Keywords Data compression, image processing, NCD, Kolmogorov complexity, JPEG, ZIP

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1 Volume 3, Issue 7, July 203 ISSN: X International Journal of Avance Research in Computer Science an Software Engineering Research Paper Available online at: wwwijarcssecom Compression Techniques for Image Processing Tasks Avi Roman-Gonzalez TELECOM Paris Tech Paris, rance Abstract This article aims to present an overview of the ifferent applications of ata compression techniques in the image processing file Since some time ago, several research groups in the worl have been eveloping various methos base on ifferent ata compression techniques to classify, segment, filter an etect igital images fakery In this sense, it is necessary to analyze an clarify the relationship between ifferent methos an put them into a framework to better unerstan an better exploit the possibilities that compression provies us respect to image processing techniques; compression becomes a very easy techniques to apply without much technical requirement In this article we will also see the types of compression an specific image compressors Keywors Data compression, image processing, NCD, Kolmogorov complexity, JPEG, ZIP I INTRODUCTION The work presente in this paper is an extension of the work presente in [] Actually aroun the worl, we can observe more often an increasingly, that various research groups an research works, using ata compression for ifferent applications in the image processing fiel In fact, we can see that many authors use ata compression techniques for classification an / or segmentation images, filter or enoising image, artifacts etection in images, etecting altere images, etc The analysis of igital images has a great importance in many fiels for which there are many methos, processes an techniques as shown in [2], an if the compression techniques can help more easily to these ifferent purposes, it is a breakthrough In [3] an [4] the authors present methos of image classification base on ata compression techniques, in the first case using a vieo compressor such as MPEG4 to texture classification an in the secon case is use as general purpose compressor as ZIP compressor an images compressor as JPEG lossless compressor In general, in [5] the author presents a summary of ifferent application of compression techniques in the classification of ifferent ata types The authors of [6] present a new general metho for etecting forge images also base on ata compression techniques an rate-istortion analysis, in this case, the author use the JPEG lossy compressor In [7] the authors apply lossy compression to filter the noise in the images Also the ata compression is use as a technique for artifacts etection in satellite images as shown in [8], [9] an [0] where the authors use both lossy compression an lossless compression The use of compression techniques in ifferent areas escribe above is very interesting an useful; it becomes possible on the basis of information theory, complexity theory an the various applications aroun these notions The information theory was evelope by Claue E Shannon in 948 to fin funamental limits in compression an reliable storage of ata communication Consiering the probability approach, we can establish a first principle of the measurement information This principle establishes that the message that has more probability, it provie less information This can be expresse as follows: I( xi ) I( xk ) P( xi ) P( xk ) () Where: I ( x i P( x i ) : Amount of information provie by x i ) : Probability of x i Accoring to this principle, it is the probability of a message to be sening an not its content, which etermines their informational value or a message x, with an occurrence probability P(x ), the information content can be expresse by: Where: I(x i ) will have as unit, the bit x log 2 Px I i (2) Within information theory, we have the algorithmic approach that talk about the Kolmogorov complexity K(x) which is efine as the length of the shortest program capable to proucing x on a universal machine Intuitively, K(x) is the minimum amount of information necessary to generate x through an algorithm 203, IJARCSSE All Rights Reserve Page 379

