Design and Implementation of Image Enhancement ...

Design and Implementation of Image Enhancement Techniques in Frequency Domain A thesis submitted to

Chhattisgarh Swami Vivekanand Technical University Bhilai (India) for fulfilment of the award of degree

DOCTOR OF PHILOSOPHY In

Electronics & Telecommunication Engineering By

Ganesh Ram Sinha

September 2009

Design and Implementation of Image Enhancement Techniques in Frequency Domain A thesis submitted to

Chhattisgarh Swami Vivekanand Technical University Bhilai (India) for fulfilment of the award of degree

DOCTOR OF PHILOSOPHY In

Electronics & Telecommunication Engineering By

Ganesh Ram Sinha Enrollment No.: AF9467 123456789512

September 2009

D E C L A R A T I O N BY THE CANDIDATE I the undersigned solemnly declare that the report of the thesis work entitled Design and Implementation of Image Enhancement Techniques in Frequency Domain is based on my own work carried out during the course of my study under the supervision of Dr. M. K. Kowar and Dr. (Mrs.) Kavita Thakur. I assert that the statements made and conclusions drawn are an outcome of my research work. I further declare that to the best of my knowledge and belief the report does not contain any part of any work which has been submitted for the award of PhD degree or any other degree/diploma/certificate in this University or any other University of India or abroad.

_________________ (Signature of the Candidate) Ganesh Ram Sinha Enrollment No.: AF9467

C E R T I F I C A T E OF THE SUPERVISORS This is to certify that the work incorporated in the thesis Design and Implementation of Image Enhancement Techniques in Frequency Domain is a record of research work carried out by Ganesh Ram Sinha bearing Enrollment No. AF9467 under our guidance and supervision for the award of Degree of Doctor of Philosophy in the faculty of Electronics & Telecommunication Engineering of Chhattisgarh Swami Vivekanand Technical University, Bhilai (C.G.), India. To the best of our knowledge and belief the thesis i) Embodies the work of the candidate him/herself, ii) Has duly been completed, iii) Fulfils the requirement of the Ordinance relating to the PhD degree of the University and iv) Is up to the desired standard both in respect of contents and language for being referred to the examiners.

___________________ (Dr. M. K. Kowar, Supervisor-I)

__________________ (Dr. (Mrs.) Kavita Thakur, Supervisor-II)

Forwarded to Chhattisgarh Swami Vivekanand Technical University Bhilai _________________ (Signature of the Head of the Approved Place of Research

ACKNOWLEDGMENT

First and foremost I acknowledge the support and guidance of my supervisors. I am highly indebted to my supervisors for their unparalleled and stimulus guidance and motivation. In particular, I would like to give special thanks to my supervisors Dr.(Mrs.) Kavita Thakur, Reader & Head ( SOS in Electronics, Pt. Ravishankar Shukla University Raipur) and Dr. M.K. Kowar, Principal (Bhilai Institute of Technology, Durg) for their continued support and encouragement. I would never have been able to complete this work without their expertise and guidance. The broad wealth of knowledge of the supervisors helped me a great deal. I would also like to extend my heartfelt thanks to Shri I.P. Mishra, President (Shri Gangajali Education Society) for providing me the necessary R&D support. I would like to thank Dr.P.B. Deshmukh (Director), Dr. M.N. Verma (Cordinnating Director) of my research center (Shri Shankaracharya College of Engineering & Technology, Bhilai) for providing me the facilities for my research work. Many thanks to my family for all of their love and support. Most importantly I would like to thank my parents for instilling in me the values and morals to succeed in life; and my wife and my daughter (Pakhi), whom I love and adore with all of my being, for their unwavering love, devotion, support and encouragement. A big thank to my god father (my school teacher) without whose blessings and support I would not have achieved this stage. I would like to extend my sincere thanks to Dr. A.N. Jha and Er. D.N. Thakur for their immense encouragement and care. Last but not the least I would like to give my most heartfelt thanks to everyone who has assisted me in the completion of this work.

i

ABSTRACT The aim of image enhancement is to improve the interpretability or perception of information in images for human viewers, or to provide `better' input for other automated image processing techniques such as biometric based techniques that include face recognition, fingerprint matching, early detection of biological disorder like cancer etc. Image enhancement techniques can be divided into two broad categories: spatial domain techniques, which operate directly on pixels, and frequency domain techniques, which operate on the Fourier transform of an image. Frequency domain image enhancement techniques are based on modifying the Fourier transform of an image. Smoothing domain filters, Sharpening domain filters, Homomorphic filters are few of them which are used for image enhancement. In the present work such filters have been designed and implemented. A comparison has been made over aforesaid frequency domain image enhancement techniques using various filters and their performances have been evaluated in terms of PSNR (peak signal to noise ratio), CNR (contrast to noise ratio), mean, variance and invariant moments. For better visual interpretation of a colour image a special technique colour image enhancement has also been successfully implemented. The results of present research work have been applied to one of the forensic science applications i.e. fingerprint matching. It has been observed that matching accuracy is improved if fingerprint image is enhanced in frequency domain before subjecting it to the matching process.

ii

CONTENTS Page No. Acknowledgement

i

Abstract

ii

Contents

iii

List of Figures

vi

List of Tables

ix

CHAPTER 1

CHAPTER 2

INTRODUCTION

1-15

1.1

Fundamentals of Digital Image Processing

1

1.2

Noise in Digital Images

3

1.3

Image Enhancement Techniques

6

1.4

Review of work done Reported in the Literature

7

1.5

Organization of the Thesis

14

IMAGE ENHANCEMENT

16-30

2.1

Spatial Domain Methods

16

2.1.1

19

2.2

Histogram Equalization

Frequency Domain Methods

20

2.2.1

Convolution Theorem

22

2.2.2

Basics of Filtering in Frequency Domain

23

2.3

Importance of Frequency Domain Techniques

25

2.4

Statistical Parameters for Performance Evaluation of the Image

26

Enhancement 2.4.1

PSNR (Peak signal-to-noise-ratio) and CNR (Contrast-to-

27

noise-ratio) 2.4.2 2.5 CHAPTER 3

Invariant moments, Mean, Variance Values, Histogram

Summary

28 30

FREQUENCY DOMAIN IMAGE ENHANCEMENT TECHNIQUES

31-51

3.1

Smoothing Domain Filters

31

3.1.1

Ideal Low Pass Filter

31

3.1.2

Butterworth Low Pass Filter

34

3.1.3

Gaussian Low Pass Filter

36

3.2

3.3

Sharpening Domain Filters

39

3.2.1

Ideal High Pass Filter

39

3.2.2

Butterworth High Pass Filter

40

3.2.3

Gaussian High Pass Filter

41

Homomorphic Filtering

42

iii

3.4

3.5 CHAPTER 4

3.4.1

Basics of RGB Image

46

3.4.2

Smoothing and Sharpening of Colour Images

48

3.4.3

Tone and Colour Correction

50

Summary

50 52-62

4.1

Databases and System Requirements

52

4.2

Flow Diagram of Present Work

55

4.3

Algorithmic Implementation

57

4.3.1

Algorithm for Smoothing Domain Filters

57

4.3.2

Algorithm for Sharpening Domain Filters

58

4.3.3

Algorithm for Homomorphic Filtering

59

4.3.4

Algorithm for Colour Image Enhancement

61

Summary

62

RESULTS AND DISCUSSION

63-105

5.1

Results of Smoothing Domain Filters

63

5.1.1

Ideal Low Pass Filter

63

5.1.2

Butterworth Low Pass Filter

71

5.1.3

Gaussian Low Pass Filter

77

5.2

CHAPTER 6

45

DATABASE AND IMPLEMENTATION

4.4 CHAPTER 5

Colour Image Enhancement

Results of Sharpening Domain Filters

84

5.2.1

Ideal High Pass Filter

84

5.2.2

Butterworth High Pass Filter

89

5.2.3

Gaussian High Pass Filter

94

5.3

Results of Homomorphic Filtering

100

5.4

Results of Colour Image Enhancement

102

5.5

Summary

104

APPLICATION OF IMAGE ENHANCEMENT IN FINGERPRINT

106-121

MATCHING 6.1

Basics of Fingerprint Recognition

106

6.2

Fingerprint Image Enhancement

108

6.2.1

108

Histogram Equalization

6.3

Fingerprint Image Binarization, Segmentation

109

6.4

Minutia Extraction

110

6.5

False Minutia Removal

112

6.6

Minutia Matching

114

6.7

Conclusion

116

6.8

Summary

121

iv

CHAPTER 7

CONCLUSIONS AND FUTURE SCOPE

122-125

7.1

Conclusions

122

7.2

Future Scope

124

REFERENES

126-141

LIST OF PUBLICATIONS RELATED TO THE PRESENT RESEARCH WORK

142-144

REPRINTS OF SOME OF THE PUBLISHED RESEARCH PAPERS

v

LIST OF FIGURES Fig.

Caption

No. 1.1

Page No.

