Analysis of Image Compression by Minimum Relative Entropy (MRE) and Restoration through Weighted Region Growing Techniques for Medical Images

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1 Egieerig Letters, 14:1, EL_14_1_16 (Advace olie publicatio: 12 February 2007) Aalysis of Image Compressio by Miimum Relative Etropy (MRE) ad Restoratio through Weighted Regio Growig s for Medical Images Dr. (Mrs.) R.Sukaesh, R.Harikumar, Member, IAENG, N.S.Balaji ad S.R.Balasubramaiam, Abstract I recet years, there is a spurt of publicatios o Iformatio Theory based Image Compressio s. Specific regioal characteristics of the images are associated with Iformatio clusters. I this paper a ovel approach of iformatio theory based Miimum Relative Etropy (MRE) ad Etropy methods for image compressio are discussed. A two stage compressio process is performed through homogeous MRE method, ad heterogeeous MRE. The compressed images are recostructed through Regio growig techiques. The performace of image compressio ad restoratio is aalyzed by the estimatio of parametric values such as Mea Square Error (MSE) ad Peak Sigal to Noise Ratio (PSNR). Higher the PSNR better the recostructio process. Six radiographic medical images of various sizes are aalyzed ad Maximum PSNR of 33 is achieved. Idex Terms Relative Etropy, Image Compressio, Regio Growig, Etropy. I. INTRODUCTION Now-a-days, iformatio theoretic approaches towards the image compressio are popular amog the research commuities. There are two fudametal cocepts beig used. They are Shao s Etropy ad Relative Etropy (also kow as Kullback-Leibler iformatio distace, directed divergece, cross etropy).the first oe aims to measure the iformatio Mauscript received 8 th Jue 2006 Dr. (Mrs.) R.Sukaesh, Professor & Divisio Head, Medical Electroics Divisio, Departmet of ECE, is with the Thiagarajar College of Egieerig, Madurai, Tamil Nadu, , Idia. (Phoe: ; fax: ; drsukaesh2003@yahoo.com). R.Harikumar, Professor of ECE, is with Baari Amma Istitute of Techology, Sathyamagalam & Research Scholar, Medical Electroics Divisio, Departmet of ECE, Thiagarajar College of Egieerig, Madurai, Idia. (Correspodig author Phoe: ; fax: ; harikumar_rajaguru@yahoo.com). N.S.Balaji, studet, Departmet of ECE, is with Thiagarajar College of Egieerig, Madurai, Tamil Nadu, , Idia (Phoe: balaji.sudarsa@gmail.com). S.R.Balasubramaiam, studet, Departmet of ECE, is with Thiagarajar College of Egieerig, Madurai, Tamil Nadu, , Idia (Phoe: cotet of a image histogram ad the latter eables us to describe the discrepacy betwee the image histograms of differet images or i the same image [1]. The histograms show the distributio of iformatio i the various regios of the image. These distributios form the Iformatio clusters. Aalysis of image through etropy clusters over a template is useful i segmetatio. I this paper the image segmetatio ad descriptio (compressio) is performed by the Miimum Relative Etropy (MRE) method of Kullback-Leibler cocept. I compressio the fudametal idea is to reduce the redudacy ad irrelevacy. Removig the duplicatio from the image is called as redudacy removal. Omittig the part of the sigal that will ot be oticed by the huma visual system (HVS) is called irrelevacy reductio. There are three types of redudacies viz., spatial redudacy, spectral redudacy ad temporal redudacy. I still image, compressio is achieved by removig spatial ad spectral redudacy [7]. A. Need for Compressio Image compressio is a method to represet a digital image with reduced amout of data. I Literature a wide rage of image compressio methods such as Trasformatio of data, the projective represetatio o a smaller set of data, ad Ecodig of the data usig ecoders are studied ad reviewed. Digital image compressio aims at reducig the codig, iter pixel ad psycho visual redudat iformatio. The probability of occurrece of evets (such as gray level values) ca be used for the codig redudacy. For reducig the iterpixel redudacy the 2D pixel array that is ormally used for huma viewig ad iterpretatio must be trasformed ito a more efficiet format. This trasformatio is called reversible if the origial image elemets ca be recostructed from the trasformed image. The psycho visual redudacies ca be reduced usig the fact that the huma eye does ot respod with equal sesitivity to all visual iformatio [7]. Therefore, without sigificatly impairig the quality of the image perceptio, certai iformatio ca be elimiated. Compressios of medical images are highly useful i telemedicie ad telediagosis of patiets whe there is trasmissio badwidth costrait. The overall orgaizatio of the paper is as follows. After the itroductio, we preset the fudametal issues of the image compressio i sectio II. Sectio III examies the methodology of Miimum Relative Etropy, Etropy Methods for compressio ad