2 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp Kx min q qq x (3) Qx is the set of coes that instantly generate x The Kolmogorov complexity K(x y) from x to y is efine as the length of the shortest program that computes x when y is given as an auxiliary input for the program The function K(x y) is the length of the shortest program that prouces the concatenation of x an y But K(x) is a non-calculable function Both, the probabilistic approach of Shannon an the algorithmic approach of Kolmogorov for information theory, have a relationship with ata compression The compression serves to transport the same information, but using the least amount of space Data compression is funamentally base on search ata series repetitions There are two general approaches for compression: lossless compression an lossy compression In lossless compression approach, we can mention ZIP compressor, JPEG-LS compressor an Delta compressor Compressor ZIP is a general purpose lossless compressor base on the combination of LZW coe an the Huffman coe The compressor JPEG-LS is a lossless compressor, the algorithm begins with a preiction process, each image pixel value is preicte base on the ajacent pixels, after that, it is necessary to apply an entropy encoer, an get the compresse image Delta compression is the process of computing a compact an invertible encoing of a target file T with respect to a source file S In lossy compression approach we can mention the JPEG -DCT Compressor, the first step in this compressor is to ivie the image into blocks of 8x8 pixels, to each block, the secon step is to apply a Discrete Cosine Transform (DCT), after that, to apply a quantifier an finally an entropy encoer for to get the image compresse The structure of this paper is as follows: In Section II we present the image classification an image segmentation methos base on compression techniques Section III presents a metho for etecting forge images base on ata compression (lossy compression) In Section IV is shown a metho where ata compression also serves for image enoising Section V presents ifferent methos for artifacts etection in satellite images inally in Section VI we present the conclusions an iscussion II IMAGE CLASSIICATION AND IMAGE SEGMENTATION BASED ON COMPRESSION Base on the Normalize Compression Distance (NCD) presente an efine in [] an [2] which is one applications of Kolmogorov complexity, in [4] the authors perform image classification The Normalize Information Distance (NID) is a similarity measure proportional to the length of the shortest program that represents x given y, as far as the shortest program that represents y given x The calculate istance is normalize, meaning that its value is between 0 an, 0 when x an y are totally equal an when the maximum ifference between them NID x, y max max K x y, Ky x K x, Ky K x, y min K x, Ky maxk x, Ky (4) Since the Kolmogorov complexity K(x) is a non-calculable function, in [] the authors approximate K(x) with C(x) where C(x) is the compression factor of x Base on this approach we obtain the Normalize Compression Distance NCD (Normalize Compression Distance) C NCD x, y x, y minc x, Cy maxc x, Cy (5) Where C(x,y) is an approximation of the Kolmogorov complexity K(x,y) an represents the file size by compressing the concatenation of x an y ig Image Classification 203, IJARCSSE All Rights Reserve Page 380

3 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp or image classification using the approach base on Normalize Compression Distance (NCD); the first step is calculate the istance matrix between the images base on NCD using the Equation 5, thus ij = NCD(I i,i j ) where I i is the i-th image of the image atabase Thus, we can calculate the istance matrix D between all images I i as: D i n i2 n2 j 2 j ij nj n 2n in nn The matrix D is a square matrix of size n x n, where n is the number of images to classify in the atabase inally we can apply a supervise or non-supervise classification metho like SVM, KNN or KMEANS In this case, we apply a non-supervise classification metho like hierarchical classification enrogram like is shown in igure The enrogram is a type of graphical representation of ata as a tree that organizes the ata into subcategories that are iviing in others to reach the level of etail esire, this type of representation allows appreciating clearly the relationship between ata classes To plot the enrogram we use the Eucliean Distance metho for evaluate the istance between the ata using the following instruction in MATLAB: Calculate the Eucliean Distance (Distance = pist(d)) Linkage the istances (Tree = linkage(distance)) Rea the labels (Labels = importata('labelstxt')) Plot the enrogram: enrogram(tree,'colorthreshol','efault','labels',labels); set(denrogram,'linewith',2) There are also applications of the classification metho base on compression techniques, in remote sensing such as those presente in [3] where the authors use the NCD to classify hyperspectral image compressing the spectral signature As for classification, we can use the same metho escribe above for image segmentation The iea is to take an image an ivie it into small pieces or patches, we can calculate the istance matrix D between these ifferent patches, an then we can classify the patches that will give us as results a segmentation of the original image This kin of application is frequently for remote sensing applications or example, if we take an image I of 024 x 024 pixels an we ivie the image I in patches p i of 64 x 64 pixels, we have 256 patches p i with i =,, 256 After applying the NCD to all patches, we obtain e istance matrix D compose by ij = NCD(p i,p j ) where p i is the i-th patch of the image D i n i2 n2 j 2 j ij nj n 2n in nn inally with this istance matrix D, we can apply a supervise or non-supervise classification metho like SVM, KNN or KMEANS ig 2 Image Segmentation 203, IJARCSSE All Rights Reserve Page 38