(a) Image Noise-fixed pattern noise due to long exposure, (b) random noise due to short

04

exposure, and (c) banding noise due to susceptible camera brightness shadows 2.1

3x3 neighborhood about a point (x, y) in an image

17

2.2

Gray level transformation functions for contrast stretch

18

2.3

Spatial Domain Image Enhancement Techniques

19

2.4

Result of histogram equalization

20

2.5

Frequency domain filtering procedure

23

2.6

Histogram as number of pixels vs. intensity value

29

2.7

(a) an image of cameraman, (b) its histogram

30

3.1

Filter radial cross section

32

3.2

Filter displayed as an image

32

3.3

Perspective plot of an Ideal LPF transfer function

33

3.4

An example showing the effect of cut-off frequency (r0)

33

3.5

Filter radial cross sections of order n=2, 4 and 8

34

3.6


35

3.7

Plot of a Butterworth LPF transfer function

35

3.8

Response of BLPF of different orders

36

3.9

1-D Gaussian distribution with mean 0 and σ = 1

37

3.10

Perspective plot of a GLPF transfer function

37

3.11


38

3.12

Filter radial cross sections for various values of D0 = r 0

38

3.13

Perspective plot, image representation, and cross section of an IHPF

40

3.14


40

3.15

Perspective plot, image representation, and cross section of a BHPF

41

3.16

Perspective plot, image representation, and cross section of a GHPF

42

3.17


42

3.18

Process flow diagram for enhancement of image f(x,y)

44

3.19

Dynamic range compression

45

3.20

Three components of RGB colour image

46

3.21

Generating the RGB image

47

3.22

The three hidden surface planes in the colour cube

48

3.23

RGB colour cube

48

3.24

Enhancement of R, G, and B components of an RGB image

49

3.25

An RGB image along with its R, G, and B components

49

vi

4.1

Ten x-ray images (a) - (j)

53

4.2

Ten fingerprint images (a - (j)

54

4.3

Ten facial images (a) - (j)

55

4.4

Flow chart of present work

56

5.1

Result of ideal low pass filter for n=2 and D0=24

63

5.2


64

5.3


65

5.4


65

5.5


66

5.6


66

5.7


67

5.8

PSNR and CNR plot for ideal low pass filter for ten faccial images

68

5.9

PSNR and CNR plot for ideal low pass filter for fingerprint images

69

5.10

PSNR and CNR plot for ideal low pass filter for x-ray images

70

5.11

Result of Butterworth low pass filter for n=2 and D0=24

71

5.12


72

5.13


72

5.14


73

5.15

PSNR and CNR plot for Butterworth low pass filter for facial images

74

5.16

PSNR and CNR plot for Butterworth low pass filter for fingerprint images

75

5.17

PSNR and CNR plot for Butterworth low pass filter for x-ray images

77

5.18

Result of Gaussian low pass filter for n=2 and D0=24

78

5.19


78

5.20


78

5.21

PSNR and CNR plot for Gaussian low pass filter for facial images

79

5.22

PSNR and CNR plot for Gaussian low pass filter for fingerprint images

80

5.23

PSNR and CNR plot for Gaussian low pass filter for x-ray images

81

5.24

Result of ideal high pass filter for n=2 and D0=24

84

5.25


85

5.26


85

5.27


86

5.28

PSNR and CNR plot for ideal high pass filter for ten facial images

87

5.29

PSNR and CNR plot for ideal high pass filter for fingerprint images

88

5.30

PSNR plot for ideal high pass filter for x-ray images

89

5.31

Result of Butterworth high pass filter for n=2 and D0=24

89

5.32


90

5.33


90

vii

5.34

PSNR and CNR plot for Butterworth high pass filter for facial images

91

5.35

PSNR plot for Butterworth high pass filter for fingerprint images

92

5.36

PSNR and CNR plot for Butterworth high pass filter for x-ray images

93

5.37

Result of Gaussian high pass filter for n=2 and D0=24

94

5.38


95

5.39


95

5.40

PSNR and CNR plot for Gaussian high pass filter for facial images

96

5.41

PSNR plot for Gaussian high pass filter for fingerprint images

97

5.42

PSNR plot for Gaussian high pass filter for x-ray images

98

5.43

Result of homomorphic filtering for face1( (a) original (b) enhanced image))

100

5.44

Result of homomorphic filtering for finger1( (a) original (b) enhanced image))

101

5.45

Result of homomorphic filtering for xray1( (a) original (b) enhanced image))

101

5.46

An RGB image of face1 along with its R, G, and B components

103

5.47

Enhanced images of red, green, blue images, and colour image

103

5.48

Gray image into colour image of face8

104

6.1

A fingerprint image

106

6.2

Minutia of fingerprint

107

6.3

Fingerprint Recognition System

107

6.4

Minutia Extractor

108

6.5

Histogram of fingerprint before and after histogram equalization

109

6.6

Direction map (Binarized fingerprint (left), Direction map (right))

110

6.7

Minutia (Bifurcation and Termination)

111

6.8

Triple counting branch

111

6.9

False Minutia Structures

112

6.10

A bifurcation to three terminations. Three neighbors become terminations (Left). Each

114

termination has their own orientation (Right) 6.11

Translation and rotation

116

6.12

Enhancement of finger3 by histogram equalization

117

6.13

Enhancement of finger3 by FFT technique

117

6.14

Binarization after enhancement

118

6.15

Direction of fingerprint

118

6.16

ROI of fingerprint

119

6.17

Minutia of fingerprint

119

6.18

Final Minutia

120

viii

LIST OF TABLES Table

Heading

No. 5.1

Comparison of ideal low pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.2

Comparison of ideal low pass filter in terms of PSNR and CNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.3

Comparison of ideal low pass filter in terms of PSNR and CNR values for ten x-ray images (n=2, 4 and 8 & D0=24, 36 and 48)

5.4

Comparison of Butterworth low pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.5

Comparison of Butterworth low pass filter in terms of PSNR and CNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.6

Comparison of Butterworth low pass filter in terms of PSNR and CNR values for ten xray images (n=2, 4 and 8 & D0=24, 36 and 48)

5.7

Comparison of Gaussian low pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.8

Comparison of Gaussian low pass filter in terms of PSNR and CNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.9

Comparison of Gaussian low pass filter in terms of PSNR and CNR values for ten x-ray images (n=2, 4 and 8 & D0=24, 36 and 48)

5.10

Mean and variance values of enhanced image for ideal low pass filter ( n=2, D0=24)

5.11

Mean and variance values of enhanced image for Butterworth low pass filter ( n=2, D0=24)

Page No. 68 69 70 74 75 76 79 80 81 82 82

5.12

Mean and variance values of enhanced image for gaussian low pass filter ( n=2, D0=24)

83

5.13

Invariant moments for ideal low pass filter (n=2, D0=24)

83

5.14

Invariant moments for Butterworth low pass filter (n=2, D0=24)

84

5.15

Comparison of ideal high pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.16

Comparison of ideal high pass filter in terms of PSNR and CNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.17

Comparison of ideal high pass filter in terms of PSNR values for ten x-ray images (n=2, 4 and 8 & D0=24, 36 and 48)

5.18

Comparison of Butterworth high pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.19

Comparison of Butterworth high pass filter in terms of PSNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.20

Comparison of Butterworth high pass filter in terms of PSNR values for ten x-ray images

86 87 88 91 92 93

ix

(n=2, 4 and 8 & D0=24, 36 and 48) 5.21

Comparison of Gaussian high pass filter in terms of PSNR and CNR values for ten facial images (n=2, 4 and 8 & D0=24, 36 and 48)

5.22

Comparison of Gaussian high pass filter in terms of PSNR values for ten fingerprint images (n=2, 4 and 8 & D0=24, 36 and 48)

5.23

Comparison of Gaussian high pass filter in terms of PSNR values for ten x-ray images (n=2, 4 and 8 & D0=24, 36 and 48)

5.24

Mean and variance values of enhanced image for ideal high pass filter ( n=2, D0=24)

5.25

Mean and variance values of enhanced image for Butterworth high pass filter ( n=2, D0=24)

96 97 98 99 99

5.26

Mean and variance values of enhanced image for Gaussian high pass filter ( n=2, D0=24)

99

5.27

PSNR and CNR values of enhanced facial images for homomorphic filtering method

102

5.28

PSNR and CNR values of enhanced fingerprint images for homomorphic filtering method

102

5.29

PSNR and CNR values of enhanced xray images for homomorphic filtering method

102

5.30

Mean values enhanced images for homomorphic filtering method

102

x

CHAPTER 1 INTRODUCTION

Processing of image signal is an important tool to know the finer details of any image. As we are living in the age of digital techniques, it is obvious that, processing of image signal digitally will be much more preferred in order to exploit the processing capabilities of computers. The technique of processing image signal using computer algorithms is known as digital image processing. The most important digital image processing technique is Image enhancement which refers to accentuation or sharpening of image features such as edges, boundaries, or contrast to make a graphic display more useful for display and analysis. The enhancement process does not increase the inherent information content in the data rather it increases the dynamic range of chosen features so that they can be detected easily. Image enhancement processes consist of a collection of techniques that seek to improve the visual appearance of an image or convert the image to a form better suited for analysis by a human or a machine. Image enhancement includes gray level and contrast manipulation, noise reduction, edge crispening and sharpening, filtering, interpolation and magnification, pseudocolouing, and so on. The image enhancement techniques would emphasize the salient features of the original image and simplify the processing task of data-extraction machine. There is no general unifying theory of image enhancement at present because there is no general standard of image quality that can serve as design criteria for an image enhancement system. Consideration is given here to a variety of techniques that have proved useful for human observation improvement and image analysis. 1.1 Fundamentals of Digital Image Processing