2 recostructio by Regio Growig. The results of the algorithm employed are discussed i sectio IV. Fially sectio V cocludes the paper. II. MATERIALS AND METHOD The followig block diagram of Fig 1. shows the process ivolved i the compressio of a digital raw image. Raw images of two sizes 256X256 ad 512X512 are aalyzed. The probability of occurrece of each pixel is obtaied by plottig the histogram of the image. The the image is segmeted as a co-occurrece regio of 4X3 cell matrix, which is the size of the template. We have fixed the compressio ratio at 12. Two types of segmetatios are performed viz homogeous method ad heterogeeous oe. From the segmeted image, the seed values are foud per co-occurrece regio. Fig. 1a. Block diagram for Etropy ad MRE based image compressio. The recostructio process is show i the fig.1b.the regio growig method is adopted for recostructio of the image from its seed values. I this paper we discuss two types of regio growig methods: 1.Ordiary fillig, which is a simple expasio of seed value i the etire sub regio of the template, ad 2.Weighted fillig, which is doe by the fillig of the regio with seed values obtaied through weighted pixel values of adjacet regios. The Peak Sigal to Noise Ratio (PSNR) value of the recostructed images is computed ad compared. The image compressio ad recostructio algorithms are discussed i the followig sectio of the paper. Fig. 1b. Recostructio of the Origial Image through Regio Growig. III. Raw Image Seed Image Regio Growig REGION SEGMENTATION Heterogeeous MRE Fillig Weighted Fillig Seed Image HOMOGENEOUS MRE AND HETEROGENEOUS ENTROPY METHODS FOR IMAGE COMPRESSION Homogeous MRE Recostructed Image PSNR PSNR This sectio gives details about the MRE compressio, ad employig both homogeeous ad heterogeeous methods i detail followed by the techique of regio growig. The mai objective of this paper is to idetify a efficiet compressio algorithm through etropy based clusters i the image. The followig tasks are idetified to accomplish efficiet image compressios which are, 1. A bitmap image (raw image) of varyig sizes 256X256 ad 512X512 are take. 2. The probability distributio of pixels i the sample image is computed through the histogram equalizatio techique. 3. The compressio of image is obtaied by computig MRE for the sample image through homogeeous ad heterogeeous methods, ad 4. The pseudo program for the MRE compressio is also depicted. A. Algorithm for MRE Compressio The geeric represetatio of MRE optimizatio is explaied, let p m ad q be probability measures for sources M ad N, respectively. The relative etropy distace D (N M) (also kow as Kullback-Leibler distace) is defied as [3], [5] D( N M ) q D (N M) is a oegative cotiuous fuctio ad equals to zero iff p m ad q coicide. Thus D (N M) ca be aturally viewed as a distace betwee the measures p m ad q. However, D (..) is ot a metric because it geerally is either symmetric, or satisfies the triagle iequality. It is ot difficult to see that we ca have D (N M) equal to zero while the coditioal etropy rate H(N M) is large ad vice versa [2]. Thus, a iformatio distace based o relative etropy ca be used as a optimizer or cluster for image compressio. To accomplish the image compressio through MRE techiques the followig procedures has to be icorporated, 1. The Bit map image is segmeted by splittig the 256X256 image matrix ito a umber of 4X3 sub blocks, which is our template or co-occurrece matrix. 2. The the 4X3 co-occurrece matrix is deduced ito 4x1 matrix viz row wise optimizatio through MRE techiques. 3. Further the 4x1 co-occurrece matrix is reduced ito oe seed value through colum wise optimizatio usig MRE i the similar maer. The above metioed tasks are carried out i phased maer of two stages such as row wise optimizatio ad colum wise optimizatio which are explaied below. B. Homogeeous Method q ( x)log p I this method both stage 1 ad stage 2 employs Miimum Relative Etropy (MRE). The two stages i image compressio are explaied below, Stage 1- Row wise Optimizatio. ( x) ( x) The row wise optimizatio idetifies the maximum possible ifluece of a particular pixel amog the other two pixels i the template. The followig stepwise procedures are adopted at stage 1 level. m (1)