4 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp In igure 2 we can observe an example of the image segmentation base on compression techniques applie to an Earth observation image We can see clearly the goo segmentation between city environment an fiel environment III IMAGE KERY DETECTION In [6] the authors use the Rate-Distortion experimental curve (RD) using lossy compression, JPEG DCT lossy compressor The RD function inirectly measure the visual complexity of the images, for example, plotting the experimental RD curve where the horizontal axis represents the compression factor (size of the compresse image file / size of the original image file) an the vertical axis represents the istortion calculate using the Mean Square Error (MSE); we can make an analysis of the image We can say that the falsification of an image can alter the experimental RD curve of the image, for example we can see from igure 3 that shown in (a) an original image an (b) the same image but with an alteration which the person has been remove (a) Original Image [6] (b) Manipulate Image [6] ig 3: (a) Original photograph of a Car Show (b) is the same image (a) but the person was erase an replace by uplication of regions Analyzing the image of igure 3 (a) an (b) using the graph of the experimental RD curves, it can be seen that there is a variation on these curves ue to the manipulation of the image igure 4 shows the variation, with the blue curve for igure 3 (b) an the green curve for igure 3 (a) Thus, using the variation in the experimental curve RD of images, we can etect when an image was manipulate or not ig 4 Rate-Distortion Experimental curve, the horizontal axis represents the compression factor (size of the compresse image file / size of the original image file), the vertical axis represents the istortion calculate using the MSE (mean square error) Blue for igure 3 (a) an green for igure 3 (b), the RD experimental curve of the original image is ifferent from the experimental curve RD for image that contains manipulations [6] 203, IJARCSSE All Rights Reserve Page 382

5 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp Also it is possible to use the Kolmogorov Structure unction (KS) for image fakery etection In [4] the authors present an analysis about the Kolmogorv s structure function The relation between an iniviual ata an its moel is expresse by Kolmogorov s structure function The original Kolmogorov structure function for a ata x is efine by: min log S : S x, K( S) hx (6) S Where: S is a contemplate moel for x α is a non-negative integer value bouning the complexity of the contemplate S The Kolmogorov s structure function h x (α) tell us all stochastic properties of ata x [4] In the same way, it is introuce the Best-it function, given by: Where: x is regare as a typical member of S ( ) min ( x S): S x, K( S) x (7) S The MDL function is given by: ( ) min ( S): S x, K( S) x (8) S Where: ( S) log S K( S) K( x) O() (9) (S) is the total length of two parts of x coe with an S moel The conitional Kolmogorov structure function is given by: h ( i y) min log S : S x, K( S y) i (0) x S The Kolmogorov structure function is a non-computable since the Kolmogorov complexity is also a non-computable function; that is the reason why we use the compression factor as an approximation to complexity The KS is an approximation of the Rate-unction Distortion using Kolmogorov complexity theory In that sense, we will use this function to see the changes in the experimental curve of the KS when the image is manipulate, we will use the same test images were use for analysis with the RD curve In igure 5 we can observe the KS curves for images in igure 3, the blue curve for the image (a) an the green curve for image (b) x ig 5 Experimental KS curve, the horizontal axis represents the Kolmogorov complexity approximation as the size of the image compresse file in bytes, the vertical axis represents the amount of bits that is neee to represent a moel of original image Blue for igure 3 (a) an green for igure 3 (b), the KS experimental curve of the original image is ifferent from the experimental curve KS for image that contains manipulations [6] It can be seen that as RD curves, in KS curves, variation may be observe when there is a manipulation of images, we use this variation to etermine whether an image has been altere or not 203, IJARCSSE All Rights Reserve Page 383 x 0 6

6 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp IV IMAGE DENOISING A metho for filtering an enoising is presente in [7] where the authors use lossy compression techniques for computing experimental RD curve of an image while calculating the Minimum Description Length function [7] an thus obtain the minimum point an ientify the image whose noise was eliminate by lossy compression Similarly, we can use a new calculation of experimental RD curve as a measure of istortion using the Normalize Compression Distance NCD between the error E (prouce by the ifference between the original image X an the compresse-ecompresse image Y) an the compresse-ecompresse image Y The Rate-NCD(E,Y) curve between the error E an the compresse-ecompresse image Y shoul have a particular behavior as shown in igure 6, for a moment, when there is not much compression, the compresse-ecompresse image Y is almost equal to the original image X an hence the error E is little information which makes the istance between E an Y large, this istance ecreases as the compression increases, because the information is going to error an this will seem a bit to the image, but there comes a point (calle here ARG point) which shoul be more information on the error E that on the compresse-ecompresse image Y thus the istance between them will increase again ARG point ig 6 Rate-NCD curve, hypothetical comparison between the error E an the compresse-ecompresse image Y In this way we can ientify the minimum point (ARG point) which woul correspon to the image without noise as shown in igure 7 (using the same image use in [7]) This process can also serve to inicate how to fin the minimum amount of information neee to interpret the information, how much etail we can loss without to arrive until a not interpretable ata In igure 7, we can see clearly that the mouse image for the minimum point has the enough etail to recognize a mouse ARG point ig 7 Image Denoising V ARTIACT DETECTION In the research works [8], [9] y [0], the authors present ifferent methos for artifacts etection in satellite images, ifferent methos base on compression techniques, lossless compression an lossy compression The metho that has better results is the metho that uses a lossy compression to calculate the experimental RD curve presente in [0] The iea is to examine how an artifact can have a high egree of regularity or irregularity for compression [0] an analyze the error space prouce by the lossy compression The RD analysis was one as the blocks iagram shown in igure 8 203, IJARCSSE All Rights Reserve Page 384

