. Fig. 5.5 shows the basic processing steps. It is summarized as follows: 1. For the given gray scale fingerprint, compute the range image R over blocks of size W W to highlight the ridges.

.

. 71

Chapter 5


2. To create a binary image of the fingerprint image, apply the local adaptive thresholding described in [59], to select an appropriate threshold level for each block of size (16×16). 3. Apply a morphological closing operation using a disk-shaped structuring element of radius r (e.g. r=6). This operation will effectively transform the fingerprint into a foreground and other isolated regions A, as shown in Fig. 5.5. Any connected spurs or noise is removed by an opening operation using the same disk-shaped structuring element. These steps may leave holes, (a hole is a background region surrounded by foreground). Filling the holes within these objects is often desirable in order that subsequent morphological processing can be carried out effectively. 4. To extract the foreground, extract the boundary of A, simply as A-AӨB, where B is a disc-shaped SE of radius r=3 (boundary thickness is directly proportional to the radius). Retain only the contour with the largest perimeter, as shown in Fig. 5.5. Note that, since the fingerprint is curved in nature, it is more logical to use a diskshaped SE for closing and opening operations. Moreover, as the separation between ridges is normally between 3-18 pixels, a disk of radius 6 pixels is sufficient for highlighting ridges and removing spurs.

5.3.3 Contour Smoothing To get a smooth contour and more compact clusters, a postprocessing step is necessary. The roughly segmented binary image, is processed by contour filtering in a complex Fourier transform domain [60] as follows: 1. Find the contour of the segmented binary image. 2. Find the coordinate (x, y) of every point on the contour. (This is simply achieved using the command [x, y] = find(boundary > 0). Then, obtain the centroid of the boundary [xc, yc]. 3. Convert [x-xc, y-yc] into polar coordinates (r, ). 4. Expand r using the complex Fourier series r   

 jn  cn e

n  

.

. 72

Chapter 5


In order to smooth out the boundary, the Fourier series expansion is truncated to N. In all of the simulation, we use N=50. The last step in Fig. 5.5 shows the result of contour smoothing.

Fingerprint

Filling holes

Large Boundary extraction

Feature extraction

Opening

Contour smoothing

Binarization

Closing

Segmented image

Figure 5.5: The proposed fingerprint segmentation algorithm. .

. 73

Chapter 5


5.4 Experimental Results The effectiveness of the proposed segmentation algorithm, is verified using the public

fingerprint

verification

competition

databases

(FVC2000,

FVC2002,

and

FVC2004). As mentioned earlier, each FVC contains 4 databases , namely DB1, DB2, DB3 and DB4. The sensor type, resolution parameters and size of images of each database are shown in table 5.2. Each of these databases contains 880 fingerprint images (i.e., there are 110 persons, and each individual has eight fingerprints), stored using 256 gray-scale levels format. The 880 fingerprints were split into set A (800 fpts.) and set B (80 fpts.). To make set B representative of the whole database, the 110 collected fingers were ordered by quality, then the 8 images from every tenth finger were included in set B. The remaining fingers constituted set A. In our simulation, the set B of the 4 databases in FVC2000 [61], FVC2002 [62] and FVC2004 [63], (i.e. containing a total of 960 fpts.), is used to validate the strength of our algorithm in segmenting fingerprints of sensors interoperability. Table 5.2: Scanners/technologies used for collecting the databases of FVC2004, FVC2002 & FVC2000

FVC2004

FVC2002

Database DB1 DB2

Technology Optical Optical

DB3 DB4 DB1 DB2 DB3

Thermal sweeping Synthetic Optical Optical Capacitive

DB4 DB1

Synthetic Low-cost Optical Sensor Low-cost Capacitive Sensor Optical Sensor Synthetic

FVC2000 DB2 DB3 DB4

Scanner CrossMatch V300 Digital Persona U.are.U 4000 Atmel FingerChip SFinGe v2.51 Identix TouchView II Biometrika FX2000 Precise Biometrics 100 SC SFinGe v2.51 Secure Desktop Scanner TouchChip

Resolution 500 dpi 500 dpi

Size 640x480 328x364

512 dpi ≈500 dpi 500 dpi 569 dpi 500 dpi

300x480 288x384 296 x560 388 x374 300 x300

500 dpi 500 dpi

288 x384 300x300

500 dpi

256x364

DF-90 SFinGe v2.51

500 dpi ≈500 dpi

448x478 240x320

.

. 74

Chapter 5


To evaluate the segmentation algorithm, the classification error is used as a performance measure. Each test, An image is selected and partitioned into a number of non overlapping blocks with the same size of WxW pixels (we set W=8). A human operator was asked to classify each block into a foreground or a background. The result of the proposed segmentation method will be compared with the human inspection results. Then, the classification error rate is computed as follows:

where Nerr is the sum of the misclassified blocks in the foreground and the background, while Ntotal is the total number of blocks. Table 5.3, compares Err of the proposed technique, with some other published results using FVC2004, FVC2002, and FVC2000 databases. These results indicate that the proposed

segmentation

algorithm

competes

very well

with

the

existing

methods.

Besides, most of the segmentation methods are either highly dependent on empirical thresholds or well trained model. Fig. 5.6, shows the segmentation of some fingerprints, using the proposed technique. All the experiments were done in Core I7 CPU 2 GHz PC. Table 5.4 gives the average time needed to segment a fingerprint image using the proposed method for each database of FVC2004, FVC2002, and FVC2000. Table 5.3: Classification error rates of FVC2004, FVC2002 & FVC2000 Algorithm

DB1

Proposed algorithm Algorithm in [55]

0.20 % 1.71 %

Proposed algorithm Algorithm in [51] Algorithm in [52] Algorithm in [55] Algorithm in [57]

0.36 % 5.65 % 1.8 % 2.57 % 1.61 %

Proposed algorithm Algorithm in [55]

5.41 % 8.43 %

DB2 FVC2004 2.37 % 5.66 % FVC2002 0.95 % 6.59 % 2.93 % 6% 1.86 % FVC2000 4.64 % 12.56 %

.

DB3

DB4

Average error

0.58 % 5%

1.07 % 5.5 %

1.05 % 4.46 %

2.32 % 7.82 % 3.53 % 5.42 % 2.26 %

0.24 % 5.32 % 1.55 % 5.21 % 1.79 %

0.97 % 6.35 % 2.45 % 4.8 % 1.88 %

1.09 % 7.53 %

0.60 % 5.45 %

2.94 % 8.49 % .