An image may be defined as a two-dimensional function, f(x, y), where x and y are spatial coordinates, and the amplitude of f(x, y) at any pair of coordinates (x, y) is called the intensity or gray level of the image at that point. An image is called a digital image when x, y, and the amplitude values of f(x, y) are all finite and discrete quantities. The

field of digital image processing refers to processing digital images by means of a digital computer. Digital image is composed of a finite number of elements, each of which has a particular location and value. These elements are referred to as picture elements, image elements, and pixels. Pixel is the term most widely used to denote the elements of a digital image. Vision is the most advanced of our senses, so it is not surprising that images play the single most important role in human perception. However, unlike humans, who are limited to the visual band of the electromagnetic (EM) spectrum, imaging machines cover almost the entire EM spectrum, ranging from gamma to radio waves. They can operate on images generated by sources that humans are not accustomed to associating with images. These include ultrasound, electron microscopy, and computer-generated images. Thus, digital image processing encompasses a wide and varied field of applications [1]. The area of image analysis (also called image understanding) is in between image processing and computer vision. There are no clear-cut boundaries in the continuum from image processing at one end to computer vision at the other. However, one useful paradigm is to consider three types of computerized processes in this continuum: low-, mid-, and high-level processes. Low-level processes involve primitive operations such as image preprocessing to reduce noise, contrast enhancement, and image sharpening. A low-level process is characterized by the fact that both its inputs and outputs are images. Mid-level processing on images involves tasks such as segmentation (partitioning an image into regions or objects), description of those objects to reduce them to a form suitable for computer processing, and classification (recognition) of individual objects. A mid-level process is characterized by the fact that its inputs generally are images, but its outputs are attributes extracted from those images (e.g., edges, contours, and the identity of individual objects). Finally, higher-level processing involves “making sense” of an ensemble of recognized objects, as in image analysis, and, at the far end of the continuum, performing the cognitive functions normally associated with vision. The digital image processing encompasses processes whose inputs and outputs are images and, in addition, encompasses processes that extract attributes from images, up to and including the recognition of individual objects. In the area of automated analysis of text, the processes of acquiring an image of the area containing the text, preprocessing 2

that image, extracting (segmenting) the individual characters, describing the characters in a form suitable for computer processing, and recognizing those individual characters are in the scope of digital image processing. Making sense of the content of the page may be viewed as being in the domain of image analysis and even computer vision, depending on the level of complexity implied by the statement “making sense”[1]. Image quality is one of the most important aspects of diagnostic radiology. The concept of image quality has been undergoing a transformation with the widespread use of digital-projection radiography. Imaging modalities, such as computed radiography (CR), are beginning to replace standard screen-film imaging systems. While many aspects of the imaging system remain unchanged, the processing of the image receptor and the viewing environment for the resulting radiographic images are significantly different. The radiologist is no longer limited to the single set of data represented by the light transmitted through a piece of film. They now have the ability to digitally manipulate the image data set and have access to the full dynamic range of information contained in that data set. Semi-qualitative methods, such as contrast-detail analysis, are tests of an imaging system’s performance as perceived by human observers. These observers subjectively evaluate, or score, images of contrast-detail phantoms. This identifies the perceived contrast-detectability in images produced by the imaging system. The results of this type of study can be used to establish threshold CNR (contrastto-noise ratio) based on the size of the objects in the phantom to determine the total number of visible objects. Therefore, it would be necessary to develop a method of applying these evaluations of imaging system performance to a perception of clinical image quality [2]. 1.2 Noise in Digital Images

Image noise is the digital equivalent of film grain for analogue cameras. Alternatively, one can think of it as analogous to the subtle background hiss that may be heard from audio system at full volume. For digital images, this noise appears as random speckles on an otherwise smooth surface and can significantly degrade image quality. Although noise often detracts from an image, it is sometimes desirable since it can add an 3

old-fashioned, grainy look to an image, which is reminiscent of early film. Some noise can also increase the apparent sharpness of an image. Noise increases with the sensitivity setting in the camera, length of the exposure, temperature, and even varies amongst different camera models. Each pixel in a camera sensor contains one or more light sensitive photodiodes, which convert the incoming light (photons) into an electrical signal, which is processed into the colour value of the pixel in the final image. If the same pixel would be exposed several times by the same amount of light, the resulting colour values would not be identical but have small statistical variations, called noise. Some degree of noise is always present in any electronic device that transmits or receives a signal. For television transmission this signal is the broadcast data transmitted over cable or received at the antenna; for digital cameras, the signal is the light, which hits the camera sensor. Even though noise is unavoidable, it can become so small relative to the signal that it appears to be nonexistent. The signal to noise ratio (SNR) is a useful and universal way of comparing the relative amount of signal and noise for any electronic system; high ratios have very little visible noise whereas the opposite is true for low ratios. Digital cameras produce three common types of noise: random noise, fixed pattern noise, and banding noise. The three qualitative examples shown in Fig. 1.1 depict pronounced and isolating cases for each type of noise against an ordinarily smooth gray background.

(a)

(b)

(c)

Fig. 1.1: (a) Image Noise-fixed pattern noise due to long exposure, (b) random noise due to short exposure, and (c) banding noise due to susceptible camera brightness shadows.

Random noise is characterized by intensity and colour fluctuations above and below the actual image intensity. There will always be some random noise at any 4

exposure length. The pattern of random noise changes even if the exposure settings are identical. Fixed pattern noise includes "hot pixels," which are the pixels having much higher intensity than that of the ambient random noise fluctuations. Fixed pattern noise generally appears in very long exposures and is exacerbated by higher temperatures. Fixed pattern noise is unique in that it shows almost the same distribution of hot pixels if taken under the same conditions viz. temperature, length of exposure, speed etc. Banding noise is highly dependent on capturing device, and is noise that is introduced by the camera when it reads data from the digital sensor. Banding noise is most visible at high speeds and in the shadows, or when an image has been excessively brightened. Banding noise can also increase for certain white balances depending on model of the capturing device. Although fixed pattern noise appears more objectionable, it is usually easier to remove since it is repeatable. A camera's internal circuitry just is to know the pattern and it can subtract this noise away to reveal the true image. Fixed pattern noise is much less of a problem than random noise in the latest generation of digital cameras, however even the slightest amount can be more distracting than random noise. The less objectionable random noise is usually much more difficult to remove without degrading the image. Computers have a difficult time discerning random noise from fine texture patterns such as those occurring in dirt or foliage [3]. There are four main sources of noise in digital camera images: Dark noise: Dark noise is an accumulation of heat-generated electrons in the sensor, which end up in the photosites and contribute a snow-like appearance in the image. The related term "dark current" refers to the rate of generation of these electrons, most of which come from boundaries between silicon and silicon dioxide in the sensor. Readout noise: Constructing an image from the sensor's photosites requires that the charge in each photosite be measured, and converted to a digital value. Making this measurement is part of the process of "reading out" the sensor. But doing so is an imperfect process. The amount of charge in the photosite is too small to be measured without prior amplification, and this is the main source of trouble: no perfect amplifier has been invented, and the amplifiers used on digital imaging sensors add a little bit of noise, similar to static in a radio signal, to the charge they are amplifying. The readout amplifier in a sensor is the main contributor to readout noise. 5

Photon noise: Photon noise is caused by the differences in arrival time of light to the sensor. If photons arrived at a constant rate, as though they were being delivered to the photosite by a conveyor belt at an efficient factory, then there would be no photon noise. But that isn't how it works. Photons arrive at the photosite irregularly. One pixel might be lucky enough to be hit with 100 photons in a given amount of time, while its neighbour only receives 80. If the photo is of an evenly illuminated surface, this photon noise will show up as one pixel having an improperly low value compared to an adjacent one. Random noise: The remaining noise is traceable to erroneous fluctuations in voltage or current in the camera's circuitry, to electromagnetic interference. Random noise will vary from image to image and is a result of many influences. One of the most significant might be random variation in the way electronic components operate at different times, temperatures, and conditions. Whatever the case, random noise is almost always infinitesimal - in most modern digital cameras, random noise will not be detectable in an 8-bit image; it may be barely measurable in a 16-bit image but will very rarely be visible in a conventional photo [4]. 1.3 Image Enhancement Techniques

The aim of image enhancement is to improve the interpretability or perception of information in images for human viewers, or to provide `better' input for other automated image processing systems. Image enhancement techniques can be divided into two broad categories: Spatial domain methods, which operate directly on pixels, and Frequency domain methods, which operate on the Fourier transform of an image. Unfortunately, there is no general theory for determining what `good’ image enhancement is when it comes to human perception. If it looks good, it is good! However, when image enhancement techniques are used as pre-processing tools for other image processing techniques, then quantitative measures can determine which techniques are most appropriate.