7 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp ig 8 Block Diagram for Rate-Distortion Analysis [0] irst the author take the image uner test I, they ive the image I in ifferent n patches X i of 64 x 64 pixels, with i =, 2,, n, thus I = {X, X 2, X n } or each i-th patch X i, they compress the patch with ifferent quality q using a lossy compression, using ifferent quality they obtain ifferent compression factor After that, they ecompress the image an obtain a ecompresse image Y iq The next step is to calculate the error for each compression factor between the original patch X i an the compresse-ecompresse patch Y iq, for calculate the error; they use the Mean Square Error (MSE) Base on the errors for each compression factor q an for each patch X i, they compose a features vector V i = [ i, i2, iq iq ] where iq = MSE(X i, Y iq ) Thus, they have a matrix: V i n i2 n2 q 2q iq nq Q 2Q iq nq inally, with this matrix V, they apply a supervise or non-supervise classification metho like SVM, KNN or KMEANS In this case, the authors use KMEANS classification metho, which is an unsupervise algorithm; KMEANS classifies ata accoring to K (positive an integer value) centrois or groups as assigne, the algorithm calculates the minimum istance of these centrois to all other ata an the group as the minimum istance or our purpose, we take a value of K = 2 that represents one group for images with artifacts an other group for images without artifacts or authors, the quality factor vary between 0 an 00, so Q = 0, an for an image of 52 x 52 pixels, we obtain 64 patches of 64 x 64 pixels, thus n woul be n = 64 An example of the application of this metho base on the RD analysis is the Dropout etection shown in igure 9, In this case it is a SPOT image containing actual artifacts, an the etection is one correctly (a) CNES (b) ig 9 Dropout (SPOT) (a) Some electronic losses uring the image formation process create these ranomly saturate pixels The ropouts often follow a line pattern (corresponing to the structure of the SPOT sensor) (b) Artifact is etecte 203, IJARCSSE All Rights Reserve Page 385

8 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp Another metho for artifacts etection is base on the similarity space using the Normalize Compression Distance (NCD), the authors propose to analysis the possible similarity between images with artifacts ue to possible similarity pattern between artifacts The first step is to take the satellite image I an ivie it into n patches X i of 64x64 pixels like is shown in igure 0, with i =, 2,, n, thus I = {X, X 2, X n } With these patches X i, after that, it is necessary to calculate the istance matrix between them using the NCD, thus we have ij = NCD(X i,x j ) Thus, it is possible to calculate the istance matrix D between all patches X i as: D i n i2 n2 j 2 j ij nj n 2n in nn The matrix D is a square matrix of size n x n, where n is the number of patches; for an image of 52 x 52 pixels, we obtain 64 patches of 64 x 64 pixels, thus n woul be n = 64 ig 0 Separate image in patches of 64x64 pixels for calculate the istance matrix between the patches inally, with this istance matrix D, the authors apply a non-supervise classification metho like hierarchical classification enrogram like is shown in igure 2 The enrogram is a type of graphical representation of ata as a tree that organizes the ata into subcategories that are iviing in others to reach the level of etail esire, this type of representation allows appreciating clearly the relationship between ata classes The blocks iagram an process for application of this metho base on NCD to artifacts etection, is represente in igure ig Experiment Process: we take the satellite image an ivie it into patches of 64x64 pixels, with these patches we calculate the istance matrix between them using NCD an finally we applie a hierarchical classification metho to cluster an ientify the patches with artifacts We use the NCD to evaluate how patches with artifacts can have a similar structure an see if it is possible to make a cluster with all patches with artifacts 203, IJARCSSE All Rights Reserve Page 386