75

Chapter 5


(a)

(d)

(b)

(e)

(g)

(c)

(f)

(h)

.

(i)

. 76

Chapter 5


(j)

(k)

(l)

Figure 5.6: Segmentation results of different databases: (a) FVC2004_DB1_103_4, (b) FVC2004_DB2_101_2, (c) FVC2004_DB3_101_4, (d) FVC2002_DB1_101_4, (e) FVC2002_DB2_106_4, (f) FVC2000_DB3_107_6, (g) FVC2000_DB1_103_7, (h) FVC2000_DB2_103_6, (i) FVC2002_DB3_107_8, (j) FVC2004_DB4_107_7, (k) FVC2002_DB4_105_1, (l) FVC2000_DB4_110_1.

Table 5.4: Average segmentation time for each DB in FVC2004, FVC2002, and FVC2000 Database

DB1

DB2

DB3

DB4

Average

FVC2004 Segmentation time (s)

0.495

0.307

0.355

0.312

0.367


0.355

0.472

0.262

0.311

0.350


0.256

0.294

0.667

0.236

0.363

.

. 77

Chapter 6

A Novel Scheme for Fingerprint Enhancement

CHAPTER 6 A Novel Scheme for Fingerprint Enhancement 6.1 Introduction Biometric recognition as explained before refers to the use of distinctive anatomical (e.g. fingerprints, face, iris) and behavioral (e.g. speech) characteristics for automatic individual recognition. In practice, fingerprint-based recognition systems are widely spread due to its uniqueness to individuals, invariant to age, and convenient in practice [42]. Automatic Fingerprint Identification System (AFIS) consists of several steps, such as fingerprint segmentation, enhancement, feature or minutiae extraction and matching. Fingerprint matching is roughly classified into two classes: minutiae-based [64-65] and image-based methods [66-67], which primarily use minutiae information or a reference point along with a number of ridge attributes for recognition. Poor quality fingerprint images can hamper both classes of recognition algorithms, as it can change the information of the minutiae points and reference points. To increase the performance of AFIS,

a

robust

enhancement

algorithm

is

required,

especially

for

low-quality

fingerprint images. Furthermore, pixel oriented enhancement schemes like histogram equalization [68], mean and variance normalization [69], and Wiener filtering [70] improve the legibility of the fingerprint but do not alter the ridge structure as shown in Fig. 6.1. An enhancement process is required that can join broken ridges, and improve the clarity of ridge/valley structures.

.

. 78

Chapter 6


(a)

(b)

(c)

(d)

Figure 6.1: (a) Original image. (b) Histogram equalized image. (c) Normalized image. (d) Image filtered using Wiener filter. In literature various fingerprint enhancement techniques have been proposed. In [71], a directional Fourier domain filtering for fingerprint enhancement, was proposed. It relies on filtering the fingerprint image by a pre-computed bandpass filter banks oriented in eight different directions, (i.e. every 22.5o). Only the one that is close

to the

pixel orientation is considered. However, as this method assumes the ridge frequency is constant all over the fingerprint and does not utilize its full contextual information, the enhancement effect is little. In [72], Hong adaptively improves the clarity of ridge and valley structures in fingerprint images by a bank of Gabor filters. Their traditional Gabor filter assume that parallel ridge and valley structure have a sinusoidal-shaped in .

. 79

Chapter 6


direction orthogonal to local orientation, therefore ridge frequency and ridge orientation must be calculated. In [73], Greenberg has improved Hong's algorithm by using a unique anisotropic filter, which utilized only orientation information instead of both local ridge orientation and local frequency information. In [74], Chikkerur proposes enhancement algorithm based on STFT analysis and contextual/non-stationary filtering in the Fourier domain. In [75], Wang suggest replacing standard Gabor filter with LogGabor filter to overcome the drawbacks that the maximum bandwidth of a Gabor filter is

limited

to

approximately

one

octave.

In

[76],

Yang

proposed

a

two-stage

enhancement method in both the spatial and frequency domains. It is based on using a spatial ridge-compensation and a frequency bandpass filters. Most of the researches are focused on the design of appropriate filters in one stage either in the spatial or the frequency domain to match the local orientation or/and frequency of the ridges, and use these information to improve the ridge structure in fingerprint images. The spatial-domain techniques involve spatial convolution of the image with filter masks, which is simple for operation. While, filters in the frequency domain can be used to calculate convolutions effectively from the entire image rather than from a small area of the filtered point in the spatial domain; therefore, this leads to more effective noise reduction in the filtered image. For low-quality fingerprint image, using only one-stage processing either in the spatial domain or the frequency domain is not enough to ensure a high-performance verification system. Although, Yang proposes a two-stage enhancement method in both the spatial and frequency domains, it was unpractical method due to the large computation time. In this thesis, we propose a novel and effective two-stage enhancement algorithm for low-quality fingerprint images. In order to restrict the enhancement technique to the fingerprint foreground area and thereby speeds up the subsequent enhancement process, a recently developed segmentation algorithm is utilized [77]. In the first stage, we use a directional mean filter which can use the context information of the local ridges to join broken fingerprint ridges (

7 pixels), as well as removing some annoying small

artifacts between the ridges. If the fingerprint image has broken ridges with large gabs, a simple interpolation technique is devised to join broken foreground ridges. Although, .

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this processing enhances the ridges, it is insufficient to enhance fairly poor fingerprint images. In the second stage, an exponential bandpass radial as well as angular filters is applied to the first enhanced image. It is noted that the parameters of the bandpass filters are learnt from the first-stage enhanced image. To improve the performance of the radial filter, an accurate estimation of the ridge-valley frequencies must be performed. It is proposed to determine the ridge frequency in a local neighborhood, using a Radon-based technique. It is shown that the projection of a local block along a direction normal to the block orientation, is periodic with the ridge frequency f0. This allows the correct design of the exponential radial filter. The exponential angular filter controls the local ridge orientation. The second stage is repeated two or three times, and in each time the parameters of the filter are learnt from the last enhanced image. The iteration

method

enhances

gradually

and

significantly

the

low

quality

fingerprint

images. Experimental results on the databases of FVC2004 and FVC2002 show that our algorithm has better performance compared to other enhancement methods.

