hiding image in image using iterated function system

Advances in Communications, Computers, Systems, Circuits and Devices

HIDING IMAGE IN IMAGE USING ITERATED FUNCTION SYSTEM (IFS) Loay E. George1

Suad K. Ahmad2

1

Department of Computer Science, University of Baghdad, Baghdad, Iraq phone: + (t. code) your phone, fax: + (int. code) your fax, email: [email protected] 2 Department of Computer System, University of Sulaimani, Sulaimani, Iraq 9647701242590, [email protected]

sion system. Today, steganographic technologies are very important in internet privacy. With the use of steganography and encryption the corporations, governments, and law enforcement agencies can communicate secretly. One of the main disadvantages of steganography is that the size of secret message is usually very smaller than the cover. Sometimes, there can be color changes, or detectable sound changes, such that they are evident; especially if a wellknown image or (audio) is chosen as the steganographic cover. Another issue to mention, text messages are limited in size for hosting data, they need redundant data to replace a secret message [1]. Steganography is the science of hiding information (Steganography is the art and science of secret communication, aiming to conceal the existence of a communication which has been used by revolutionaries, spies,th e military, and perhaps terrorists)[17]. Whereas the goal of cryptography is to make data unreadable by a third party, the goal of steganography is to hide the information and be undetectable to human eyes. Steganography focuses on the means of communication and the development of a covert channel. Steganography focuses entirely on keeping the adversary completely unaware of the communication, while cryptography focuses on keeping the communication contents secret. These purpose differences were first recognized during the 18th century when the two issues were split into separate fields of study; which we are currently familiar with. Cryptography shares many common characteristics with steganography, although the functions of the two have remained largely separate. Importantly, the implementation of both has started to converge, and in-line the attacks on both have begun to look remarkably similar. The differences between steganography and cryptography will be underscored with the two divergent purposes of both [2]. There are several information hiding techniques, they could be classified according to the media where the information are hidden. First, Hiding in Text, methods such as line-shift coding, word shift coding, and feature coding are the commonly used methods to hide data in text. When using a text data as a host media, the embedded data are usually codeword that are hidden within the text by altering their different textual features [1]. Second, data hiding in image, the least significant bit insertion method is a common simple approach for embedding infor-

ABSTRACT In this paper, an image high hiding steganographic method for concealing digital image in a cover image is introduced, and implemented. The proposed method exhibits the following advantages over the existing methods, first, it shows high hiding rate such that the embedded secret image can be larger than the cover image. Second, the quality of stegoimage is little degraded. Third, a small difference exists between the extracted secret image and the original secret. In embedding phase, the cover image is partitioned into overlapped blocks, but the secret image is partitioned into nonoverlapped blocks, and converted from RGB space to YUV color space, then the chromatic bands U and V space are downsampled. Then, the linear affine mapping is applied to represent the blocks of bands of secret image in terms of cover image blocks using IFS-code. To speed up the mapping-search process a moment based classifier is used to classify the secret and cover blocks to reduced the encoding time without causing a reduction in image fidelity, where the encoding time of whole hiding process becomes within [6.94-9.67] second for a 24-bitmap color secret image its size is 256x256 pixels, the size of the color secret image (24bitmap) is 1.48 times the size of cover image. The technique used to embed the generated IFS-code, is the LeastSignificant-Bit (LSB) substitution method. The embedded secret image can be extracted from the resulting stegoimage without need to referencing to the original secret image. The experimental results demonstrated that the values of the PSNR fidelity measure ranging between (31.04-31.41) decibels when the ration of secret image size to that of cover image is (100% and 123%), respectively, and also the difference between the stego-image and the cover image is almost imperceptible. Index Terms— Hiding image, steganography, IFS, high hiding rate, affine transform. 1.