9 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp Patches without Artifacts Patches with Artifacts ig 2 Hierarchical Classification of the Patches: we can see two cluster, re cluster for patches with artifacts, an cyan cluster for patches without artifacts In this enrogram representation, we can observe clearly how the patches with artifacts an the patches without artifacts can form two ifferent clusters in certain hierarchical level VI CONCLUSIONS AND DISCUSSION As has been seen, there are many stuies which use ata compression techniques for image processing purposes In this paper we have trie to present the ifferent evelopments mae by numerous research groups aroun the worl about the applications of ata compression, specifically in image processing Each group uses ifferent techniques, ifferent types of compression methos an ifferent approaches for ifferent applications but all of them relate to two important points: the compression an its application to image analysis in orer to make this task easier, unerstanable an with goo results The use of compression techniques in image processing, makes this task easier an more accessible, since everyboy know to use a compressor, everyboy use a compressors in your aily lives to reuce the size of the files an to transmit or transport them more efficiently No specific knowlege is neee to use a compressor Through this article, we provie the backgroun an funaments to better unerstan why we can use ata compression on igital image analysis an thus continue to evelop more applications an improving existing ones It was clearly observe that the application of ata compression for image processing is entirely feasible It is possible because ata compression is fully relate to the information theory in the two approaches In the image processing an image analyzing, the important thing is the image information content, base on this information we can reach a correct analysis The results obtaine in the ifferent applications are very encouraging, so it is necessary to continue in this line of research an evelop more applications REERENCES [] A Roman-Gonzalez, K Asale-Alvarez, Image Processing by Compression, Worl Congress on Engineering an Computer Science WCECS 202; San rancisco USA; October 202; pp [2] A Roman-Gonzalez, Digital Images Analysis, Revista ECIPeru, vol 9, N, 202, pp 6-68 [3] BJL Campana y EJ Keogh, A Compression Base Distance Measure for Texture, University of California, Riversie, EEUU , IJARCSSE All Rights Reserve Page 387

10 Gonzalez et al, International Journal of Avance Research in Computer Science an Software Engineering 3(7), July - 203, pp [4] M R Quispe-Ayala, K Asale-Alvarez, A Roman-Gonzalez, Image Classification Using Data Compression Techniques ; 200 IEEE 26th Convention of Electrical an Electronics Engineers in Israel IEEEI 200; Eilat Israel; November 200, pp [5] A Roman-Gonzalez, Clasificación e Datos Basao en Compresión, Revista ECIPeru, vol 9, N, 202, pp [6] A Roman-Gonzalez, CJ Reynaga-Carenas, Implementacion e un Métoo General para la Detección e Imágenes Alteraas Utilizano Técnicas e Compresion, Engineering Thesis, Universia Anina el Cusco, 202 [7] S Rooij, P Vitanyi, Approximating Rate-Distortion Graphs of iniviual Data: Experiments in Lossy Compression an Denoising, IEEE Transaction on Computers, vol6, N 3, March 202, pp [8] A Roman-Gonzalez, M Datcu, Satellite Image Artifacts Detection Base on Complexity istortion Theory, IEEE International Geosciences an Remote Sensing Symposium IGARSS 20, Vancouver Canaa, July 20, pp [9] A Roman-Gonzalez, M Datcu, Data Cleaning: Approaches for Earth Observation Image Information Mining, ESA-JRC-EUSC Image Information Mining: Geospatial Intelligence from Earth Observation Conference, Ispra Italy, March 30 April, 200, pp 7-20 [0] A Roman-Gonzalez, M Datcu, Parameter ree Image Artifacts Detection: A Compression Base Approach, 200 SPIE Remote Sensing, vol 7830, , Toulouse rance, September 200 [] M Li an P Vitányi, The Similarity Metric, IEEE Transaction on Information Theory, vol 50, N 2, 2004, pp [2] R Cilibrasi, P M B Vitanyi; Clustering by Compression, IEEE Transaction on Information Theory, vol 5, N 4, April 2005, pp [3] A Roman-Gonzalez, M A Veganzones, M Graña, M Datcu, A Novel Data Compression for Remote Sensing ata Mining, ESA-JRC-EUSC Image Information Mining: Geospatial Intelligence from Earth Observation Conference, Ispra Italy, March 30 April, 200, pp 0-04 [4] N K Vereshchagin, P M B Vitanyi; (2004, iciembre); Kolmogorov s Structure unctions an Moel Selection ; IEEE Transaction on Information Theory, Vol 50, N 2, pp [5] Tussell, Complejia Estocástica, San Sebastián 996 [6] D McKay, Information Theory, Inference, an Learning Algorithms, Cambrige University Press, , IJARCSSE All Rights Reserve Page 388

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