6.2 The Pre-Processing Step In this step, the fingerprint image is prepared for the subsequent enhancement stages. In order to speed up the enhancement process, a fingerprint segmentation is carried out. The pre-processing step consists of three stages namely: image segmentation, local normalization, and local orientation estimation. It is summarized as follows: 1) Image Segmentation: This step is responsible for separating the fingerprint area (foreground) from the image background, (area surrounding the fingertip region and is mainly noisy). Several methods have been proposed for segmentation, [52-57,77]. In the previous chapter, an efficient computationally simple technique is proposed. It is based on applying some morphological opening and closing operation on the range image. The range image is constructed by finding the range of the fingerprint grayscale image. Complex Fourier series expansion is used to smooth out the resulting contour. Fig. 6.2(b, f), shows the result of this operation on two specific fingerprint images. 2) Local Normalization: In order to reduce the local variations along ridges and valleys, the fingerprint image within the segmentation contour, is normalized to a pre.

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specified mean and variance. Normalization is achieved by decomposing the fingerprint image into W W non-overlapping blocks (e.g. W=16). Each block is normalized using the following equation: N(i, j) = M0 + V0/V

*

(I(i, j) − M)

(6.1)

Where I(i, j), N(i, j) are the fingerprint and normalized images, respectively. M and V are the block mean and variance, respectively. M0 and V0 are the desired mean and variance values, respectively. Experimentally, we use M0 = 0.5 and V0 = 0.25. Fig. 6.2(c, g) shows the result of this operation. 3) Local Orientation Estimation: In this step, the dominant directions of the ridges in the normalized fingerprint image, is obtained. The least mean square algorithm [72], is used. It is summarized as follows: 

Evaluate the horizontal and vertical gradients Gx(i, j) and Gy(i, j), through filtering the normalized fingerprint, using any edge finding scheme, i.e. Sobel filter.



For each pixel (i, j) in the image, centered in a block of size W W, add the pixel gradients as in (6.2) and (6.3) to obtain the horizontal and vertical block gradients Gxx and Gxy.

(6.2)

(6.3)



Determine the pixel orientation O(i, j) using the horizontal and vertical block gradients, as follows: (6.4)

.

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Chapter 6


Due to the presence of noise, Smoothing the orientation values using a Gaussian window is necessary to correct the estimation.

6.3 The First Stage Enhancement: Spatial Filter Due to light fingertip pressure, noise, or dry skin, fingerprint images may contain broken ridges. The first-stage enhancement scheme use the estimated orientation and normalized image to connect broken ridges and remove small artifacts in the valleys. There are two proposed methods, directional mean filtering (DMF) and a simple interpolation technique. The two methods are explained as follows: 1) Directional Mean Filtering: According to Gonzalez [68] and Solomon [58], the mean filter operates by replacing every pixel in the output image with the mean value from its N M neighborhood. In particular, the mean filter performs well in suppressing noise in an image and smoothing the image. In fingerprint image processing, the standard mean filter with rectangle topology appears to be difficult in achieving significant results. Even worse, filtering using standard mean filter breaks up complete bifurcation minutiae due to orientation uncertainty surrounding it and generates also some false minutiae. The ridges and valleys in a fingerprint image alternate in a relatively stable frequency, flowing in a local constant direction [72]. Pixels in the broken ridge gab or small artifacts in the valleys are considered as impulse noises. These noises can be removed by calculating the mean over a rectangle of width 1 pixel and length N pixels, and rotated to match the local ridge orientation, as shown in Fig. 6.3. The main steps of directional mean filtering can be summarized as follows: 

The fingerprint ridge flow structure is partitioned to sixteen different orientations as shown in Fig. 6.4.



Each pixel is categorized to one of the sixteen different orientations.



For each pixel in the output, Calculate the mean over a rectangle in a direction parallel to the local ridge.

.

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The length of filter window must be carefully chosen so that filtering can achieve optimal results. Small window might fail to reduce noise adequately, large window might produce unnecessary distortions or artifacts. In this thesis, the window size is set to 9 pixels based on empirical data. Fig. 6.2(d, h) shows how our proposed directional mean filter eliminate efficiently noises in the valleys and completes the broken fingerprint ridges.

(a)

(e)

(b)

(f)

(c)

(g)

.

. 84

Chapter 6


(d)

(h)

Figure 6.2: The steps of the first-stage enhancement method. (a, e) Original image. (b, f) Segmented image. (c, g) Normalized image. (d, h) Image filtered using DMF.

Figure 6.3: Demonstration of a rotated rectangle to match the local orientation.

Figure 6.4: Orientation of Fingerprint Ridge Flow.

2) Interpolation Technique: The proposed technique eliminates the existence of these broken ridges as well as narrow cracks and artifacts. It based on using interpolation to join broken ridges. The proposed procedure can be summarized as follows: 

Decompose the fingerprint image into W W overlapping blocks. Overlapping is used, to preserves ridge continuity and eliminate blocking effects. The number of overlapping blocks is taken to be W/2.



For each block, evaluate the orientation θ at each pixel (i, j) as described above. As θ is slowly varying, assign a mean orientation θm to that block.



Rotate the block under investigation by - θm.

.

. 85

Chapter 6 


Scan the rotated block row by row. If over a specified row there is a sudden intensity increase, then this means that a broken ridge exists. If this is the case, interpolate the broken segment using the remaining row values, (values before and after the cut).



De-rotate the scanned block by θm . Eliminate the excess zero rows and columns generated by the rotation algorithm, to make sure that the resulting block of the same size as the original one.

To smooth out the resulting ridge structure, it is further filtered by 3x3 averaging filter. Fig. (6.5)d, shows the result of this operation, the red ellipses in the figure show the mending of the broken ridges. Fig. (6.6), illustrates the effect of applying this technique on a block of size 19x19 containing broken ridges. This figure, indicates the ability of the proposed correction technique to enhance damaged fingerprint images.

(a)

(b)

(c)

(d)

Figure 6.5: The steps of the first-stage enhancement method. (a) Original image. (b) Segmented image. (c) Normalized image. (d) The proposed broken ridge interpolation technique.

Original Block

Corrected Block

Figure 6.6: Performance of the proposed interpolation technique. .

