Jamuna S R Assistant professor Dept of CSE Sri Eshwar college of Engineering. `Coimbatore

Transcription

1 Hacking Intrinsic Fingerprints in Fractal Image Compression Using Genetic Algorithm Jamuna S R Assistant professor Dept of CSE Sri Eshwar college of Engineering. `Coimbatore jamuna.s.r@sece.ac.in C.V.Arulkumar, Assistant professor Dept of CSE Sri Eshwar college of Engineering. `Coimbatore arulkumaran.ckpc@gmail.com M. Praveen Kumar CEO Aarha Technologies connectopraveen@gmail.com Abstract Over the decade, the world has completely depended upon digital images for communicating visual information. Many compression techniques have been used and compared to minimal the size of the image that has been transferred over the Internet. In this paper, we use the Fractal Image Compression which minimal the size of the image by using the property of self-similar or self-affine transformation and also has the feature of resolution independent. On the other side many forensic technique have been developed to verify the authenticity of digital images. One amongst and the most successful technique is to make use of an image s compression history and its associated compression fingerprints. But, there is a chance for anti-forensic techniques which are capable of fooling forensic algorithm. In this paper, we compress the image by using Genetic Algorithm in Fractal Image Compression. Then we develop a set of antiforensic technique which is designed to remove significant indicators of compression from an image. For that, the first step is to develop a generalised framework for an anti-forensic technique for removing the compression fingerprints from an image transform coefficients. The framework which we developed operates by calculating the overall distribution of an image s transform coefficients before compression, after then adding antiforensic dither to the transform coefficients of a compressed image such that their distribution matches the estimated one. This framework is then used to develop anti-forensic techniques for erasing compression fingerprints left by Fractal Image Compression. Through a series of experiments, we demonstrate that the antiforensic technique which we developed is capable of removing forensically detectable traces of image compression without affecting an image s visual quality. Index Terms Anti-forensics, anti-forensic dither, framework,transform coefficients, Fractal Image compression using Genetic Algorithm 1. INTRODUCTION Due to the widespread availability of digital cameras and the rise of the Internet as a means of communication, digital images have become an important method of conveying visual information. The rapid growth in the multimedia applications and digital transmission, image compression techniques have become a very important aspect in the field of image processing. The most common compressed graphic image format widely used in the Internet is JPEG and GIF format. Other image compression technique include the use of fractals and wavelets. However, in recent the fractal image compression has been highly explored because they offer higher compression ratios than the JPEG or GIF methods. Though using effective compression methods, the authenticity of digital images is often in doubt as the digital images can be manipulated by photo editing software. To avoid forgeries of digital images from being passed off as unaltered originals, researchers have developed a number of digital image forensic techniques. These techniques are developed to identify an image s authenticity, an image s originating camera and trace its processing history without access to the original image. All these techniques make use of intrinsic fingerprints formed in an image by editing or image formation process. The compression fingerprints of an image is a particular significance of any forensic techniques due to the fact that most of the digital images are being compressed either for the purpose of image storage process or for the digital transmission over the Internet. There are a number of challenging fields in the research area on image processing; one amongst them is image compression. The technology of Compression and Decompression of a digital image is an important aspect in the storing and transferring of digital images over the Internet. The compression of an image is essential in order to minimize the number of bits used to represent an image by removing as much redundancies as