6

1.4 Review of work done Reported in the Literature

Weighted median filters are well known for their outlier suppression and detail preservation properties. This is extended to quadratic sample case yielding a filter structure that exploits the higher order statistics of the observed samples and simultaneously suppresses the noise and enhances the details [5]. Fuzzy detection method is mainly based on the calculation of fuzzy gradient values. Experiments show that this filter can be used for efficient removal of impulse noise from colour images. A new fuzzy logic filter for image enhancement with edge preserving technique has been presented [6-9]. Vector quantization and fuzzy ranks for image construction has been presented to the problem of quality enhancement in lossy compression. It is shown that the filters using fuzzy measures are able to suppress impulsive and Gaussian noise [10, 11]. Shape based averaging (SBA) filter improves the contiguity and accuracy of average image segmentations. Piecewise constant simulations helps denoising the image corrupted by white Gaussian noise. Partition based Weighted sum filtering is an effective method for non-stationary signals [12-17]. Gaussian membership function is proposed to fuzzify the image information in spatial domain for global contrast intensification [18]. Julie Delon et al. [19] proposed histogram segmentation approach to avoid over and under segmentation. Cluster-based linear discriminant approach helps in the feature extraction in face recognition [20, 21]. Max Mignotte [22] proposed segmentation based regularization term for image deconvolution for optimal restoration. Then Rafael Molina et al. [23] proposed blind deconvolution for the estimation of parameter, image and blur. The algorithms were tested experimentally and compared with existing deconvolution methods. Sub pixel registration can be performed directly in the Fourier domain by counting the number of cycles of phase difference matrix along with frequency axis [24]. A multiscale morphological algorithm for contrast enhancement of colour images is presented. This hue preservation technique is tested on several colour images. The enhanced

red,

blue,

and

green

images

are

obtained

by

combining

the

enhanced magnitude image [25]. Speckle reduction imaging allows to smooth regions where no features and edges appear and maintain or enhance edges and borders [26-28]. Contrast enhancement 7

technique has been proposed for dark blurred images by using 3 x 3 window and sigmoid function [29-33]. New algorithm for infrared small target image enhancement was presented that based on wavelet transform and human visual properties.

Contrast

nonlinear algorithm is proposed to human visual properties, which have noise reducing performance, preserving edges and improving the visual quality of images. Gray scale image enhancement as an automatic process driven by evolution was also presented [3435]. Enhancement in spatial domain of micro tubes in EM tomography results that the approach has excellent noise removal [36-38]. Amir Averbuch et al. [39] proposed edge enhancement post processing using canny edge detectors for the improvement of quality of images. Blue-noise halftoning method for hexagonal grids explained the Fourier analysis of blue-noise dither patterns on both rectangular and hexagonal sampling grids [40, 41]. Reliable fingerprint recognition is still a difficult problem. Extracting features out of poor image quality of fingerprints is the most challenging problem in this area. Fingerprint image enhancement using short time Fourier transform (STFT) is proposed to extract fingerprint ridges easily. Then almost similar approach was proposed but using a combination of filters in spatial domain for fingerprint image enhancement [42-44]. A new approach to image enhancement of frontal chest radiographs is presented, with the goal of making abnormalities more conspicuous. Images were enhanced by common pass and uncommon pass filters. The results suggest that visualization of image becomes very good for future applications to a wide range of pathologies [45-47]. Yinpeng Jin et al. [48] presented contrast enhancement by using adaptive histogram equalization to eliminate artifacts from the radiographs. Shih-Chang Hsia et al. [49] presented light balancing technique to compensate uneven illumination based on adaptive signal processing. A piecewise non-linear gain function is proposed for histogram equalization. Mammograms depict most of the significant changes in the breast disease. An artifactfree enhancement algorithm is presented where an image was decomposed using a fast wavelet transform algorithm. Compared to existing multiscale enhancement techniques, images processed with this method appeared more familiar to radiologists due to localized enhancement of features [50]. An illuminant and device invariant colour using histogram equalization was also proposed [51]. Neutron radiography lags behind in terms of image spatial resolution compared to X-ray radiography. An iterative, accelerated, 8

damped algorithm has been developed to reduce blur artifacts in images obtained from neutron radiography [52]. A technique for merging the information from both images is introduced including signal to noise ratio weighting, contrast transfer function correction, and optional Weiner filtration. This produces a composite image with reduced contrast transfer function artifacts and optimized contrast. This is useful in numerous cases where low-contrast images are produced, such as small particles, proteins solubilized in detergent or projects with high resolution goals when the first image is taken very close to focus [53, 54]. Zhi Yu Chen et al. [55, 56] proposed Gray-level grouping: an automatic method for optimized image contrast enhancement. The basic procedure is to first group the histogram components of a low contrast image, redistribute the gray-levels and then ungrouping the previously grouped gray-levels. The methods are very useful for eliminating background noise and enhancing a specific segment of histogram. The extension of this algorithm is used for colour image processing. A pilot study for monitoring breast cancer response using contrast-enhanced MRI (magnetic resonance imaging). A high special resolution, parametric method was presented based on dynamic contrast enhancement [57-65]. Visual enhancement of medical ultrasound images was presented in wavelet domain to de-speckle the noisy ultrasound images. Reduction of speckle is calculated in terms of SNR improvement [66-77]. Image enhancement by acoustic conditioning of ultrasound contrast agents has been developed for use with micro

bubbles

contrast

agents.

This

technique

is

unique

for

blood-to-

tissue image contrast [78]. Most important properties of Gabor filters are related to invariance to illumination, rotation, scale and translation making use in feature extraction [79]. A method is described for enhancing low contrast curvilinear features in imagery using directional filter for aerial imagery [80, 81]. Jinshan Tang, et al. [82] and Michael Elad, et al. [83] presented an algorithm using JPEG standard within the discrete cosine transform (DCT) domain. The algorithm does not affect the compressibility of original image because it enhances the image in decompressed stage. Moreover, the algorithm is characterized by low computational complexity. Hilda Frazi, et al. [84] proposed CCD noise removal in digital images. Experimental results suggest that light spacing denoising is more efficient for CCD noise problems. Additionally, a novel Gabor texture feature for 9

the grayscale as well as the colour domain is proposed. It relies on local phase changes characterizing the homogeneity of a texture in the spatial frequency domain. Several classification experiments on two image databases are performed to study the texture features according to different colour spaces and Gabor filter bank variants. The colour features show significantly better results than the grayscale features. Although they are completely intensity-independent, the features on the basis of the complex colour space show satisfying results. The RGB based features, where colour and intensity work inherently together, perform best. Especially the local phase change measure supplements the known amplitude measure appropriately [85]. Jinshan Tang, et al. [86] developed an image enhancement algorithm for low-vision patients for images compressed using JPEG standard. This algorithm enhances the image in the discrete cosine transform domain by weighing the quantization table in the decoder. Experiments with visually impaired persons show improved perceived image quality at moderate levels of enhancement but rejection of artifacts caused by higher levels of enhancement. Any image processing technique which is used to improve the appearance of an image for human perception or machine analysis should incorporate the characteristics of the human visual system. One of the major characteristics of the human visual system is the logarithmic response to light intensity [87-92]. Some new algorithms for image enhancement, edge detection and smoothing have been described and their results are presented. Only the edge detection technique is space-variant [93, 94]. Strzelecki M, et al. [95] proposed a new hierarchical 3D facial model that conforms to the human facial anatomy for realistic facial expression animation. The facial model has a hierarchical biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically motivated facial muscle actuators and underlying skull structure. The deformable skin model has multi-layer structure to approximate different types of soft tissue. It takes into account the nonlinear stress-strain relationship of the skin and the fact that soft tissue is almost incompressible. Different kinds of muscle models have been developed to simulate the distribution of the muscle force on the skin due to muscle contraction. By the presence of the skull model, our facial model takes advantage of both more accurate facial deformation and the consideration of facial anatomy during the interactive definition of facial muscles. Under 10

the muscular force, the deformation of the facial skin is evaluated by solving the governing dynamic equation numerically. The algorithms' computational complexity is decreased via a fast calculation of an auxiliary transform that takes values in special algebraic structures [96]. A new approach to colour image segmentation is demonstrated. The colour image, which is usually in the RGB space, is translated into the colour space. The three components are smoothed using a variation-based approach. By minimizing energy functional with a non-convex regular function, we can get a smoothed image. During the iteration, the edges of the image are preserved. A soft C-means clustering algorithm, which is an improvement on the hard C-means algorithm, is employed to segment them after smoothing. This algorithm overcomes the problem of dependence on the initializations [97]. In the context of image indexing for the purpose of retrieval, coloured object recognition methods tend to fail when the illumination of the objects varies from an image to another. A new approach to indexing images of persons is proposed, which copes with the variations of the lighting conditions. We assume that illumination changes can be described using a simple linear transform. For comparing two images, we transform the colours of the target one according to the colours of the query one by means of an original colour histogram specification based on colour invariant evaluation. For the retrieval purpose, we evaluate invariant colour signatures of the query image and the transformed target image through the use of colour cooccurrence matrices. Tests on real images are very encouraging, with substantially better results than those obtained with other well-established indexing and retrieval schemes [98-101]. A novel approach of fingerprint image enhancement that relies on detecting the fingerprint ridges as image regions where the second directional derivative of the digital image is positive. A facet model is used in order to approximate the derivatives at each image pixel based on the intensity values of pixels located in a certain neighborhood. Using neighborhoods of various sizes, the proposed algorithm determines several candidate binary representations of the input fingerprint pattern. Two public domain collections of fingerprint images are used in order to objectively assess the performance of the proposed fingerprint image enhancement approach [102]. A structure similarity approach of fingerprint image enhancement technique proposes spatial domain methods 11