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Chapter 6


The performance of the interpolation-based and directional-based filters is compared in Fig. 6.7. It is clear that the first approach manages to join large gabs while the other works for small gabs and yield a more smoother ridges. Thus, for gabs less than 7 pixels it is more efficient to use a directional mean filter while the interpolation technique is used for larger gabs. Also, table 6.1 shows that the directional mean filter has less computation time than the interpolation based technique.

(a)

(b)

(c)

(d)

Figure 6.7: (a) Original image. (b) Normalized image. (c) Image filtered using DMF. (d) The interpolated image. Table 6.1. Average time (second) of the 1st enhancement stage for each database in FVC2004. DB1

DB2

DB3

DB4

DMF

1.41

1.22

1.56

1.18

Interpolation technique

8.78

6.22

7.88

5.55

6.4 The Second Stage Enhancement: Frequency Bandpass Filter Although the first stage enhances the ridges, it is insufficient to enhance fairly poor fingerprint images. The aim of this enhancement stage, is to retain the original fingerprint information, while removing any excess noise manifested as isolated regions in the valleys. Fig. 6.8, shows a sample case where the valley's black regions may be .

. 87

Chapter 6


due to excess ink, or dirty fingertip. At this point, it worth mentioning that the intensity variations over ridges and valleys in local neighborhood can be modeled as a sinusoidal shaped wave along a direction normal to the local ridge direction as shown in Fig. (6.9). Therefore, a bandpass filter tuned to the corresponding frequency and orientation can efficiently remove undesired noise and preserve the ridge and valley structure. To estimate the ridge-valley frequencies, a simple Radon-based technique is proposed. Radon transform is a continuous transform that provide a 1-D projection of a 2-D image along a specific direction θ. For projecting a 2-D image x(u, v) along a direction θ, the Radon transform is denoted by R( , ) and is defined as: 

R( , ) 



 

x(u, v)  (u cos   v sin    ) du dv (6.5)

  





x( cos    sin  , sin    cos  ) d 



Where  is the projection angle and  is the projection axis. Also, (  ,  ) denote the rotated coordinate space of the original coordinate space (u, v) [82]. Subsequently, the image can be reconstructed from its projections along different θ's using Inverse Radon transform. Moreover, from the properties of Radon transform [82], if

x(t1 , t2 )  R( , )  x(t1  k1 , t2  k2 )  R( (  k1 cos   k2 sin  ), )

(6.6)

Figure 6.9: Ridge-valley intensity variations over a local block [72].

Figure 6.8: A low quality 4_8.tif fingerprint image from FVC2004. .

. 88

Chapter 6


This means that if x(t1,t2) is periodic, then R( , ) is also periodic, i.e. if x(t1,t2)

is

periodic along the normal direction, then R( , ) is periodic along that direction. Thus, the spatial spacing can be estimated as follows: 1. Decompose the fingerprint image into WxW non-overlapping blocks. Determine the mean orientation angle θm of each block. 2. Compute the Radon transform R, of the block under investigation in the direction 90o + θm. 3. The average spatial ridge-valley spacing d as well as the ridge-valley frequency f0 over a block, is given by, dm = N/Nx and f0=1/dm where Nx is the ordinate of the peak amplitude of an N-point Fast Fourier Transform (FFT) of R(90o + θm). If the FFT has no peaks other than at f=0, (i.e. R is monotonic), this means that the block has no ridges, and f0 is set to -1. Fig. 6.10, illustrates the Radon transform along the normal orientations of two 30 30 fingerprint patches, one contains definite ridges and valleys while the other does not. Original Block

Original Block

Normal OrientionRadon Variation

Normal OrientionRadon Variation

12

50 40

10 30

8 Amplitude

Amplitude

20 10

6

0

4 -10

2

-20 -30

0

5

10

15 20 25 Sample Number

30

35

0

40

0

5

10

15 Sample Number

20

25

30

Figure 6.10: Radon transform behavior along the normal of the orientation direction. These modifications can help in improving the performance of the existing frequencybased fingerprint enhancing techniques. Now, several approaches have been described for fingerprint enhancement [71,74]. In order to deal with fingerprint high curvature .

. 89

Chapter 6


areas, the image is processed by two types of filters, radial and angular filters. In [74], the radial filter is a bandpass Butterworth filter centered at f0, whereas the angular filter is a raised cosine filter centered at θm. However, as the Butterworth bandpass filter does not have the desired attenuation, the improvements are not significant especially in case of low quality fingerprint images. Instead, it is proposed in [76] to use exponential bandpass filter as a radial filter, as it has fast and sharp attenuation. The bandpass exponential filter is a 2-D directional Gabor filter defined in the frequency domain. In this thesis, we propose to use exponential radial as well as exponential angular filters. The filter that is separable in the radial and angular domains is explained as follows: (6.4)

(6.5)

(6.6)

Here

is a bandpass radial filter which controls the local ridge spacing where

is the center frequency and

is the bandwidth.

controls the local ridge orientation where

is an angular filter which

is the angular bandwidth and

is its

orientation. The Gabor filter is used due to its fast and sharp attenuation so it can reduce the noise very clearly. In regions of high curvature, the assumption of a single dominant ridge direction is not valid. Having a fixed angular bandwidth for angular filter leads to spurious artifacts and subsequently spurious minutiae. Thus, high curvature regions need large angular bandwidth. Sherlock et al. [71] proposes to use the angular bandwidth of the filter as a piecewise linear function of the distance from the singular points such as core and delta. However, this requires that the singular point be estimated accurately, a difficult task in poor quality images. In our algorithm, we utilize the angular coherence measure proposed by Rao [80]. This is more robust to errors in the orientation estimation and .

. 90

Chapter 6


does not require us to compute the singular point locations. In the experiments, we use three different angular filters according to the computed coherence values as follows:

For the radial filter, the center frequency is the local ridge frequency and the bandwidth is the range of allowed ridge frequencies. The blocks near the fingerprint contour are of low quality and the estimated orientation at this blocks is not accurate. To reduce the number of false minutiae in this blocks, we proposed to replace the blocks orientation with those of the nearest blocks. Also, the angular and radial filters use small bandwidths to obtain well oriented ridges and valleys at the contour. The overall enhancement scheme can be summarized as follows: 1. Apply the first stage enhancement scheme described in Sec. (6.3). 2. Decompose the fingerprint image into W W overlapped blocks. This preserves the ridge continuity and eliminates the blocking effect. Then, for each block, 3. Apply a coarse bandpass filter (as a cascade of a low and high pass filters) to ensure that only valid ridge frequencies are considered. Since the inter-ridge distance varies in the range of 3–18 pixels per ridge [70]. 4. Determine the local ridge orientation

and the ridge-valley center frequency f0.