3 1. 4x3 co-occurrece matrix W (i,j), corer elemets are padded with the same elemets to avoid log (a i /a i ) =0 where a i is the probability of ith elemet. 2. Relative Etropy of P i,1 (i,j) i th elemet i the first row of W(i,j) matrix is foud out through four eighbourhoods. Cosiderig Pi,1 (i,j) as source ad P(i-1,j),P(i+1,j),P(i,j+1),ad P(i,j-1) as destiatio elemets through equatio(1) 4x1 matrix. Stage 2. The colum wise optimizatio is the same method which is used for homogeeous MRE is adopted. Pseudo Codig for the Homogeous MRE method is depicted below: P i,1 (i,j)= P(i-1,j)+P(i+1,j)+P(i,j+1)+P(i,j-1) (2) Where Relative Etropy P (i-1,j)=a i-1 l(a i-1 /a i ). 3. Likewise the Relative Etropy for other two elemets i the row are calculated P i,2 (i,j+1),ad P i,3 (i,j-1), 4. Fid the miimum of row wise relative etropy as mi (P i,1 (i,j), P i,2 (i,j+1), P i,3 (i,j-1)). 5. Now the row of three elemets is coverted ito sigle elemet ad replace the value of mi (P (i,j)) with origial probability values. This is repeated for all the 4 rows ad ow the matrix is reduced ito 4x1 matrix. Stage 2 - Colum wise Optimizatio. Colum wise optimizatio idetifies the relative ess amog the four pixels i the 4x1 matrix. This is accomplished by Usig adjacet eighbourhoods of the (i,1) elemet i 4x1 row optimized template matrix ad the same is show below. 1. We fid relative etropy of i th P(i)=P(i+1)+P(i-1), where P(i) as the source elemet ad P(i+1),ad P(i-1) as destiatio through equatio(1). Subsequetly other relative etropies P(i+1)=P(i)+P(i+2), ad P(i-1)=P(i)+P(i-2) are foud out. 2. Fid the mi {P(i),P(i+1), P(i-1)}for the i th member i that particular group. 3. This procedure is repeated util a sigle optimum value is arrived. This sigle value represets the seed value of 4x3 co-occurrece matrix. C. Heterogeeous Method I this method, stage 1 Row wise optimizatio uses the traditioal etropy method, which is defied as [6] E i 1 p i log p i The followig step wise procedure adopted i this method is explaied below, 1. Etropy of all pixels i the template 4x3 matrix is calculated through equatio (3). 2. The average Etropy of a particular i th row of three elemets as E i,avg =1/3 x(e i,1 +E i,2 + E i,3 ) 3. Fid miimum of mi (E i,avg -E i,j ) 2 where j=1,2, ad 3. Select the pixel which has miimum square differece betwee its etropy ad average etropy i that particular row. This would reduce the 4x3 matrix ito (3) Fig. 2. Pseudo code for Compressio D. Recostructio of the Origial Image from the Seed Image through Regio Growig Regio growig is a procedure that groups pixels or sub regios ito larger regios based o predefied criteria. The basic approach is to start with a set of seed poits ad from these grow regios by appedig to each seed those eighbourig pixels that have properties similar to the seed (such as specific rages of grey level).regio growig approach is the opposite of the split ad merge approach. A iitial set of small areas are iteratively merged accordig to similarity costraits. Fig 3 depicts the regio growig process of recostructio of the image. Start from the seed pixel obtaied from the segmeted image Regio is grow by fillig the eighborig pixels i two methods. I the ordiary fillig method1 the etire is sub block legth (4X3) is expaded with the seed pixel value. This is repeated over the other templates ad a ew image is recostructed ad its PSNR value is calculated. Image Name Homogeeous MRE (PSNR i db) Method 1 Method 2 Heterogeeous MRE (PSNR i db) Method 1 Method 2 Xray Xray Xray