and contrast image enhancement of fingerprints. Decimation free directional adaptive mean filtering has been introduced providing maximum energy [103,104]. Modern medicine is a field that has been revolutionized by the emergence of computer and imaging technology. It is increasingly difficult, however, to manage the ever-growing enormous amount of medical imaging information available in digital formats. The wavelet transforms have proven prominently useful not only for biomedical imaging but also for signal and image processing in general. Wavelet transforms decompose a signal into frequency bands, the width of which is determined by a dyadic scheme. This review represents a survey of the most significant practical and theoretical advances in the field of wavelet-based imaging informatics [105-108]. The output image of digital camera is subjected to severe degradation due to noise in sensor. A novel technique is proposed to combine demosaicing and denoising procedures systematically into a single operation by exploiting their obvious similarities. Whiteboard scanning and image enhancement suggested a system that automatically locates the boundary of a whiteboard, crops out the whiteboard region and corrects the colour [109,110]. A new method for processing low-light-level moving image is presented; in which a novel algorithm based on difference processing has been developed to determine the image features along with improved SNR (signal-to-noise-ratio) [111,112]. Techniques for image enhancement and segmentation of tomographic images of porous materials suggest that anisotropic diffusion removes noise while preserving image features. The second stage of this method is applied as sharpening filters for edge enhancement [113-117]. The degradation of photographic image can be filtered effectively by using Weiner filtration [118]. Real-time image enhancement preprocessor for CMOS sensor was designed for colour interpolation, gamma correction and automatic exposure control [119]. A robust content-based digital image watermarking scheme is presented which combines reduction of geometric distortions and various common JPEG compression, filtering, enhancement and quantization [120]. Colour image watermarking using multidimensional Fourier transform presents two watermarking schemes that are based on use of Fourier transform and demonstrates how to embed watermarks in frequency domain that is consistent with our human visual system [121]. Enhancement of image 12

watermark retrieval based on genetic algorithms was proposed in addition to correct fragile watermarking rounding errors and to achieve higher watermarked image quality [122]. A method for estimating the instantaneous frequency, image processing technique in time-frequency domain is presented that involves transformation of 1-D signal into 2D signal in time-frequency domain [123,124]. Air and vehicle borne sensor based technique is potentially attractive approach to fast detecting landmines and locating landmines field towards humanitarian demining. The performance of detector was evaluated in terms of detectibility, localization and automatic scale selection of the detector [125]. Fourier transform method for processing the images of extensive air showers detected by imaging atmospheric Cherenkov telescopes was presented. This approach allows very deep tail and image cuts. It has significant noise suppression capability by using low pass filtering in frequency domain [126]. Noise reduction in high dynamic range imaging was presented which does not introduce blur or other artifacts, and leverages the wealth of information available in a sequence of aligned exposures [127]. Enhancement of photolithography resolution can also be achieved by using fractional Fourier domain filtering. This filtering improves image fidelity, reduces the optical proximity effect and increases the depth of focus. The theory of partial coherence diffractions combined with fractional frequency domain filter [128-130]. A technique for enhancing the perceptual sharpness of an image is described. The enhancement augments the frequency content of the image using shape-invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics. Phase-correlation is computationally efficient scheme to improve registration of rotated images in the Fourier domain [131,132]. Enhancement of the centroiding algorithm for star tracker measure refinement is introduced as an image processing technique employing back propagation algorithm of neural network to reduce the signal errors [133]. The wavelet transforms in medical imaging addresses the problems of image compression, edge and feature selection, denoising, contrast enhancement and image fusion [134]. Enhancement of portioning techniques for image compression using weighted finite automata is proposed. The choice of the image portioning technique is important to achieve good compression results [135]. Enhancement and feature extraction for images of incised and 13

ink texts are described. This technique includes homomorphic filtering to correct uneven illumination, high pass filtering to remove shading for a text recognition system [136, 137]. Phase contrast radiography is an enhancement technique, which allows visualizing objects providing very low contrast with conventional absorption radiography technique [138]. Hue preserving colour image enhancement without gamut problem is proposed for processing of intensity and saturation of colour images. The developed principle is to generalize the histogram equalization of gray scale images to colour images [139]. A novel approach for colour image denoising is proposed via chromaticity diffusion that is based on separating the colour data into chromaticity and brightness and then processing each one of these components with partial differential equations [140]. Adaptive mammographic image enhancement using first derivative and local statistics is presented. This method helped particularly reducing the micro calcifications [141]. The logarithmic image processing is mathematical framework that provides a set of specific algebraic and functional operations and structures that are well adapted to the representation and processing of nonlinear images. Experimental results show that this medical enhancement includes wide application are like digital X-ray, digital mammography, computer tomography scans etc. [142]. The research papers reported in the literature have one thing in common i.e. they are all application specific. The image enhancement is not robust which can be applied to a variety of applications. In the present work, set of filters will be designed and implemented for many applications such as forensic science application, face recognition, detection of biological disorder etc. Feature extraction also becomes much easier in the present frequency domain image enhancement techniques. 1.5 Organization of the Thesis The present chapter has covered introduction of digital image processing and enhancement techniques, different types of noise signals present in digital images and detailed review of literature in the concerned field. A background of image enhancement techniques is given in Chapter 2. It includes introduction of spatial domain enhancement techniques, frequency domain techniques, and the importance of frequency domain 14

techniques. This chapter has also addressed the statistical parameters to be used for comparison of various techniques. Frequency domain image enhancement techniques to be implemented and designed are covered in Chapter 3 which includes Smoothing domain filters, Sharpening domain filters and Homomorphic filtering.

A special technique of colour image

enhancement has been discussed. The design and implementation of algorithms for all the filters are presented in detailed in Chapter 4. This chapter also includes databases, system requirements and flow diagram of the research work. Chapter 5 describes the results for all the filters along with their comparative study. The comparison is made in terms of image statistical parameters. The application based on the findings is reported in Chapter 6 which describes the process of fingerprint feature extraction and matching; using image enhancement as pre-processing step. Chapter 7 includes conclusions, findings of the study, as well as recommendations for further research on this topic.

15

CHAPTER 2 IMAGE ENHANCEMENT The principal objective of enhancement is to process an image so that the result becomes more suitable than the original image for a specific application [143-148]. Image enhancement techniques, to be applied on an image basically depend upon the type of the image, mode of capturing device and application of the information obtained from the images. For example, a method that is quite useful for enhancing X-ray images may not necessarily be the best approach for enhancing pictures of Mars transmitted by a space probe. Image enhancement approaches fall into two broad categories: spatial domain methods and frequency domain methods. The term spatial domain refers to the image plane itself, and approaches in this category are based on direct manipulation of pixels in an image. Frequency domain processing techniques are based on modifying the Fourier transform of an image [1, 2,149-151]. 2.1 Spatial Domain Methods

The term spatial domain refers to the aggregate of pixels composing an image. Spatial domain methods are procedures that operate directly on these pixels. Spatial domain processes will be denoted by the expression: G(x, y) = T[ f(x, y)]

…..(2.1)

where f(x, y) is the input image, g(x, y), the processed image, and T, an operator on f(x, y) defined over some neighborhood of (x, y). In addition T can operate on a set of input images, such as performing the pixel-by-pixel sum of K images for noise reduction. The principal approach in defining a neighborhood about a point (x, y) is to use a square or rectangular sub image area centered at (x, y), as shown in Fig. 2.1. The center of the sub image is moved from pixel to pixel starting, say, at the top left corner. The operator T is applied at each location (x, y) to yield the output, g, at that location [1, 2]. The simplest form of T is when the neighborhood is of size 1x1 (that is, a single pixel). In this case, g depends only on the value of f at (x, y), and T becomes a gray-level

(also called an intensity or mapping) transformation function of the form: s = T(r)

…..(2.2)

where, r and s are variables denoting, respectively, the gray level of f(x, y) and g(x, y) at any point (x, y). For example, if T(r) has the form as shown in Fig. 2.2(a), the effect of this transformation would be to produce an image of higher contrast than the original by darkening the levels below m and brightening the levels above m in the original image. In this technique, known as contrast stretching, the values of r below m are compressed by the transformation function into a narrow range of s, toward black. The opposite effect takes place for values of r above m. In the limiting case as shown in Fig. 2.2(b), T(r) produces a two-level (binary) image. A mapping of this form is called a thresholding function. Enhancement at any point in an image depends only on the gray level at that point; techniques in this category often are referred to as point processing.

Fig. 2.1: 3x3 neighborhood about a point (x, y) in an image.

17

(a) Contrast Stretching

(b) Thresholding

Fig. 2.2: Gray level transformation functions for contrast stretch.