5. Compute the coherence, which can be defined as the relationship between the orientation of the central block and those of its neighbors in the orientation map. The coherence is calculated as follows:

(6.7) 6. Construct the 2-D N-point FFT of each block X. 7. The enhanced block is given the 2-D IFFT of Y, (Y =

.

X ).

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Chapter 6


8. Repeat the steps from 3-6 two or three times, each time the enhancement performance increases. 9. Increase the block contrast, by mapping the block intensity values to a new predefined values. The steps of our proposed algorithm are shown in Fig. 6.11. The iteration gives significant results in enhancing the ridge and valley structure in low quality fingerprint images. If the fingerprint image is of very low quality, the whole enhancement process can be repeated to increase the performance of the enhancement process.

(a)

(b)

(c)

(d)

Figure 6.11: (a) Original image. (b) 1st stage enhanced image. (c) 1st stage + 2nd stage enhanced image (before iteration step). (d) Our proposed two stage enhanced image.

.

. 92

Chapter 6


6.5 Experimental Results The public fingerprint image databases of the Fingerprint Verification Competition (FVC2000 [61], FVC2002 [62], and FVC2004 [63]) were established to test fingerprint recognition techniques. Each competition contains four distinct databases collected with four different sensors. For each database, there are 880 fingerprint images (i.e., there are 110 persons, and each individual has eight fingerprints) in 256 gray-scale levels. Fig. (6.12) compares our proposed enhancement algorithm with other algorithms such as Hong algorithm [72], STFT algorithm [74], and Yang algorithm [76]. We can conclude

that

our

proposed

enhancement

algorithm

is

more

effective

in

the

enhancement of low-quality images than other methods.

(a)

(b)

(f)

(g)

.

(k)

(l) .

93

Chapter 6


(c)

(d)

(e)

(h)

(i)

(j)

(m)

(n)

(o)

Figure 6.12: (a),(f),(k) Original fingerprint images. (b),(g),(l) Hong enhanced image. (c),(h),(m) STFT enhanced image. (d),(i),(n) Yang enhanced image. (e),(j),(o) Our proposed enhanced image. .

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Chapter 6


6.6 Application in Minutiae Extraction Once, the fingerprint image is enhanced the minutiae can be extracted to show that our proposed method is effective. The chain-code based method is used for extracting minutiae (e.g. endpoints and branchpoints). The chain-code based method is obtained by scanning the image from top to bottom and right to left. The transitions from white (background) to black (foreground) are detected. The contour is then traced counterclockwise and expressed as an array of contour elements. Each contour element represents a pixel on the contour. It contains fields for the xy coordinates of the pixel, the slope or direction of the contour into the pixel, and auxiliary information such as curvature. Tracing a ridge line along its boundary

in

counterclockwise

direction,

a

termination

minutia

(ridge

ending)

is

detected when the trace makes a significant left turn. Similarly, a bifurcation minutia (a fork) is detected when the trace makes a significant right turn [78]. The chain-code-based minutiae extraction method was combined with the proposed enhancement method and some well-known enhancement algorithms. The experiments were conducted for nine images. The following terms are defined for the purpose of comparing the simulation results: 1) True minutiae (TM): are minutiae picked by an expert. 2) Paired minutiae (PM): minutiae extracted by system which coincide with TM. 3) False minutiae (FM): minutiae extracted by system which don't coincide with TM. 4) Dropped minutiae (DM): minutiae extracted by expert which are not extracted by the system. 5) Exchanged minutiae (EM): minutiae extracted by system which coincide with TM except the type. We define the True Minutiae Ratio (TMR), False Minutiae Ratio (FMR), Dropped Minutiae Ratio (DMR), and Exchanged Minutiae Ratio (EMR) as the ratio of the number of true minutiae, false minutiae, dropped minutiae, and exchanged minutiae divided by the total number of minutiae, respectively [79]. The definitions are normal as a baseline to evaluate the minutiae error in the fingerprint recognition system. The .

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Chapter 6


false and dropped minutiae are the main error criteria, when evaluating a minutiaebased method. Table 6.2: Average TMR (%), FMR (%), DMR (%), and EMR (%) for different enhancement algorithms. TMR (%)

FMR (%)

DMR (%) EMR (%)

No enhancement

45.64

47.64

4.90

1.82

Hong

56.47

25.64

14.62

3.27

STFT

60.04

26.38

11.31

2.27

Wang

61.08

24.57

12.99

1.36

Proposed method

63.72

24.22

10.00

2.06

In Table 6.2, we present a comparison of the average results of TMR, FMR, DMR, and EMR percentage of the system’s performance combined with no enhancement, Hong algorithm, STFT algorithm, Yang algorithm and our proposed method. The test was conducted for 9 images. In Table 6.2, we can see that the average TMR is 45.64 % for input images without enhancing. Our two-stage enhancement achieves the highest average TMR of 63.72 % and has the lowest average (FMR+DMR) of 34.22 %. All the experiments were done in Core I7 CPU 2 GHz PC. Table 6.3 gives the average time needed to enhance a fingerprint image for each database of FVC2004 using different enhancement methods including the proposed method. The proposed enhancement method has computation time less than Wang method and has better performance than other methods. Therefore, it is suitable for high-quality real-time fingerprint identification system. Table 6.3: Average enhancement time (second) for each DB in FVC2004. DB1

DB2

DB3

DB4

Hong

0.6

0.37

0.45

0.27

STFT

0.96

0.44

0.47

0.34

Wang

13.22

12.12

15.79

11.47

Proposed method

2.72

2.32

2.85

2.31

.

. 96

Chapter 7

Conclusion

Chapter 7 Conclusion Here we recapitulate the ideas proposed in this thesis. The contribution of this thesis is fourfold:

1. We introduced an efficient technique for improving performance of pseudo Zernike moment computations for small images. Pseudo Zernike Moments (PZM), are extensively used in pattern recognition and image classification. However, they suffer from severe computational errors especially as the moment order increases. In order to reduce the effects of these errors and make PZM suitable for image processing applications, it is proposed to compute PZM for a decimated image, and use Bspline interpolation to interpolate between image pixels. This significantly improves PZM computations due it is smooth and robust performance. Further improvements are also possible, by basing our computations on least squares Bspline decimated images, as well as optimizing some of PZM coefficients. Experiments indicates that the Bspline, least squares Bspline interpolation yields a significant image quality improvement over the used Bi-cubic interpolation, and competes very well with the 256x256 un-decimated case.