2 possible. The compression is either classified as lossy or lossless compression. And most of the methods which are in use can be categorised under the head of lossy compression. It means that only the approximation of the original image is obtained in the reconstructed image, which is the result of the lossy compression. There are issues related to image quality when lossy compression is used in medical image as the reconstructed image seems to lose diagnostically relevant information. But the lossy compression can be used for other natural images for a digital transformations. There exist many forensic techniques which are able to detect a number of image manipulations, these technique do not concentrate for the possibility that many anti-forensic operations may designed to hide the fingerprints of the image manipulation. An image forger who is familiar with signal processing able to develop anti-forensic operations to create undetectable image forgeries. Hence, many of the existing forensic techniques are in doubt that it may contain unknown vulnerabilities. It is necessary for image forensic researchers to develop and study anti-forensic operations in order to avoid the creation and spread of undetectable image forgeries. Also the forensic researchers should capable of evaluating the degree of confidence in finding the authenticity of the images, thus by establishing which forensic technique is capable of being deceived by an anti-forensic operation. Though anti-forensic operation is capable of fooling forensic technique, the antiforensic technique itself will leave some detectable fingerprints in an image on which it is operated. If a forensic researcher designed a technique to detect those fingerprints left behind by an anti-forensic operation, then the image forgeries can be detected more accurately though anti-forensic operation takes place. For the purpose of detecting the fingerprints left by an antiforensic operation, it is mandatory for a forensic researcher to develop an anti-forensic technique against a forensic technique. Once, the researcher is familiar with anti-forensic operation, then it is easy to develop a technique to detect the anti-forensic operation over the image. In this paper, we develop an anti-forensic technique by tracing out the compression fingerprints of an image using fractal image compression using genetic algorithm. For this we calculate, the self-affine transform coefficients of an image before compression. Based on that, we develop an anti-forensic dither for an image. Then we add this dither to the transform coefficients of a compressed image which has been compressed using the technique of FIC using GA. Hence, the result will be approximately equal between the original image and the compressed image, as the proposed technique hides the compression fingerprints of an image. 2. FRACTAL IMAGE COMPRESSION The Fractal Image Compression technique is an idea from the mathematical theory called Iterated Function Systems (IFS). The FIC is best suited for self-similar or self-affine images which have the interrelation between the local data n global data. The FIC is an example of asymmetrical method of image compression which takes more time or effort for compressing an image that can be decompressed very quickly. The FIC takes the advantage of similarities within an image, an advancement in the detailed interpolation of the image, high theoretical compression rates and the minimum decompression times. 2.1 Self-affine and Self-similar transformations In this section we present the basic theory involved in Fractal Image Compression. It is basically based on fractal theory of self-affine transformations and selfsimilar transformations. A self-affine transformation W : R n R n Is a transformation of the FormW(x) = T(x) + b, where T is a linear transformation on R n and b R n is a vector. A mapping W : D D, D R n is called a contraction On D if there is real number c, 0 < c < 1 such that d(w(x), W(y)) cd(x,y) For x, y D and for a metric d on R. The real number c is called contractivity of W. d(w(x), W(y)) = cd(x,y) then W is called similarity. A family of {w 1,.w m } of contractions is known as Iterated function scheme (IFS). If there is a subset F Dsuch that for IFS {w 1,.w m }then F = m i= 1wi(F) Then F is said to be invariant for the IFS. If F is invariant under a collection of similarities, F is known a self-similar set. Thus this is the method of calculating the self-similar or self-affine property of an image in FIC. 2.2 Fractal Image Encoding Process The basic concept of fractal image coding is based on iterated function system, attractor theorem and Collage theorem. Fractal Image coding makes good use of Image self-similarity property or self-affine property in