INTRODUCTION

The aim of steganography is to hide information, such that the transmission of messages is transparent to any given viewer. Messages can be hided in different formats, such that they are undetectable and un-noticeable by human vi-

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Where,

mation in image file. When applying LSB insertion method on each byte of a 24-bit image, three bits can be encoded into each pixel (because each pixel is represented by three bytes). Any changes in the pixel bits will be indiscernible to the human eye. When using LSB techniques on 8-bit color images (i.e., palate driven), more care need to be taken. So, for 8-bit images only the grey images are recommended for data hiding [2]. Masking and filtering are the anther techniques which are more suitable for use in lossy JPEG images [3]. All the above mentioned hiding methods for image steganography have different strong and weak points and it is important to ensure that one uses the most suitable method for an application. All steganographic methods have to comply be applied with a few basic requirements (i.e., invisibility, payload capacity, robustness against statistical attacks, robustness against image manipulation, independent of file format, and unsuspicious files [4]. Many research effort have been spend to develop coding systems for hiding, compression or both [14, 15]

r = scaling factor on x, θ = angle of rotation on x, e = translation on x,

s = scaling factor on y. φ = angle of rotation on y. f = translation on y.

PIFS image encoder consists of a set of transforms applied on the region of the image (i.e., secret image). The transforms are, firstly, used to generate the overlapped domain (cover) regions. Secondly, a set of spatial contractive affine transforms are used to approximate the range (secret) blocks by linearly mapping the most similar cover block [8].The contractive affine transform which is adopted in this paper is:

ri' = s (d i − d ) + r ,………………………..…...... (2) Where,

r=

1 m−1 1 m−1 , r d = ∑i ∑ di m i =0 m i =0

To determine the scale (s) value, the method of least mean square errors (depicted in equation 2) is applied to get, 2.

MATERIALS AND METHODS

 1 m−1  m ∑ d i ri − r d if σ d2 > 0 ,….…….... (4) s =  i =0 2 σd   0 if σ d2 = 0

2.1 Fractal Coding Fractal is first introduced in geometry field. The birth of fractal geometry is usually traced back to the IBM mathematician Benoit B. Mandelbrot when he published his book “The Fractal Geometry of Nature” at 1977. Later, Michael Barnsley, a leading researcher from Georgia Tech, found a way of applying this idea to data representation and compression using the mathematics of Iterated Functions Systems (IFS). Regarding the computational complexity, fractal compression algorithm based on IFS was not practical to be use at that time. And, it is Arnode Jacquin, one of Barnsley’s PhD students, who finally steeled down this problem using Partitioned Iterated Function Systems (PIFS), which is modified from IFS by partitioning the domain space into subspaces [5]. IFS Fractals were developed by Michael Barnsley, he referred that this system has the ability to create realistic images with very small sets of numbers and it can encode a scene of almost any level of complexity and detail by a small group of numbers, thereby achieving amazing compression ratios of images of 100 or more. Barnsley's collage theorem provides the basis for converting natural images into IFS code, and a random iteration algorithm could be used to "decode" the data back to images. The IFS code is actually a set of affine transformations. An affine transformation maps a point back into the same set of points it came from [6]. General form for an affine transformation:

 x   a b  x   e   +  W   =   y   c d  y   f

  ax + by + e  =    cx + dy + f

χ

2 m−1   = σ r2 + s  s σ r2 + 2d r − ∑ d i ri  ,……. (5) m i =0  

Where,

σ d2 =

2 1 m −1 2 d i − d ,………….…………..….... (6) ∑ m i=0

σ r2 =

1 m −1 2 2 ∑ r i − r ,………..……….………..… (7) m i =0

Objects are represented as a collection of pixels in an image. Thus, for the purpose of recognition the properties of groups of pixels are needed to be determined. The description is often just a set of numbers (i.e., the object’s descriptors). Moments describe the shape’s layout (i.e., the arrangement of its pixels), a bit like area. Compactness and irregularity order descriptions. Moments offer a global description of the shape. Like Fourier descriptors, they have build-in ability to discern and filter noise [9]. The calculation of moment invariants for any shape requires knowledge about both the shape boundary and its interior region. The moments used to construct the moment invariants are defined to be continuous but for practical implementation they are computed in the discrete form. Given a function f(x,y), the regular moments are defined as [8]:

  

If the translations, rotations, and scaling that make up W are known in advance, then the coefficients may be calculated by [7]:

m pq = ∫ x p y q f ( x, y ) dxdy ,……………………... (8)

a = r cos θ , b = − sin φ , c = r sin θ , d = s cos φ

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 M (0, n)   M (n,0) (ii) Rn =   M (n,0)  M (0, n) 

m pq is a two-dimensional moment of the function f(x,y), the order of the moment is (p+q), where p and q are both integer numbers. For implementation in digital the above equation becomes:

m pq = ∑∑ x p y q f ( x, y ) ,………….…………... (9) x

y

Rnd = Rnr , ………………………………..…. (19) Where,

,…….………………….…. (10)

x

The above implies that "if any two blocks (secret and cover) satisfy the contractive affine transform (equation 2), then their moments-based descriptor values should have similar d

values ( Rn

,..…….…. (11)