2. We also proposed to use the rotation invariant feature of PZM, in modifying a watermarking scheme to be insensitive to rotation attacks. In this respect, a watermarking technique based on using Natural Preserving Transform NPT, known for its robustness against cropping, compression and noise attacks is modified to be insensitive to rotation attacks.

3. An algorithm for fingerprint segmentation is presented. The segmentation uses only one block feature with some morphological operations to extract the fingerprint. Then, the output of the morphological processing is processed by contour filtering to get a smooth contour. Apart from technique simplicity, it is .

. 97

Chapter 7

Conclusion

characterized by being

neither

depend

on

empirical

thresholds

chosen

by

experts or a learned model trained by elements generated from manually segmented fingerprints. The performance of the proposed technique is checked by evaluating the classification error (Err). Experimental results have shown that when analyzing FVC2004, FVC2002, and FVC2000 databases using the proposed algorithm, the average classification error rates are much less than those obtained by other approaches.

4. Finally, an effective two-stage enhancement scheme in both the spatial domain and the frequency domain for low quality fingerprint images has been proposed. Emphasizing

the

enhancement

of

the

low-quality

images,

the

first-stage

enhancement scheme has been designed to enhance the fingerprint image in the spatial domain with a directional mean filter or a simple interpolation technique. The first stage can join broken fingerprint ridges and separate merged ridges. In the second stage, the image is processed by two types of filters, namely exponential

bandpass

radial

and

exponential

angular

filters.

The

center

frequency of the radial filter is accurately determined using a novel Radonbased technique. The re-iterating of the second stage for few cycles enhances gradually and significantly low quality images.

Experimental results show that

our proposed algorithm gives better results compared with other methods described in the literature. It is noted that the operation has been performed on MATLAB platform in our simulation. It can run fast by optimizing the code or run in C code.

.

. 98

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[46] Gonzalez, Woods, and Eddins. "Digital Image Processing". Prentice Hall, 2004.

[47]

Ardeshir

Goshtasby.

"Piecewise

linear

mapping

functions

for

image

registration".

Pattern

"Piecewise

cubic

mapping

functions

for

image

registration".

Pattern

Recognition, 19(6), 1986.

[48]

Ardeshir

Goshtasby.

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[55] E. Liu, H. Zhao, F. Guo, J. Liang and J. Tian, "Fingerprint segmentation based on an AdaBoost classifier", Frontiers of Computer Science journal in China, Volume 5, Issue 2 , pp 148-157, 2011.

[56]

G.

Yang, G.

Zhou, Y.

Yin, X.

Yang, "K-Means

Based

Fingerprint

Segmentation

with

Sensor

Interoperability". EURASIP J. Adv. Sig. Proc, vol. 2010, no. 54, 2010.

[57] Y. Li, Y. Yin, G. Yang. "Sensor-oriented feature usability evaluation in fingerprint segmentation", Optical Engineering , 52(6), pp: 067201-1-12, 2013.

[58] Chris Solomon, Toby Breckon, "Fundamentals of Digital Image Processing", 1st edition, 2011.

[59] http://homepages.inf.ed.ac.uk/rbf/HIPR2/adpthrsh.htm. 2013.

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[61] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, A. K. Jain. FVC2000: fingerprint verification competition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(3): 402–412.

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S.

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M.

Aladjem,

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D.

Kogan,

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filtering

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Alen Docef, "A Study Guide For Digital Image Processing", Published

.

. 105

List of Published Papers 1. M. F. Fahmy, G. M. Abdel Raheem, and M. A. Thabet, "A Zernike Moment Based Rotational Invariant Watermarking Scheme", 30th National Radio Science Conference, April 2013. 2. M. F. Fahmy, and M. A. Thabet, "An Enhanced Bspline Based Zernike Moment

Evaluations

With

Watermarking

Applications",

International Symposium on Signal Processing and

13th

IEEE

Information Technology,

2013. 3. M. F. Fahmy, and M. A. Thabet, "A Fingerprint segmentation technique based on morphological processing", 13th IEEE International Symposium on Signal Processing and Information Technology, 2013. 4. M. F. Fahmy, and M. A. Thabet, "A Novel Scheme for Fingerprint Enhancement", 31th National Radio Science Conference, April 2014.

.

. 106

‫كليـــة الهندســــــة‬

‫استخراج السمات المميزة للصور و استخدامها في تحسين اداء الصور‬ ‫و تصنيف البصمات‬

‫رسالة مقدمة كجزء من متطلبات نيل درجة الماجستير‬ ‫قسم الهندسة الكهربائية ‪ -‬كلية الهندسة ‪ -‬جامعة اسيوط‬

‫مقدمة من‬

‫المهندس‪ /‬مينا عادل ثابت بشاى‬

‫المعيد بقسم الهندسة الكهربائية‬ ‫كلية الهندسة‪ -‬جامعة أسيوط‬ ‫مارس ‪٤١٠٢‬‬

‫الملخص العربي‬ ‫الهددددن اسددددجاا دددد‬

‫ا االسددددالماالاا دددد افددددااسمددددل اسصللمددددباال ددددالاودددداامطسدددد ا مدددد االادددداال االا ا ددددبا‬

‫لاصددماسماا دددبا ط ددد اسدددجاالط ل دددلما ددجان تدددماملاتددد االط ل دددلماالان دددبا لدد اسماا دددباسدددجاالسدددالماالاا ددد ‪.‬ا‬ ‫مصدددناسشددد باملنتدددناسماا دددبالنا دددباس ل دددطباسدددجاالسدددالمالغددد‬ ‫ال صدددد‬

‫ددد ماسدددجاالاشدددل اا‬

‫ا دددد ااالشدددد ل ‪.‬اأ ددددناالل ددددا اودددداااال دددد ل اسددددجا‪Moments‬افددددااوصددددمااالشدددد ل ‪،‬اودددد اااللدددد القدددداا‬