3 space by calculating and removing image geometric redundant. The Encoding process of Fractal Image Compression is quite complicated but Decoding process is very simple, takes less time and resolution independent which makes use of potentials in high compression ratio. Fractal Image coding attempts to find a set of contractive transformations that map (possibly overlapping) domain cells onto a set of range cells that tile the image. Figure 1 Domain to Range block transformations The basic algorithm for fractal encoding is as follows: i. The image is partitioned into non overlapping range cells which may be rectangular or any other shape such as triangles. In this paper rectangular range cells are used. {Ri} ii. The image is covered with a sequence of possibly overlapping domain cells. The domain cells occur in variety of sizes and they may be in large number. iii. For each range cell the domain cell and corresponding transformation that best covers the range cell is identified. The transformations are generally the affined transformations. For the best match the transformation parameters such as contrast and brightness are adjusted as shown in Figure-1. iv. The code for fractal encoded image is a list consisting of information for each range cell which includes the location of range cell, the domain that map onto that range cell and parameters that describe the transformation mapping the domain onto the range. One attractive feature of fractal image compression is that it is resolution independent in the sense that when decompressing, it is not necessary that the dimensions of the decompressed image be the same as that of original image. The Collage Theorem of FIC states that if the error difference between the target image and the transformation of that image is less than a certain value the transforms are an equivalent representation of the image. The two main and major advantage of converting and compressing image into fractal code or data is, i) The extremely very small when compared to the memory required to store the original bitmap data memory size required to store fractal code is ii) The image can be scaled up or down a size that is zooming easily without disturbing the image details as the image information has becomes mathematical on conversion of image data to fractal codes, thus it supports the resolution independent. The steps involved in image decoding process in FIC is as follows: i) In each range block the mean information is extracted from the fractal codes to construct the mean image. ii) The obtained mean image is partitioned using the same size as the range block to reconstruct the domain block. iii) The mean value alone is used to decompress the image block which are smooth and contractive affine transformation using the fractal codes is applied for rough blocks. 3. GENETIC ALGORITHM Genetic Algorithm (GA) is a deterministic algorithm simulating the process of natural evolution, by which the controlled parameters and constrained functions have been optimized by applying. An improved genetic algorithm proposed for obtaining matching domain blocks of fractal partition in image compression, which uses the partition iterated function system and fractal image compression.. GA is used to solve optimization problems. The major advantage in GA is it use multiple search points, instead of using one search point at a time. GA is attempt to find near-optimal solutions without going through a in depth search mechanism, thus there is large reduction in search space and time. The process to map the domain block and range block is very complex in compression technique. GA technique is used to avoid such complexity to find the optimal solution. The basic components and features of GA are: a) Initialization procedure b) Representation of problem to be solved. c) Fitness Function d) Genetic operators (selection, crossover, mutation) The first step in GA is initialization procedure for generating or initializing the first population. i.e. Population size which specifies the no of individuals in each generated population which is constant during all steps. According to the fitness value each of the members of the population is evaluated and assigned a

4 probability to be selected for reproduction. Here the crossover rate operator is used for assigning the probability for each individual members of the population. The genetic operators select some of the individuals based ont the probability distribution. The mutation operator is responsible for selecting two members of the population and changes the part of the chromosome. Parent A Parent B Child A Child B Figure 2. Binary Crossover Child A New Child A search mechanism. The number of possible domain blocks to be searched can be represented as (w 2b) * (w 2b) and the number of transformations for each domain block which has to be searched has been considered as eight. Hence, the space to be searched consists of M elements, where M is cardinality of the search space. Here, M = 8(w 2b) 2 Let P represents the space to be searched, where P = {1,2,, (w 2b)} * {1,2,, (w-2b)} *{ 1,2,,8} The elements of P are represented by Binary Strings. The set of 2 l binary strings are used each of length l and it depends on the value of w and b. Thus the MSE between given range block and the obtained range block is considered as fitness value. Let S be the population size and T be the maximum number of iterations for GA. And S * T is the total number of strings searched up to T iterations. Therefore, M/ST provides the search space reduction ratio for each rough type range block. Figure 3. Binary Mutation The algorithm for GA is as follows: i) GA takes pairs of strings and based on our necessity random numbers of strings are created and their decoded values are noted down by setting up maximum allowable generation. ii) The corresponding values of above created strings are calculated by the mapping rule. iii) The above value is used to find the fitness function value. iv) A mating pool is created to carry out the process of reproduction on the strings. v) The crossover and mutation operator is also applied on the string. vi) Once the termination criteria is found, the value of string with minimum fitness function value is taken as optimum value. 4. GENETIC ALGORITHM TO FIND FRACTAL CODES The main objective of fractal image coding is to find a perfect domain block and for a rough type range block a transformation is to be evaluated. Thus Fractal based image coding is considered as a search problem. GA is used to find the near optimal solution instead of a global 5. ANTI-FORENSIC FRAMEWORK The anti-forensic framework can be developed for an image by estimating the transform coefficients of an image before compression. Then the anti-forensic dither is added to the compressed image on behalf of the transform coefficients which is estimated before compression of an image. In FIC by using vector quantization technique the transform coefficient can be estimated. Depends on the transform coefficient estimated, a dither is reproduced for an image. Then the image is compressed in FIC. The anti-forensic dither is added to the compressed image, by evenly distribution of the transform coefficients by unaltering the image. These fingerprints, known as transform coefficients quantization artifacts, are used by the majority of compression artefact-based forensic techniques to single or double compression; determine an image s origin also to identify image forgeries. If the image was divided into segments during compression another compression fingerprints may arise. Because of the lossy an unquantized coefficient and its corresponding coefficient value. 6. FIC ANTI-FORENSICS For a gray-scale image, FIC compression begins by segmenting an image into a series of non-overlapping blocks called range blocks, then computing two-