= Rnr ) whatever their isometry state. This does

not mean that any two blocks have similar R factors are necessarily similar to each other" [8].

y

For an image block ƒ(x,y) the central moment of order (p+q), around the block’s central point (xc,yc), is defined as [8]:

2.2 Hiding system Figure (1) presents a functional description of the proposed system. When the cover and secret images are loaded, then the hiding module applies affine transform to encode secret blocks, and then the produced transform coefficients are embedded using LSB insertion method. The output of hiding stage is a stego image which is sent from sender side to recipient side. Once the recipient receives the stego-cover image, then the process of extraction could be applied to get an approximate (called, reconstructed image) to the secret image from the stego image. The extraction module consists of many stages; the main stages are the LSB extraction and affine transform. The inputs of the hiding unit are both: cover image and secret image. The size of secret image can reach the size of cover image (or a little bit higher). The output of this unit is a stego-object, which is saved as a bitmap image (24-bit resolution) and it has exactly the same size of the cover image.

M ( p, q ) = ∑∑ ( x − xc ) p ( y − y c ) q f ( x, y ) ,.…(12) x

Rnd is the descriptor value of the domain block, and

Rnr is the range block descriptor value.

The central moments can be defined in their discrete representation as:

µ pq = ∑∑ ( x − x ) p ( y − y )q f ( x, y )

if M (0, n) > M (n,0)

,………........... (18b) Combining equation (2) with equations (13-16), and substitute the result in equation (18) or (18) we can easily prove that:

To translation invariance, in the image plane, the image centroids are used to define the central moments. The coordinates of the center of gravity of the image are calculated using the following equations:

M M x = 10 , y = 01 M 00 M 00

if M (0, n) ≤ M (n,0)

y

When this definition is applied to determine the nth order central moments of the zero mean range and domain image blocks, we get: m =1

M d (n,0) = ∑ ( xi − Lc ) n (d i − d ) ,….………... (13) i =0 m =1

M d (0, n) = ∑ ( yi − Lc ) n (d i − d ) ,…..……...... (14) i =0 m =1

M r (n,0) = ∑ ( xi − Lc ) n (ri − r ) , …….……..... (15) i =0 m =1

M r (0, n) = ∑ ( y i − Lc ) n (ri − r ) , …………..... (16) i =0

Where,

Lc = L

L −1 ,……………….…............................... (17) 2 is the block width (or height) of the image

is the number of block elements m ( xi , yi ) are the x and y coordinates of ith elements (pixel). From the pair of nth moments {i.e., M (n,0) & M (0, n) } the following moments blocks descriptors could defined:

M 2 (0, n) − M 2 (n,0) (i) Rn = , .…………..(18a) M 2 (0, n) + M 2 (n,0) Fig (1) System module

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At each affine matching instance the determined transform coefficients (i.e., scale and block average) are of float type, and they require large number of bits to represent each value of them, and this large number causes an increase in the total number of bits required to represent, values of the transform coefficients; and this in turn leads to significant decrease in hiding capacity. To handle this problem a uniform scalar quantization (is a lossy image compression technique. It has a simple structure, especially in the decoding phase) [16], have been applied to represent the value of transform coefficients with less number of bits, but with less precision, and consequently the level or error in representing the secret blocks will increase, but this error is still kept under the permissible secret level. Within the loop of secret blocks; after finding the best cover block that can be used to represent the secret block. Its transform parameters (i.e., quantization indexes of scale parameter and block average value, the position reference indexes, J x and Jy , of the block) could be used to as a set to repre-