‫او السددلا ط دد اافددااالسدد ااماا‬ ‫الاا ددد ‪.‬افدددااوددد اال‬ ‫ا‬

‫اال‬

‫ل ددد بافدددااا ظادددبا‬

‫دد ‪.‬اومسدد ناالصنتددناسددجاال ط قددلمافددااسصللمددباال ددالا دد اا دد‬

‫دددللب‪،‬ا قدددنراأل ددد ا دددهلسلمال لسددد جا صددد‬

‫ا االسددالما‬

‫اال ط قدددلم فدددااسمدددل اال دددالاال ددداامسددد نا ددد ا‬

‫ا او االسالم‪.‬‬

‫أوال‪،‬اان‬ ‫ال دددغ‬

‫ددددلامق ددددلماةنتددددن ال تددددل ا ددددل ا سددددل ا‪moments‬‬

‫‪Zernike‬‬

‫‪Pseudo‬ا(‪)PZM‬ال‬

‫ددددالا‬

‫‪.‬ا ددد ااف ضددد لام دددغ اال دددال اوا اددد ا‪Bspline interpolation‬اا ددد جاا سددد م‪.‬اوددد ااتلسدددجا‬

‫شدددد اس لددددا ا سددددل لما‪PZM‬ا سددددطداا ا االم ددددنالهدددد ااال ددددا اسددددجا‪.interpolation‬اس تددددناسددددجاال لسدددد لما‬ ‫تا دددجاالل دددا ا هدددلا دددجان تدددماا ددد نارا‪،least square Bspline‬افضددد ا دددجاملسددد جا صددد‬ ‫‪.PZM‬ا وا لل دددددلل ا ددددد‬

‫اسصدددلس ما‬

‫واملسدددددجاس لدددددا افددددد اةدددددا اال دددددال االا ا دددددبااسدددددجا‪PMZ‬ا دددددجالدددددااا ددددد نس لا‬

‫‪Bicubic interpolation‬ا‪.‬‬ ‫ثل دددل‪،‬اتددد اا ددد نارا لصددد بااناسقدددنالا‪PMZ‬اثل ددد االات ددد ث ا دددنولاناال دددال ‪،‬افددد ا اددد ا‬ ‫ماسدددد افدددداا للددددبا ولاناال ددددال ‪.‬امق ددددباا ا‪Transform‬‬

‫‪Preserving‬‬

‫سدددلماسل ددد االا‬

‫‪Natural‬اانددددنامسدددد نرافدددد ا ادددد ا‬

‫سددددلماسل دددد االام دددد ث ا ضددددغ اال ددددال اأوان دددد اةدددد اس هددددلاأوا إضددددلفبا‪،esion‬اوفدددد ااودددد ااالطلدددد اةص هددددلا‬ ‫أتضلاالام ث ا نولاناال ال ‪.‬اا‬ ‫ثللثدددل‪،‬اتددد اا ددد ناراالسدددالماالاا دددد ال لسددد جاف ددد ا‬ ‫ال‬

‫دددااماال سددد بال ظدددلراال صددد‬

‫فدددااوددد اال‬

‫ااآللددداا ددد االط دددالم‪.‬اوددد اال‬

‫دددللب‪،‬ا ددد قنران تقدددب ةنتدددن ال‬

‫فدددا ددد اس ددد اسدددجاال دددال اسددد ا صددد‬ ‫ن قبا للاقلل باس اال‬ ‫أ ددد ا‪،‬امددد ا‬

‫اا‬

‫دددالماا صدددل‬

‫ددد ا‬

‫ددددجاال‬

‫دددبا‪،‬و مص طددد اوا دددن اسددددجا‬ ‫ددداام‪.‬اوا‬

‫دددا اس دددن افددداامسددد ت ا دددلنااال‬

‫دددالماا صدددل اواال ددداامقددداراأ ل دددلا ددد ا سدددل افددد‬

‫االصا دددلماال شددد‬

‫باال ددد‬

‫ا االط دددالم‪.‬اماف ال‬

‫تقدددباالاق‬

‫اال دددانا‬ ‫دددبا دددل ا‬

‫ى‪.‬‬

‫دددل ا هددد اةنتدددنال لسددد ج ةدددا ا‬

‫دددالماا صدددل ‪ ،‬سادددلات مددددا ددد املسددد جاا ددد‬

‫الاا ددد اسدددجاالط دددالماذاماالمدددا اال تئدددب‪.‬اوتسددد ناأ ددد ا اال لسددد جا ددد االسدددالماالاسددد‬ ‫سثددد ااممدددل اال دددا افددداااالصدددل اوم‬

‫ودددل‪.‬ا تضددد ا سددد نراسددد‬

‫ا االسدددالما‬

‫ةباسدددجاالط دددالما‬

‫جال لسددد جافددداا ددد اسدددجاالامدددل االا دددل ااوا‬

‫ال ددد‬

‫ي‪.‬افدددااالامدددل االا دددل اا سددد نراف ددد اتلسدددداالا ا ددد افددداااممدددل اال دددا ااواتصاددد ا‪.interpolation‬اثددد ‪،‬ا‬

‫تصادددد اس شدددد افددددااالامددددل اال دددد‬

‫دددد المدددد تجاشددددصل ااوزاوي‪.‬اتدددد املنتددددناال دددد‬

‫ياواودددد ااالا شدددد ات‬

‫الا دددد يال ا شدددد االشددددصل اا ننددددبا ل دددد نارامق ددددبامسدددد نال لاتدددد الا ون‪.‬اوم دددد لاالا‬ ‫ثددد‬

‫اسددد ام‪.‬اوددد ااال ددد الاتلسدددجامدددنلتم لاو شددد ا ط ددد اسدددجاةدددا ا‬ ‫ا‬

‫االزس باال لس جاو هللاسني سل باو نباال ص‬

‫ا‬

‫ددددباالثل ددددباسدددد م جاأوا‬

‫دددالماا صدددل ‪.‬او لقدددنامددد ان دددل افصلل دددبا‬ ‫الماا صل ‪.‬‬

‫ااالش لصاسجا‬

‫تم تنظيم هذه الرسالة كاآلتي‪:‬‬ ‫تقددددنر الفصلللل االولا ظدددد ا لسددددبا ددددج ال صدددد‬ ‫س لنشدددب صددد‬