4 PSNR(Db) Xray0 Xray1 Xray2 Homo-Stage1 Homo-Stage2 Hetero-Stage1 Hetero-Stage2 Fig. 4. Compariso of PSNR of the two stages of differet compressio techiques applied to image of size 256X256. Fig. 3. Process of Regio Growig. The weighted fillig method 2 is a two step process. I step 1core area of the sub regio is filled by the seed values, ad i step 2 the adjacet regios betwee the templates are filled with the weighted value of the seeds This method gives a PSNR value which is quite higher tha the previous oe obtaied i method 1. This method provides gradual variatio of cotrast amog the regios which is kow as image ehacemet. The simulatio of these algorithms is performed usig Image Processig toolbox of Matlab 6.1[4] ad the results are discussed i the followig sectio of the paper. IV. RESULTS AND DISCUSSION To idetify better algorithms for image compressio ad recostructio a comparative study is doe based o their descriptor metrics. Two objective measures such as, MSE ad PSNR are used for aalysig the descriptors. A. Fitess Evaluatio I image compressio, the ideal measure of fitess would be the performace i a actual trasform coder. PSNR is used as a fitess measure. PSNR is computed as [5] 1 MSE m m1 1 i0 j0 I( i, j) K( i, j) 2 (4) Table I ad Fig.4, shows the PSNR values for the images of size (256X256). It is observed that Homogeeous MRE techique PSNR values are placed at higher values for the images xray0ad1. While the PSNR of the image xray2 through Heterogeeous MRE method is settled at higher value tha its couterpart. I average 2.4% improvemet which accouts 0.57 db improvemets i PSNR value is achieved betwee method 1 ad method 2 recostructios of Homogeeous MRE Compressed images. I the case of heterogeeous MRE compressed images the achieved PSNR improvemet amog the method 1 ad method 2 recostructio processes is about 3.6% ad 0.88 db. The followig Table II ad Fig. 5 presets the compariso of the PSNR values for the two methods i the Homogeeous MRE ad Heterogeeous MRE compressed images of size 512X512. Homogeeous MRE compressed images are recostructed with higher PSNR values tha their cotemporaries. Durig the recostructio process both compressio methodology show same level of 2.5% average improvemet i the PSNR values amog the methods 1 ad 2. This idicates that Homogeous method outperforms Heterogeeous method for the images X-ray 0,2,3,4 ad 5 with the higher value of PSNR. Heterogeeous is settled at higher PSNR for the image X-ray1. Table. II Compariso of PSNR for image of Size 512X512 2 MAX I PSNR 10.log log MSE MAXI MSE Here, MAX I is the maximum pixel value of the image. Whe the pixels are represeted usig 8 bits per sample, this is 255. The obtaied results for various sizes of sample images are tabulated i tablei ad tableii. Table.I Compariso of PSNR for image of Size 256X (5)

5 Image Name Homogeeous MRE Heterogeous MRE (PSNR i db) (PSNR i db) Method Method Method Method Xray Xray g h i Fig. 6. a, d, g are the origial X-ray 0, 1, 2 images of size 256X256. b, e, h Method 1 recostructed images from homogeeous MRE compressio. c, f, i Method 1 recostructed images from heterogeeous MRE compressio. Xray a b c PSNR(Db) Homo-Stage1 Homo-Stage2 Hetero-Stage1 Hetero-Stage2 0 Xray3 Xray4 Xray5 d e f Fig.5. Compariso of PSNR of the two stages of differet compressio techiques applied to image of size 512X512. B. Iput Image ad Recostructed Images The figure 6 ad figure 7 depicts the six radiographic X-Ray images used for aalyzig the MRE based image compressio ad regio growig restoratio algorithms. g h i Fig. 7. a, d, g are the origial X-ray 3, 4, 5 images of size 512X512. b, e, h Method 2 recostructed images from homogeeous MRE compressio. c, f, i Method 2 recostructed images from heterogeeous MRE compressio a b c d e f V. CONCLUSION The statistical methods ad hypothesis testig are widely used for image compressio. We have utilized the Miimum Relative Etropy ad Etropy for Image Compressio ad Image Recostructio is performed by Regio Growig Methods. A stadard compressio ratio of 12 is obtaied i our method. The PSNR of the recostructed images shows that the utilized methodology is highly image specific i ature. Regio growig recostructio method is ofte plugged with low PSNR values. This is due to more umber of edges i the radio graphic images. I future a combiatio of algorithms such as edge preservatio oe above said MRE methods will be studied to improve the PSNR values. Further research will be i the