The input to the extraction unit is the stego-cover image only; the output is the reconstructed secret image. One of the main conditions to assure successful reconstruction is feeding the extractor the same values of system coding parameters which have been used in hiding phase. The structure of the hiding unit mainly it consists of seven modules: (i) image loader (for secret and cover images), (ii) hiding capacity checker, (iii) color transform, (iv) downsampler, (v) affine transform encoder, (vi) LSB embedder, and (vii) stego cover image saving. One of the main stages in affine transform coding module is the partitioning. In this paper the fixed size partitioning scheme is adopted to partition the secret and cover color bands, this kind of partitioning requires less computation time than other partitioning schemes. Before applying this kind of partitioning the size of the block should be chosen, then the color bands (Y-band, and the downsampled bands U and V) of the secret image are partitioned into non overlapped blocks called "range blocks". Figure (2) illustrates the conversion to YUV bands.

sent the secret block. The main disadvantage of classical affine transform scheme is the greedy search in domain pool which is time consuming. In this paper some improvements have been made on the searching scheme to be selective instead of exhaustive. The improvements aimed to speed up the affine transform coding drastically without causing degradation in secret image quality. To make the searching process selective two momentsbased descriptor have been used to index (i.e., classify) the cover and secret blocks listed in domain and range pools, respectively. As mentioned before, the first introduced block index parameter is used to describe the isometric state of the block, while the second parameter is used to classify the blocks into categories. In the following, the steps taken to apply the stage of mapping the range blocks as a part of the enhanced affine transform coding scheme are listed: Firstly: Predefine some of the involved system coding parameters (i.e., the jump step between neighboring cover blocks the size of blocks).At first, the number of blocks ( N r ) in range pool are determined. Secondly: In this stage the secret and cover blocks are indexed using moment based descriptor. In this stage the moments ( M x , M y ) of each block are determined, and then

Original Secret image

Y

U

V

Fig (2) Original image, conversion to YUV bands Also, the red, green, blue bands of the cover image are partitioned to overlapped blocks called “domain blocks”. The classical scheme of the affine transform coding is based on testing all cover blocks to find the best matched block (i.e., approximate) for each secret block, and for each tested cover block its eight isometric states are taken into consideration in the testing stage. At each matching instance, the affine mapping coefficients are determined using equations (4 and 5). The reference coordinates of the cover block that led to less χ2; with its isometric state and the corresponding transform coefficients (i.e., scale and offset) are registered as the affine code set represents the secret block. In the proposed enhanced scheme of affine transform coding; instead of testing all cover blocks only the blocks have similar moment descriptors to that of the secret block are tested, and not all isometric states of the cover block are tested. In the proposed scheme the required isometric process is assessed using a predefined lookup table whose indices depends on the isometric indexes of the two matched blocks. The isometric mapping process is required to make the cover block in its proper state (i.e., to get the minimum possible matching error between each pair of cover and secret blocks).

ISBN: 978-960-474-250-9

the block is indexed using equation (3.15), or equation (3.16). Also its symmetry (or isometric state) is indexed using the following three Boolean criteria: (1) is

M x ≥ M y or not?

(2) is

M x ≥ 0 or not?

(3) is

M y ≥ 0 or not?

Table (1) shows the indexing table of the 8-isometry states (according to the above 3 criterion). Table (2) shows the introduced predictor output when have isometric state indexes of the range-domain pair of blocks

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Table (1) The isometric states according of Boolean criterion

F

2

T

F

T

3

T

F

F

4

F

T

T

5

F

T

F

6

F

F

T

7

F

F

F

By using the set of pointers and the temporary list (TR) of affine records; then for each range block, the system matches only the domain blocks whose block descriptor ( I d ) is equal to the descriptor value of the tested range block. If the domain block satisfy the condition I d = I r then it is mapped

Identity

0

6

4

2

5

1

3

7

Rot.(90) Rot.(180) Rot.(270) Ref. at Xaxis Ref. & Rot. (90) Ref. & Rot. (180) Ref. & Rot. (270)

6 4 2

0 2 4

2 0 6

4 6 0

1 3 7

5 7 3

7 5 1

3 1 5

5

1

3

7

0

6

4

2

1

5

7

3

6

0

2

4

3

7

5

1

4

2

0

6

7

3

1

5

2

4

6

0

Least-significant-bit (LSB) insertion is the last stage in hiding unit; it receives the outcome of affine mapping stage (i.e., the determined sets of transform coefficients. After the conversion of these coefficients into a sequence of bits, then these bits are embedded as last significant bits in the elements of the blue, green and red components of the cover image data. After embedding the secret bits, are saved at a stego-cover image file. Figure (3) illustrates the structure of extraction unit; stages of this unit are arranged in reverse order to the hiding unit.