‫اا ددداا‬

‫‪Moments‬اسثددد ‪Geometric, Legendre, Pseudo Zernike moments :‬ا‬

‫و ددااصا دد اس هددلاوا‬ ‫اتضددلافددااودد ااال‬

‫ا ددددااال ددددالا ل دددد نارا ظ تددددبا‪،Moments‬اوف هددددل مدددد ا‬

‫ددبام دداتجاال ددالاسددجاودد ا‪.Moments‬ا اددلامدد اس لنشددب اال‬

‫ددل اال لممددباسددجا سددل هل‪.‬ا‬ ‫ددل االلسددل با‬

‫دد اوضددل لان تقددبا ددل قباسط ددبا ددا ‪Bicubic interpolation‬ال ق دد ااال‬

‫ل ‪.Pseudo Zernike moments‬ا‬ ‫تطددددنأاالفصلللل الثلللل‬

‫ا قددددنت ا ظدددد ا لسددددبا ددددج ملسدددد جا سددددل‬

‫ل ددد نار ‪.Bspline interpolation‬ات دددااذلدددااشددد‬ ‫ددبا ا د‬ ‫الاق‬

‫اال‬

‫‪moments‬‬

‫دددباال تلضددد بالددد‬

‫‪Zernike‬‬

‫‪Pseudo‬ا‬

‫‪Bspline interpolation‬اوا‬ ‫اال د‬

‫ا‬

‫‪interpolation‬ا ل د ناراس س س د م ‪.Bspline‬او فددا هلتددب و د ا ال‬

‫دددباالاط دددبا ددداا ‪Least square Bspline, Bspline interpolation‬اوا دددااملسددد جا صددد‬

‫ا‬

‫سصلس ما‪Pseudo Zernike moments‬ال ق ااال‬ ‫تقدددنراالفصللل الث لللل انددد‬

‫ل افاا سل هل‪.‬‬

‫اوضددد االص سدددلماالال دددبافدددااال دددالاوا‬

‫‪.Natural Preserving Transform‬‬

‫د ‪ ،‬ت د اش د‬

‫ادددلاتاضددد ااناوددد اال‬

‫دددباا ددد‬

‫اةهلا ل ددد ناران تقدددبا‬

‫تقدددباالام دددلث ا ق ددد اةددد اسدددجاال دددال ااوا‬

‫ضددغ هلااوا لضددلفب ‪noise‬ا هددلاوال هددلام ددلث ا ددنولاناال ددال ‪.‬ااتضددلافددااودد ااال‬

‫دد ا ق دد‬

‫ان تقددباةنتددن ا‬

‫لمص االص سلماالال باالام لث ا نولاناال ال ‪.‬ا‬ ‫تاضدددد االفصلللل ال ا لللل ا ظدددد ا لسددددبا ددددجاالق ل ددددلماالط اس تددددب‪.‬اواف هددددلاتدددد اس لنشددددباا دددداا االق ل ددددلما‬ ‫الط اس تدددباسثددد ا‬

‫دددالمااالصدددل اواصدددامااال سدددلناوا سضدددل او‬

‫االشددد لصاسدددجا ددد‬ ‫ال شللولاالاا اواتش‬

‫االق ل دددلماالط اس تدددب و‬ ‫ام ات هلاواالسالماالاا‬

‫دددبامق ددد ا ظدددلراال صددد‬ ‫الهلاو مات اسقلل با‬

‫يوضححح الفصلللل الخلللامس ن تقدددباةنتدددنال لسددد ج ف ددد ا‬ ‫قدددنت ا ظددد ا لسدددبا دددجاال ددد‬

‫االاسددد نسبا دددل ق ال‬

‫ودددل‪.‬اأتضدددلاتشددد‬ ‫‪.‬اثددد ات‬

‫ا‬

‫دددصافددداا‬

‫دددباال صددد‬

‫ا ددداا‬

‫دددالمااالصدددل ا‬

‫ا ج‪.‬ا‬

‫دددالماا صدددل‬

‫دددجاال‬

‫دددب‪.‬اواتطدددنأاوددد ااال‬

‫ددد االط دددالماواالاشدددل اال ددداام دددل طهل ثددد ا قدددارا شددد‬

‫ددد ا‬ ‫ا‬

‫دددااماال‬

‫دددباوال ددداام ددداناسدددجاا ددد‬

‫تقدددباالاق‬

‫ا االسدددالماالاا ددد اثددد ا اددد ا صددد‬

‫وفددددااال هلتددددبا قددددارا صدددد ااالنددددللاالدددد ياتل دددداياالط دددداب‪ .‬واا دددد آا صدددد‬ ‫لل‬

‫ااال‬

‫ظدد ا لسددبا دددجاندد‬ ‫وال دداام دداناسددجا‬

‫مددد امقدددنت ان تقدددباةنتدددنال لسددد جاةدددا ا‬

‫اال‬

‫دددالماا صدددل اواتطدددنأاوددد ااال‬

‫االسدددل قبال لسدد جاواالاشددل اال ددداام ددل طهلاثددد اتقددارا شدد‬ ‫ددام جال سدد ج‪.‬اثدد اتشدد‬

‫اال‬

‫ا‬

‫دددااماال‬

‫ددد ا ل‬

‫دددل ا‬

‫تقددباالاق‬

‫دددبا‬

‫ددا ااالولددااواال دداا سدد نرا هددلاف دد اتلسددداالا ا دد افدداا‬

‫اممدددل اال دددا ااواتصاددد ا‪.interpolation‬اوااتضدددلاتقدددنراال‬ ‫ال دددد‬

‫ا ددددل اودددد اال‬

‫تقددددباواسقلل هددددلا‬

‫ي‪.‬‬

‫فدددااالفصللل السللل‬

‫ياس‬

‫االصا دددلماال شددد‬

‫با‬

‫دددا االثل دددباواال ددداا سددد نرا هدددلاس شددد افدددااالامدددل ا‬

‫دددد المدددد جاشددددصل ااوزاوي‪.‬اوافددددااال هلتددددبا صدددد‬

‫ي‪ .‬وأخيرا‪ ،‬الفصل السابع يلخص االستنتاجات الرئيسية ‪.‬‬

‫ا ددددل اودددد اال‬

‫تقددددباواسقلل هددددلا ددددلل‬

‫ا‬

Feature Extraction and its Use in Enhancing Image ...

Feature Extraction and its Use in Enhancing Image ...

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