Larger neighborhoods allow considerably more flexibility. The general approach is to use a function of the values of f in a predefined neighborhood of (x, y) to determine the value of g at (x, y). One of the principal approaches in this formulation is based on the use of so-called masks (also referred to as filters, kernels, templates, or windows). Basically, a mask is a small (say, 3x3) 2-D array, such as the one shown in Fig. 2.1, in which the values of the mask coefficients determine the nature of the process, such as image sharpening. Enhancement techniques based on this type of approach often are referred to as mask processing or filtering [1, 2, 151]. Spatial domain image enhancement techniques are classified into mainly four categories: Point processing, image subtraction, image averaging and spatial filtering. Point processing is further divided into two types: gray scale modification and histogram processing.

Similarly, Gray scale modification may fall into three categories: Log

transformation, Power law transformation and Piecewise transformation. Finally, piecewise transformation can include contrast stretching, gray level slicing and bit plane slicing. Spatial filtering may use Weiner filtering, Gabor filtering in spatial domain [2]. Spatial domain techniques are shown in Fig. 2.3.

18

Fig. 2.3: Spatial Domain Image Enhancement Techniques.

2.1.1 Histogram Equalization

Histogram equalization is a common technique for enhancing the appearance of images. The histogram of an image that is predominantly dark would be skewed towards the lower end of the gray scale and all the image detail is compressed into the dark end of the histogram. If gray levels are stretched out at the dark end to produce a more uniformly distributed histogram then the image would become much clearer. Histogram equalization involves finding a gray scale transformation function that creates an output image with a uniform histogram [1, 2]. A transformation T must be found that maps gray

19

values r in the input image F to gray values s = T(r) in the transformed image

Λ

F.

It is

assumed that (a) T is single valued and monotonically increasing, and (b) 0 ≤ T(r) ≤ 1 for 0 ≤ r ≤ 1. If one of the images from the database of images is subjected to histogram equalization method, then it produces the result shown in Fig. 2.4. The original image and its histogram are shown in Fig. 2.4 (a) & Fig. 2.4 (c) respectively. Similarly enhanced image and its histogram are shown in Fig. 2.4 (b) & Fig. 2.4 (d) respectively. In the Fig. 2.4 (d), uniform distribution of gray values can be seen which resulted the enhanced image of Fig. 2.4 (b).

(a) Original Image

(c) Histogram of original image

(b) Histogram Equalized image

(d) Histogram of enhanced image

Fig. 2.4: Result of histogram equalization.

2.2 Frequency Domain Methods Frequency domain methods are the methods that modify the Fourier transform of the image. First, compute the Fourier transform of the image. Then alter the Fourier 20

transform of the image by multiplying a filter transfer function. Finally, an inverse transform is used to get the modified image. The key is the filter transfer function which includes low pass filter, high pass filter, and Butterworth filter. The enhanced image is produced by simply computing Fourier transform of the image to be enhanced, multiplying the result by a filter (rather than convolve in the spatial domain), and taking the inverse transform. The idea of blurring an image by reducing its high frequency components or sharpening an image by increasing the magnitude of its high frequency components is intuitively easy to understand. However, computationally, it is often more efficient to implement these operations as convolutions by small spatial filters in the spatial domain [1, 2]. Low pass filtering involves the elimination of the high frequency components in the image. It results in blurring of the image and thus a reduction in sharp transitions associated with noise. An ideal low pass filter would retain all the low frequency components, and eliminate all the high frequency components. However, ideal filters suffer from two problems: blurring and ringing. These problems are caused by the shape of the

associated spatial domain filter, which has a

large

number

of

undulations.

Smoother transitions in the frequency domain filter, such as the Butterworth filter, achieve much better results [150,151]. Images normally consist of light reflected from objects. The basic nature of the image f(x,y) may be characterized by two components: the amount of source light incident on the scene being viewed and the amount of light reflected by the objects in the scene. These portions of light are called the illumination and reflectance components, and are denoted i(x,y) and r(x,y) respectively. The functions i and r combine multiplicatively to give the image function f(x,y): f(x,y) = i(x,y)r(x,y)

…..(2.3)

where 0 < i(x, y) < ∞ and 0 < r(x,y) < 1. Homomorphic filtering is applied to separately enhance these components in frequency domain. Image processing for colour image enhancement is also achieved in frequency domain [1, 2]. The following four techniques of image enhancement in frequency domain will be implemented: 21

(a) Low pass filtering or smoothing domain filters, (b) High pass filtering or sharpening domain filters, (c) Homomorphic filtering, and (d) Colour image enhancement. 2.2.1 Convolution Theorem

The Fourier Transform is used to convert images from the spatial domain into the frequency domain and vice-versa. Convolution is one of the most important concepts in Fourier theory. Mathematically, a convolution is defined as the integral over all space of one function at x times another function at u-x.

f ∗g = ∫

∞

−∞

∞

f (τ ) g (t − τ )dτ = ∫ g (τ ) f (t −τ )dτ −∞

….. (2.4)

The convolution theorem is useful because it gives us a way to simplify many calculations. Convolutions can be very difficult to calculate directly, but are often much easier to calculate using Fourier transforms and multiplication. There are two ways of expressing the convolution theorem: (a) Fourier transform of a convolution is the product of the Fourier transforms [1]. (b) Fourier transform of a product is the convolution of the Fourier transforms. Let F and G be the Fourier transform of functions f and g respectively. Then ℑ( f ∗ g ) = ℑ( f ).ℑ( g ) = F .G

…..(2.5)

where ‘.’(dot) denotes the element-by-element multiplication and ℑ is Fourier transform operator. Also, the Fourier transform of a product is the convolution of the Fourier transforms:

ℑ (f·g) = ℑ (f) * ℑ (g) = F * G

…..(2.6)

By using the inverse Fourier transform F -1, we can write -1

ℑ (F · G) = f * g -1

ℑ (F * G) = f · g

…..(2.7) …..(2.8)

The most fundamental relationship between spatial and frequency domain is established. Formally, the discrete convolution of two functions f(x, y) and h(x, y) of size M x N is defined by the expression: 22

1 M −1 f (x, y) ∗ h(x, y) = ∑ MN m=0

N −1

∑ f (m, n)h(x − m, y − n) n=0

.....(2.9)

2.2.2 Basics of Filtering in Frequency Domain

Before discussing filtering, it’s important to understand what does high and low frequency component mean in an image. If an image has large values at high frequency components then the data (gray level) is changing rapidly on a short distance scale, e.g., a page of text, edges and noise. If the image has large low frequency components then the large scale features of the picture are more important, e.g., a single fairly simple object which occupies most of the image. For colour images, the frequency content depends on the colour components and their variation [2]. Filtering in the frequency domain is a common image and signal processing technique. It can smooth, sharpen, de-blur, and restore some images. Essentially, filtering is equal to convolving a function with a specific filter function. So one possibility to convolve two functions could be to transform them to the frequency domain, multiply them and transform them back to spatial domain. The filtering procedure is summarized in Fig. 2.5.

Fig. 2.5: Frequency domain filtering procedure.

23

Basic steps of filtering in the frequency domain are as under [1]: 1. Multiply the input image f (x, y) by (-1) (x + y) to center the transform, as indicated in the equation: ℑ [f(x, y) (-1) (x + y) ] = F (u - M/2, υ - N/2). 2. Compute F (u, υ), the DFT of the input image from step 1. 3. Multiply F (u, υ) by a filter function H (u, υ). 4. Compute the inverse DFT of the result out of step 3. 5. Obtain the real part of the output of step 4. 6. Multiply the result in step 5 by (-1) (x + y). The Two-Dimensional DFT and its inverse are computed with the help of the following equation:

F( u ,v ) =

1 M −1 N −1 − j 2 π( ux / M +vy / N ) ∑ ∑ f ( x, y )e MN x=0 y =0

…..(2.10)

f ( x, y) =

1 M −1 N −1 F (u, v)e j 2π (ux / M +vy / N ) ∑ MN u∑ =0 v =0

…..(2.11)

and

The Fourier transform of the filtered image in step 3 is given by: G (u, υ) = F (u, υ) H (u, υ)

…..(2.12)

where F(u, υ) and H(u, υ) denote the Fourier transform of the input image f (x, y), and the filter function h(x, y), respectively. G (u, υ) is the Fourier Transform of the filtered image, which is the multiplication of two two-dimensional functions H and F on an element-by-element basis [1]. The important point to keep in mind is that the filtering process is based on modifying the transform of an image (frequency) in some way via a filter function, and then taking the inverse of the result to obtain the filtered image i.e. Filtered Image = ℑ -1[G (u, υ)].