using the isometric mapping process that assigned by the isometry predictor. Then the mapped domain block is matched with range block, and the coefficients S , O and χ2 are determined by equations (4, 5). Then, compare the result χ2 with the registered χ2min , if χ2 is smaller than χ2min then register its value as χ2min , and register the associated values of affine transform parameters (i.e., sym , x d , y d , s, o ) of the matched domain block as the best found affine transform set. In the case that the new registered minimum error χ2min is less than the permissible level ( T1 ) of error then the search process is stopped as best encountered affine match for the tested range block, and then start repeat this process with the next range block may exist in the rang pool. Otherwise, start testing the next set of domain blocks whose descriptor ( I d ) values are ( I r m 1 ) to get the best affine trans-

Load stegocover image

Saving reconstructed image

LSB decoding

Affine transform decoding

Color transformation

form match, if they also don’t met acceptable match criteria (i.e., χ2< T2 ), then the matching module starts the domain

Fig (3) Structure of extraction unit

blocks whose ( I d ) values are ( I r

3. RESULTS AND DISCUSSION

m 2 ),…. and so forth, till reaching the set of domain block (i.e., χ2< T2 ), then the matching module starts the domain blocks whose ( I d ) values are ( I r m 2 ),…. and so forth, till reaching the set of domain block whose descriptors ( I d ) is I r m Wr , in such

Upsampling

3.1 System Evaluation To evaluate the performance of the established hiding system several tests have been performed. Some of these test results are listed below, they explore the effectiveness of the following system coding parameters on the hiding performance parameters of the established system: 1. Moment descriptor type. 2. Secret image size.

case the registered minimum error χ2min is considered as the best found error value (whether is satisfy), otherwise the condition (χ2min< T2 ) or not. After getting the best match then the best registered set of affine transform coefficient ( sym , x d , y d , s q , o q ) for the tested range block. This

1. Moment descriptor type. Figure (4) shows samples of the stego cover images and reconstructed secret images which are produced by one of the above mentioned six schemes. Also, in this figure the values of determined performance parameters (i.e., MSE and PSNR) for reconstructed secret image besides encoding (hiding) time are listed.

matching process should be performed on all range blocks listed in range pool.

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Ref.& Rot.(270)

T

T

Ref.& Rot.(180)

T

T

Ref. & Rot.(90)

T

1

Ref. at Xaxis

0

Rot.(Rotatio n) Ref.(Reflect ion

Rot. (270)

My ≥0

Rot. (180)

Mx ≥ 0

Rot. (90)

Abs(M x ) ≥ Abs(M y )

Identity

State

Table (2) The introduced predictor output

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214x246 Original cover image

Stego image

256x256 Original secret image

Stego image Extracted secret image Hiding rate=100% PSNR=31.04 dB MSE=51.20 Time= 6.06 second

Stego image

214x246 Cover image

Extracted secret image Extracted secret image Hiding classical method Hiding with Moment descriptor Time= 1539.58 sec Time= 7.02 sec PSNR= 33.26 dB PSNR= 31.41 dB MSE= 46.99 MSE= 30.71 Fig (4) The effect of the descriptor type on the hiding performance parameters

Stego image Hiding rate =123% MSE=46.99

256x256 Secret image

Extracted secret image PSNR=31.41 dB Time= 7.02 second

3. Secret Image Size Figure (5) shows the effect of the secret image size on the hiding parameters (i.e., quality of the retrieved secret image and hiding time).

214x246 Cover image

214x246 Cover image

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214x246 Secret image

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280x250 Secret image

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Stego image Hiding rate =132% MSE=78.64