5 dimensional VQT for each block, which results as domain block. The resulting transform coefficients are quantized by dividing each coefficient value by its corresponding entry in predetermined quantization matrix, then rounding the result to the nearest integer. The resulting pixel values are projected back into the set of P of allowable pixel values. Now the quantization fingerprint can be removed. Thus the FIC Anti-forensic operation can be performed and implemented. Figure 4. (a) Original Lena Image Figure 4. (b) Reconstructed image using GA Figure 4. (c) After Compression fingerprint Removal matching the original image. 7. CONCLUSION In this paper we proposed a set of anti-forensic technique which is able to remove the compression fingerprints from digital images. For this we developed a generalized anti-forensic framework for the removal of quantization fingerprints from the coefficients of an image transform before compression, then adding antiforensic dither to the compressed image s transform coefficients such that the anti-forensically modified distribution of the image s transform coefficient matches the estimated distribution before compression. We propose this anti-forensic technique to remove quantization coefficient of Fractal Image Compression Using Genetic Algorithm Technique. REFERENCES [1] M. F. Barnsley, Fractals Everywhere. New York: Academic, [2] A. E. Jacquin, Fractal image coding: A review, Proc. IEEE, vol. 81, pp , [3], Image coding based on a fractal theory of iterated contractive image transformations, IEEE Trans. Image Processing, vol. 1, pp , [4] B. Ramamurthi and A. Gersho, Classified vector quantization of images, IEEE Trans. Commun., vol. COMM- 34, pp , [5] Y. Fisher, E. W. Jacbos, and R. D. Boss, Fractal image compression using iterated transforms, in Image and Text Compression, J. A. Storer, Ed. Boston, MA: Kluwer, 1992, pp [6] D. E. Goldberg, Genetic Algorithm in Search, ptimization and Machine Learning. Reading, MA: Addison-Wesley, [7] L. Davis, Handbook of Genetic Algorithms. New York: Van Nostrand Reinhold, [8] Z. Michalewicz, Genetic Algorithms + Data Structure = Evolution Programs. New York: Springer-Verlag, [9] B. P. Buckles and F. E. Petry, Eds., Genetic Algorithms. Los Alamitos, CA: IEEE Comput. Soc. Press, [10] S. Forrest, Ed., Proc. 5th Int. Conf. Genetic Algorithms, San Mateo, CA, July [11] S. K. Pal, D. Bhandari, and M. K. Kundu, Genetic algorithms for optimal image enhancement, Pattern Recognit. Lett., vol. 15, pp , [12] S. K. Pal and P. P. Wang, Eds., Genetic Algorithms for Pattern Recognition. Boca Raton, FL: CRC, June [13] G. A. Edger, Measure, Topology, and Fractal Geometry. New York: Springer Verlag, [14] J. Feder, Fractals. New York: Plenum, IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 7, NO. 4, APRIL [15] D. Bhandari, C. A. Murthy, and S. K. Pal, Genetic algorithm with elitist model and its convergence, Int. J. Pattern Recognit. Artif. Intell., vol. 10, pp , [16] S. Bandyopadhyay, C. A. Murthy, and S. K. Pal, Pattern classification with genetic algorithms, Pattern Recognit. Lett., vol. 16, pp , [17] C. A. Murthy and N. Chowdhury, In search of optimal clusters using genetic algorithm, Pattern Recognit. Lett., vol. 17, pp , [18] S. Daly, The visual difference predictor: An algorithm for the assessment of image fidelity, in SPIE Conf. Human Vision, Visual Processing and Digital Display III, San Jose, CA, 1992, pp [19] C. A. Murthy and S. K. Pal, Histogram thresholding by minimizing gray level fuzzyness, Inform. Sci., vol. 60, pp , [20] X. Ran and N. Farvardin, A perceptually motivated three-component image model Part I: Description of the model, IEEE Trans. Image Processing, vol. 4, pp , 1995.

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