24

2.3 Importance of Frequency Domain Techniques

There is great utility of working in frequency domain to perform certain image measurement and processing operations. Such operations can be performed in the original (spatial or pixel domain) image only with significantly greater computational effort. However, the typical image analyst interested in applying computer methods to images for purposes of enhancement or measurement may not be comfortable with the mathematics. Furthermore, he or she may not have the fortitude to relate these concepts to the operation of a dedicated image-analysis computer. This is a loss, because the use of frequency-space methods can offer benefits in many real-life applications, and it is not essential to deal deeply with the mathematics to arrive at a practical working knowledge of these techniques. The Fourier transform and other frequency-space transforms are applied to twodimensional images for many different reasons. Some of these have little to do with the purposes of enhancing visibility and selection of features or structures of interest for measurement. For instance, some of these transform methods are used as a means of image compression to reduce the amount of data in the original image for greater efficiency in transmittal or storage. In this type of application, it is necessary to reconstruct the image (bring it back from the frequency to the spatial domain) for viewing. It is desirable to be able to accomplish both the forward and reverse transform rapidly and with a minimum loss of image quality. Image quality is a somewhat elusive concept that certainly includes the alteration of brightness levels and colour values, definition and location of feature boundaries, and introduction or removal of fine-scale texture in the image. Generally, the greater the degree of compression, the more the loss of image fidelity. Speed is usually a less important concern to image measurement applications, since the acquisition and subsequent analysis of the images are likely to require some time anyway, but the computational advances (both in hardware and software or algorithms) made to accommodate the requirements of the data compression application help to shorten the time for some other processing operations as well. On the other hand, the amount of image degradation that can be tolerated by most visual uses of 25

the compressed and restored images is far greater than is usually acceptable for imageanalysis purposes. Consequently, the amount of image compression that can be achieved with minimal loss of fidelity is rather small. Since in most cases the transmission of an image from the point of acquisition to the computer used for analysis is not a major concern, we will ignore this entire subject here and assume that the transform retains all of the data, even if this means that there is no compression at all. The transform encodes the image information completely and it can be exactly reconstructed, at least to within the arithmetic precision of the computer being used (which is generally better than the precision of the original image sensor or analog-todigital converter). Although there are many different types of image transformation techniques that can be used, the best known is the Fourier transform. This is due to the availability of a powerful, efficient algorithm for computing it, known as the Fast Fourier Transform (FFT). The usual approach to develop the mathematical background of the Fourier transforms begins with a one-dimensional waveform and then expands to two dimensions (an image). In principle, this can also be extended to three dimensions or more, although it becomes more difficult to visualize or display. 2.4 Statistical Parameters for Performance Evaluation of the Image Enhancement

Image quality is one of the most important aspects of diagnostic radiology. The concept of image quality has been undergoing a transformation with the widespread use of digital-projection radiography. The radiologist is no longer limited to the single set of data represented by the light transmitted through a piece of film. They now have the ability to digitally manipulate the image data set and have access to the full dynamic range of information contained in that data set [152-154]. Traditionally, an image quality is evaluated in two separate ways, quantitatively or qualitatively. Quantitative methods, such as the calculation of the PSNR, variance values are tests of the imaging system performance. Semi-qualitative methods, such as contrast-detail analysis, are tests of an imaging system’s performance as perceived by human observers. These observers subjectively evaluate, or score, images of contrastdetail phantoms. This identifies the perceived contrast-detectability in images produced 26

by the imaging system. The results of this type of study can be used to establish threshold contrast-to-noise ratios (CNR) based on the size of the objects in the phantom to determine the total number of visible objects. This type of study will provide a quantitative parameter based on a semi-qualitative evaluation that does not have to be repeated. Therefore, it would be ideal to develop a method of applying these evaluations of imaging system performance to a perception of image quality [152]. 2.4.1 PSNR (Peak signal-to-noise-ratio) and CNR (Contrast-to-noise-ratio)

One problem common to all imaging modalities is noise. Some noise is attributable to object motion produced during the long scan times, while other noise components may be due to system hardware itself [153]. PSNR and CNR estimation technique were proposed to improve image SNR, and CNR [154]. SNR = σs/σn

…..(2.13)

where σs is standard deviation of the image signal and σn is standard deviation of noise signal. The SNR is defined as above since the standard deviation of the signal includes more overall image content than simply the signal mean. Defining the SNR in this manner, however, requires that we use two image acquisitions [155]. An image may be expressed as sum of base signal and additive uncorrelated noise signal. Consider images i1(x,y) and i2(x,y) as: i1(x,y) = s(x,y) + n1(x,y)

…..(2.14)

i2(x,y) = s(x,y) + n2(x,y)

…..(2.15)

where s(x,y) is base signal; n1(x,y) and n2(x,y) are additive uncorrelated noise signals present in i1(x,y) and i2(x,y) respectively. The cross-correlation function (CCF) of the

images

can

be

defined

as

i1 ∗ i2 = s ∗ s + n1 ∗ s + n2 ∗ s + n1 ∗ n2

the

convolution

of

the

images: …..(2.16)

However, because the noise components are uncorrelated both to the images and each other, the above expression simplifies to: i1 ∗ i2 = s ∗ s. Then a cross-correlation coefficient (CCC) can be defined as: 27

σ(x, y) = (i1 ∗ i2 - )/σ1σ2

…..(2.17)

where < > is the mean; σ1, σ2 are the standard deviation of images i1(x,y) and i2(x,y) respectively. The maximum of the CCC can be calculated as ρm. Consequently: SNR = sqrt(ρ m/(1-ρ m))

……(2.18)

Clearly, it is now fairly simple to obtain an estimate of the SNR from two consecutive acquisitions of the same image. Maximum value of SNR is PSNR. Another required definition is: Contrast to Noise Ratio (CNR) = (-)/σn

…..(2.19)

In this definition, we subtract the difference in means between two regions (sa & sb ) in the image and divide by the standard deviation of the noise (σn). Ideally, the CNR should follow the SNR. 2.4.2 Invariant moments, Mean, Variance Values, Histogram A set of seven invariant moments can be derived from the second and third moments [1]. These moments are listed below: Φ1 = η20 + η02

…..(2.20)

Φ2 = (Φ1)2 + 4 η11)^2

…..(2.21)

Φ3 = (η30 - 3* η12)^2 + (3* η21 - η)^2

…..(2.22)

Φ4 = (η30 + 3* η12)^2 + (η21 + η03)^2

…..(2.23)

Φ5 =( η30 - 3* η12)*( η30 + η12)* ((η30 + η12)^2 - 3*( η21 + η03)^2) + (3* η21 - η03)*( η21 + η03)* (3*( η30 + η12)^2 - (η21 + η03)^2) …..(2.24) Φ6 =(η20 - η02)*(( η30 + η12)^2 - (η21 + η03)^2) + 4*η11 * (η30 + η12)*( η21 + η03)

…..(2.25)

Φ7 =(3*η21 - η03)*( η30 + η12)* ((η30 + η12)^2 - 3*( η21 + η03)^2) + (3* η12 - η 03)*( η21 + η03)* (3*( η30 + η12)^2 - (η21 + η03)^2)

…..(2.26)

This set of moments is invariant to translation, rotation and scale change. Average or mean value is the mean value of the elements in X if X is vector. For matrices, MEAN(X) is a row vector containing the mean value of each column. For N28

dimensional arrays, MEAN(X) is the mean value of the elements along the first nonsingleton dimension of X. For vectors, VAR(X) returns the variance of X. For matrices, VAR(X) is a row vector containing the variance of each column of X.

VAR(X)

normalizes by N-1 where N is the sequence length. This makes VAR(X) the best unbiased estimate of the variance if X is a sample from a normal distribution. VAR(X, 1) normalizes by N and produces the second moment of the sample about its mean. VAR(X, W) computes the variance using the weight vector, W. The number of elements in W must equal the number of rows in X unless W = 1 which is treated as a short-cut for a vector of ones. The elements of W must be positive. VAR normalizes W by dividing each element in W by the sum of all its elements. The variance is the square of the standard deviation [156,157]. The histogram of a digital image shows the distribution of its pixel intensities. The histogram plots the number of pixels in the image (vertical axis) with a particular brightness value (horizontal axis) shown in Fig. 2.6. In Fig. 2.7, an image of cameraman and its histogram have been shown. The histogram shows that the most of the pixels are having their gray scale values in the range 150-200 and 0-20.

Fig. 2.6: Histogram as number of pixels vs. intensity value.

29

. (a) An Image of cameraman

(b) Histogram of the image

Fig. 2.7: (a) an image of cameraman, (b) its histogram.

2.5 Summary

This chapter addressed overview of image enhancement techniques. Spatial domain image enhancement technique has been discussed in terms of neighbourhood processing, gray level transformation and histogram equalization. Frequency domain image enhancement technique has been introduced with the help of convolution theorem, necessary steps of filtering and importance of frequency domain technique as compared to spatial domain techniques. Statistical image parameters used for evaluation of performance of the filters has been summarized. These discussions pave the path for the design and implementation aspects of frequency domain image enhancement techniques.