References [1] Jawad M. J., ”Hiding Audio Using Wavelet Transform”, M.Sc. thesis, college of science, Al-Nahrain University, Iraq, 2005. [2] Kessler G. C., “Hiding Data Within Data”, paper, Champlain College in Burlington, 2001. http://www.garykessler.net/library/steganography.html [3] Gulati K., “Information Hiding Using Fractal Encoding”, M.Sc. thesis, Indian Institute of Technology Bombay Mumbai, roll no. 01329011, 2003. [4] Morkel T., Eloff J. H. P., and Olivier M. S., “An Overview of Image Steganography”, Information and Computer Security Architecture (ICSA) Research Group, University of Pretoria, South Africa, 2005. [5] Xiao H., “Fractal Compression“, related topic report, Queen’s university, Kingston, Ontario, Canada, 2005. http://research.cs.queensu.ca/home/xiao/doc/Thesis.pdf [6] Jones D. M., “Mathematical of Iterated Function System (IFS) Fractal”, 1999. http://www.hiddendimension.com/IFS_Fractals_Main.html [7] Ali M., and Clarkson T. G., “Fractal Image Compression”, 1991. http://www.inf.unionstanz.de/cgip/fractal2//pdf/AlCl91.pdf [8] George L. E., “Fast Coding for Zero-Mean Image Block Using Moment Indexing Method“, Journal of Science, vol. 6, no. 1, pp. 8-14, 2006. [9] Nixon M. S., and Aguado A. S., ”Feature Extraction & Image Processing”, book, ISBN 07506 5078 8, British Library Cataloguing in Publication Data, 2005. [10] Wu N., “A Study on Data Hiding for Gray-Level and Binary Images”, M.Sc. thesis, etd-0707104-144705, National Chiao Tung University, Taiwan, 2004. [11] Li S., Leung K., Cheng L. M. and Chan C., “A Novel Image-Hiding Scheme Based on Block Difference”, article, Science Direct, vol. 39, no.6, pp. 1168-1176, 2006. [12] Wang R. Z., and Tasi Y. D., “An Image-Hiding Method With High Hiding Capacity Based on Best-Block Matching and K-Means Clustering”, paper, vol. 40, issue 2, pages 398409, ISSN: 0031-3203, 2007. [13] Moustafa K. A. and Badawy W., “(Color/Gray) Image in Color Cover Hiding Using Modification of Spatial Domain Hiding Method”, paper, IEEE vol. 1, ISBN 0-7695-3048-6, NRSC.2007.371344, 2007. [14] Racuciu C., Jula N. and Pop F. M., “About An adapted Image Compression Algorithm for Surveillance Flying Systems”, paper, International Journal of Mathematical Models and Methods in Applied Sciences, vol. 1, issue 2, 2007. [15] Yeh J. P., Lu C. W., Lin H. J., and Wu H. H., “Watermarking Technique Based on DWT Associated With Emdedding Rule” , International Journal of Circuits, Systems and Signal Processing, vol. 4, issue 2, 2010. [16] Chen L. S., Su W. K., and Lin J. C., “Secret Image Sharing based on Vector Quantization “, International Journal of Circuits, Systems and Signal Processing, vol. 3, issue 3, 2009. [17] Din R., Samsudin A., “Digital Steganalysis: Computational Intelligence Approach”, International Journal of Computers, vol. 3, issue 1, 2009.

Extracted secret image PSNR=29.17 dB Time= 6.94 second

Fig (5) The effect of the size of secret image on the retrieved secret image quality 3.2 Comparison with Results of Other Studies Table (3) lists the hiding results (i.e., PSNR and hiding rate) of some previous works (for the researchers [Wu04] ,[Li06], [Wan07], and [Mou08]) with the results of our proposed system, taking into consideration that some of previous works were tested on gray images which certainly have significant effect on the hiding results. Table (3) The results of the our proposed hiding system and the results previous studies

[Wu04] [10] [Li06] [11] [Wan07] [12] [Mou08] [13]

Type of cover and secret images Gray images Gray images Gray images Color images

Proposed research

Color images

Original cover and cover-stego images (dB)

Secret and extracted secret images (dB)

27.20%

30.61

---

50%

41.2

----

100%

44.05

31.61

25%

51.6

32.78

123%

52.05

31.41

Hiding rate

3.

CONCLUSIONS

Using the symmetry descriptor decreases the hiding process time about 20%, while, the use of second descriptor (i.e., block descriptor), the hiding time was decreased markedly (about 450%), with little decrease in the image quality (i.e., in terms of PSNR it is about 1.37 dB), and Achieving high hiding rate (i.e., greater than 100%) need to set the block size bigger than (4x4). Taking into consideration, that big block sizes raises the level of degradation of the secret image. The increase of window size parameter value causes an increase in the number of tested blocks in search area (i.e., cover image), and this leads to an increase in both hiding time and quality of secret image.

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