6 directio of geeric image recostructio through kowledge based techiques. VI ACKNOWLEDGMENT The authors thak the Maagemet ad Pricipal of Baari Amma Istitute of Techology, Sathyamagalam ad the Maagemet of Thiagarajar College of Egieerig, Madurai, Idia for providig computig facilities ad research ecouragemets. REFERENCES [1] Rafael Gozalez, Richard E. Woods, Digital Image Processig, Secod Editio, Pearso Educatio, [2] S.Biswas, Segmetatio based compressio for Gray level Images, Patter Recogitio, Vol.36,2003, pp [3] R.R.Coifma ad M.V.Wickerhauser, Etropy based algorithm for best basis selectio, IEEE Tras. Iformatio Theory,vol,38, 1992,pp [4] Image Processig Toolbox for use with Matlab. The Math works Ic., Natick MA, secod editio, [5] Jiawei Wag et al, Relative Etropy Based Methods for Image Thresholdig, vol-ii, Proc of IEEE Iteratioal Coferece o Image Processig, 2002,pp II-265-II268. [6] C-I Chag et al, A relative etropy based approach to image thresholdig, PatterRecogitio,vol, 27,o9, 1994, pp [7] M.Li.Z. Che ad H.Zhag, Statistical Correlatio aalysis i Image Retrieval, Patter Recogitio,vol,35,2002,pp Dr. (Mrs.) R.Sukaesh R.Harikumar Dr. (Mrs.).R.Sukaesh received her bachelor s degree i ECE from Govermet College of Techology Coimbatore i1982. She obtaied her M.E (Commuicatio Systems) degree from PSG College of Techology, Coimbatore i 1985 ad PhD i Bio Medical Egieerig from Madurai Kamaraj Uiversity, Madurai i 1999.Sice 1985 she is workig as a faculty i the Departmet of ECE at Thiagarajar College of Egieerig, Madurai ad presetly, she is Professor of ECE ad Heads the Medical Electroics Divisio i the same College. Her mai research area icludes Biomedical Istrumetatio, Neural Networks, Bio Sigal Processig ad Mobile Commuicatio. She is guidig twelve PhD theses i these areas. She has published several papers i Iteratioal ad Natioal Jourals ad also published aroud sixty papers i Iteratioal ad Natioal Cofereces coducted both i Idia ad abroad. She has delivered a umber of ivited lectures i various Uiversities. She has a Diploma i Higher Learig ad has co authored a book o Gadhia Thoughts. She is life member of Bio medical Society of Idia, Idia Associatio of Bio medical Scietist ad ISTE. R.Harikumar received his B.E (ECE) degree from REC Trichy i 1988.He obtaied his M.E (Applied Electroics) degree from College of Egieerig, Guidy, Aa uiversity Cheai i He has 15 years of teachig experiece at college level. He worked as faculty i the Departmet of ECE at PSNA College of Egieerig & Techology, Didigul. He was Assistat Professor i IT at PSG College of Techology, Coimbatore. He also worked as Assistat Professor i ECE at Amrita Istitute of Techology, Coimbatore. Curretly, he is Professor ECE, Baari Amma Istitute of Techology, Sathyamagalam ad he is pursuig his doctoral programme i Bio-Medical N.S.Balaji S.R.Balasubramaiam Egieerig uder guidace of Dr. (Mrs.) R.Sukaesh at Departmet of ECE, Thiagarajar College of Egieerig, Madurai. He has published twelve papers i Iteratioal ad Natioal Jourals ad also published aroud thirty papers i Iteratioal ad Natioal Cofereces coducted both i Idia ad abroad. His area of iterest is Bio sigal Processig, Soft computig, VLSI Desig ad Commuicatio Egieerig. He is life member of IETE ad ISTE. N.S.Balaji was bor i Madurai, Idia o 28 th Jue Curretly he is pursuig his fial year Bachelors degree i Electroics ad Commuicatio Egieerig at Thiagarajar College of Egieerig, Madurai, Idia. His field of iterest icludes Image Compressio, Image oise removal ad cotrast Improvemet, Multicamera Image Correspodece, ad Image Feature Extractio. He is a member of Iteratioal Society of Techical Educatio (ISTE) S.R.Balasubramaiam was bor i Madurai, Idia o 14 th Jue Curretly he is pursuig his fial year Bachelors degree i Electroics ad Commuicatio Egieerig at Thiagarajar College of Egieerig, Madurai, Idia. His field of iterest icludes Image Compressio,Image Segmetatio, Biometrics, Medical Imagig ad Image Feature Extractio. He is a member of Iteratioal Society of Techical Educatio (ISTE) ad Istitute of Egieers (IE). He has preseted a paper at the Iteratioal Coferece of Cogitio ad Recogitio (ICCR 05).