30

CHAPTER 3 FREQUENCY DOMAIN IMAGE ENHANCEMENT TECHNIQUES Image enhancement in the frequency domain is straightforward. We simply compute the Fourier transform of the image to be enhanced, multiply the result by a filter (rather than convolve in the spatial domain), and take the inverse transform to produce the enhanced image. The idea of blurring an image by reducing its high frequency components or sharpening an image by increasing the magnitude of its high frequency components is intuitively easy to understand. The key is the filter transfer function – examples include low pass filter, high pass filter and homomorphic filter. 3.1 Smoothing Domain Filters The edges and noises and other sharp transitions in the gray level contribute significantly to the high frequency. Hence smoothing or blurring is achieved by attenuating a specified range of high frequency components in the transform of a given image, which can be done using a low pass filter. Low pass filter is a filter that attenuates high frequencies and retains low frequencies unchanged. This results a smoothing filter in the spatial domain since high frequencies are blocked. Three types of low pass filters in the present report are Ideal, Gaussian and Butterworth [1, 2]. 3.1.1 Ideal Low Pass Filter The most simple low pass filter is the ideal low pass filter. It suppresses all frequencies higher than the cut-off frequency r0 and leaves smaller frequencies unchanged:

1, if D( u ,v ) ≤ r0 H(u, v) =

0, if D( u ,v ) > r0

…..(3.1)

where r0 is called the cutoff frequency (nonnegative quantity), and D(u, v) is the distance from point (u, v) to the frequency rectangle [1, 2]. If the image is of size M x N, then

D(u, v) = (u −

M 2 N ) + (v − )2 2 2

…..(3.2)

The low pass filters considered here are radially symmetric about the origin. Using Fig. 3.1 as the cross section that extending as a function of distance from the origin along a radial line, Fig. 3.3 is obtained, this is the perspective plot of an Ideal LPF transfer function. Fig. 3.2 is the filter displayed as an image.

Fig. 3.1: Filter radial cross section.

Fig. 3.2: Filter displayed as an image.

32

Fig. 3.3: Perspective plot of an Ideal LPF transfer function.

The drawback of the ideal low pass filter function is a ringing effect that occurs along the edges of the filtered image. In fact, ringing behavior is a characteristic of ILPF (Ideal Low Pass Filter). As mentioned earlier, multiplication in the Fourier domain corresponds to a convolution in the spatial domain. Due to the multiple peaks of the ideal filter in the spatial domain, the filtered image produces ringing along intensity edges in the spatial domain. The cutoff frequency r0 of the ILPF determines the amount of frequency components passed by the filter. Smaller the value of r0, more the number of image components eliminated by the filter. In general, the value of r0 is chosen such that most components of interest are passed through, while most components not of interest are eliminated. As can be seen in Fig. 3.4, the filtered image is blurred and ringing is more severe as r0 become smaller. It is clear from this example that ILPF is not very practical.

(a) Original Image

(b) r0 = 26

(c) r0 = 36

(d) r0 = 57

Fig. 3.4: An example showing the effect of cut-off frequency (r0).

33

3.1.2 Butterworth Low Pass Filter [1, 2] A commonly used discrete approximation to the Gaussian is the Butterworth filter. Applying this filter in the frequency domain shows a similar result to the Gaussian smoothing in the spatial domain. The transfer function of a Butterworth low pass filter (BLPF) of order n, and with cut-off frequency at a distance r0 from the origin, is defined as

H (u, v) =

1  D(u, v)    r0 

…..(3.3) 2n

1+ 

As can be seen in Fig. 3.5, frequency response of the BLPF does not have a sharp transition as in the ideal LPF and as the filter order increases, the transition from the pass band to the stop band gets steeper. This means as the order of BLPF increases, it will exhibit the characteristics of the ILPF. The difference can be clearly seen between two images with different orders but the same cutoff frequency. Fig. 3.5 shows the cross section that extends as a function of distance from the origin along a radial line Fig. 3.7 is obtained. Fig. 3.6 is the filter displayed as an image.

Fig. 3.5: Filter radial cross sections of order n=2, 4 and 8.

34


Fig. 3.7: Plot of a Butterworth LPF transfer function.

Fig. 3.8 shows the comparison between the spatial representations of various orders with cut-off frequency of 5 pixels, also the corresponding gray level profiles through the center of the filter. As can be seen, BLPF of order 1 has no ringing and order of 2 has mild ringing. So, this method is more appropriate for image smoothing than the ideal low pass filter. Ringing in the BLPF becomes significant for higher order.

35

(a) BLPF of order 1

(b) BLPF of order 2

(c) BLPF of order 5

(d) BLPF of order 20

Fig. 3.8: Response of BLPF of different orders.

3.1.3 Gaussian Low Pass Filter

Gaussian filters are important in many signal processing, image processing and communication applications. These filters are characterized by narrow bandwidths, sharp cutoffs, and low overshoots. A key feature of Gaussian filters is that the Fourier transform of a Gaussian is also a Gaussian, so the filter has the same response shape in both the spatial and frequency domains [1, 2]. The form of a Gaussian low pass filter in two-dimensions is given by

H (u, v) = e− D

2 (u ,v)/2σ 2

…..(3.4)

The parameter σ measures the spread or dispersion of the Gaussian curve as shown in Fig. 3.9. Larger the value of σ, larger the cutoff frequency and milder the filtering is. When letting σ = r0, which leads a more familiar form as previous discussion. So Equation 3.4 becomes: H (u , v ) = e

− D 2(u ,v ) / 2 r02

…..(3.5)

36

Fig. 3.9: 1-D Gaussian distribution with mean 0 and σ = 1.

When D(u, v) = r0, the filter is down to 0.607 of its maximum value of 1 [1,2]. A perspective plot, image display, and radial cross section of a GLPF function are shown in Fig. 3.10, Fig. 3.11 and Fig. 3.12 respectively.

Fig. 3.10: Perspective plot of a GLPF transfer function.

37


Fig. 3.12: Filter radial cross sections for various values of D0 = r 0.

As mentioned earlier, the Gaussian has the same shape in the spatial and Fourier domains and therefore does not incur the ringing effect in the spatial domain of the filtered image. This is an advantage over ILPF and BLPF, especially in some situations where any type of artifact is not acceptable, such as medical image. In the case where tight control over transition between low and high frequency needed, Butterworth low pass filter provides better choice over Gaussian low pass filter; however, tradeoff is ringing effect. The Butterworth filter is a commonly used discrete approximation to the Gaussian. Applying this filter in the frequency domain shows a similar result to the 38

Gaussian smoothing in the spatial domain. But the difference is that the computational cost of the spatial filter increases with the standard deviation (e.g the size of the filter kernel), whereas the costs for a frequency filter are independent of the filter function. Hence, the Butterworth filter is a better implementation for wide low pass filters, while the spatial Gaussian filter is more appropriate for narrow low pass filters.

3.2 Sharpening Domain Filters

Sharpening filters emphasize the edges, or the differences between adjacent light and dark sample points in an image. A high pass filter yields edge enhancement or edge detection in the spatial domain, because edges contain many high frequencies. Areas of rather constant gray level consist of mainly low frequencies and are therefore suppressed. A high pass filter function is obtained by inverting the corresponding low pass filter. An ideal high pass filter blocks all frequencies smaller than r0 and leaves the others unchanged. The transfer function of low pass filter and high pass filter can be related as follows: Hhp (u, v) = 1 – Hlp(u, v)

…..(3.6)

where Hhp (u, v) and Hlp(u, v) are the transfer function of highpass and lowpass filter respectively [1,2,151]. 3.2.1 Ideal High Pass Filter

The transfer function of an ideal high pass filter with the cutoff frequency r0 is:

0, if D( u ,v ) ≤ r0 H(u, v) =

1, if D( u ,v ) > r0

……(3.7)

Plot, image representation and its cross section of the transfer function are shown in Fig. 3.13.

39

( a) Plot

(b) Image representation

(c) Cross section

Fig. 3.13: Perspective plot, image representation, and cross section of an IHPF.

Because the transfer functions of low pass filter and high pass filter are related as shown in Equation 3.6, one can expect ideal high pass filter (IHPF) to have the same ringing properties as ILPF. This is demonstrated clearly in the example as shown in Fig. 3.14.

(a)Original Image

(b) r0 = 18

(c) r0 = 26

(d) r0 = 36


3.2.2 Butterworth High Pass Filter [1, 2]

The transfer function of Butterworth high pass filter (BHPF) of order n and with cutoff frequency r0 is given by:

H (u, v) =

1 2n  r0  1+    D(u, v) 

.….(3.8)

40

Fig. 3.15 shows perspective plot, image representation, and cross section of BHPF.

(a) Plot


(c) Cross section

Fig. 3.15: Perspective plot, image representation, and cross section of a BHPF.

The frequency response does not have a sharp transition as in the IHPF. It can be seen that BHPF behaves smoother and has less distortion than IHPF. Therefore, BHPF is more appropriate for image sharpening than the IHPF. Also less ringing is introduced with small value of the order n of BHPF.

3.2.3 Gaussian High Pass Filter The transfer function of a Gaussian high pass filter (GHPF) with the cutoff frequency r0 is given by:

H (u, v) = 1− e− D

2 (u ,v )/2r 2 0

…..(3.9)

The parameter σ, measures the spread or dispersion of the Gaussian curve. Larger the value of σ, larger the cutoff frequency and milder the filtering is [1, 2]. Fig. 3.16 shows perspective plot, image representation, and cross section of GHPF.

41

(a) Plot


(c) Cross section

Fig. 3.16: Perspective plot, image representation, and cross section of a GHPF.

An example of high pass filtering the image using GHPF of order 2 is shown in Fig. 3.17.

(a) Original

(b) r0 =15

(c) r0 =30

(d) r0 =80


3.3 Homomorphic Filtering An image can be expressed as the product of illumination and reflectance components [1,2]: f(x,y) = i(x,y)r(x,y)

…..(3.10)

where i(x,y) and r(x,y) are illumination and reflectance components respectively; f(x,y) must be non zero and finite; that is, 0 < f(x,y)

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