An Entropy Maximization based technique for Progressive Transmission of MRI Images

Transcription

1 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April A Etropy Maximizatio based techique for Progressive Trasmissio of MRI Images Aruava De, Dr. Aup Kumar Bhattacharee, Dr. Chada Kumar Chada, Dr. Basibada Mai Natioal Istitute of Techology, Durgapur, Idia Summary We have devised a way of segmetatio ad progressive trasmissio of MRI images. Etropy maximizatio usig Particle Swarm Algorithm (PSO) is used to get the Regio of Iterest (ROI). The ROI is de-oised usig Multi-Wavelet Aalysis. Soft Thresholdig together with Statioary Wavelet is used for de-oisig purpose. Varyig percetages of Discrete Cosie Trasform Coefficiets are used for the purpose of progressive trasmissio. K-Meas clusterig is used for aalysis of the MRI. Keywords Regio of Iterest,Discrete Cosie Trasform, Particle Swarm Optimizatio,Computed Tomography, Magetic Resoace Imagig, Withi-class variace, Etropy, Itesity cotrast, Progressive Trasmissio, Multi-resolutio Wavelet Aalysis,Statioary Wavelet Trasform,Soft Thresholdig 1. Itroductio Thresholdig is a oe of the very importat techique for image segmetatio. Bi-modal image has a sigle obect ad backgroud as opposed to multimodal images where there are multiple obects ad backgroud. A pictorial depictio of the bi-modal ad multi-modal image histogram is give i Figure 1 ad Figure 2.The bi-modal image histogram has two peaks ad a valley i betwee whereas multi-modal image has a umber of peaks ad valleys. Valley detectio ad criteria optimizatio [2,3] are oe of the may thresholdig approaches that are already defied. Miimum error thresholdig method (MiError) assumes the ormal distributio of obect ad backgroud [4,5]. Referece [6] estimated the parameters of ormal distributio from a trucated ormal distributio correspodig to obect ad backgroud. Referece [7] was the first to propose a thresholdig method based o maximum etropy priciple whereas [8] employed cross etropy for threshold selectio. Referece [9] applied fuzzy c- partitio to gray level images ad maximized fuzzy etropy to select the threshold. Referece [10] itroduced a eergy criterio formulated by itesitybased class ucertaity ad regio homogeeity. The threshold is selected by miimizig the eergy. Referece [11] applied the idea of maximizig the betwee class variace ito histogram-based thresholdig. The method shows satisfactory results i various applicatios. However, it teds to split the larger part whe the sizes of obect ad backgroud are uequal [12]. Referece [6] poited out that the separatio of obect ad backgroud caot geerally be determied uiquely by the image histogram. Prior kowledge about the relatio ad properties of obect ad backgroud ca be helpful to improve the performace of thresholdig methods. Referece [13] took advatage of the kowledge about the rage of backgroud proportio to the ROI to cofie the rage of threshold selectio ad achieved reliable results i segmetig magetic resoace (MR) ad computed tomography (CT) images of the huma brai. Referece [1] demostrated that threshold ca be obtaied by optimizig the weighted sum of the withi-class variace ad the itesity cotrast. Referece [16] foud that usig Etropy maximizatio usig PSO algorithm gives better results i compariso with other methods [14]. Referece [15] proposed a method of progressive trasmissio of MRI image. Referece [16] demostrated that etropy maximizatio usig Particle swarm algorithm ca be used to segmet a diseased area of a MRI from a o diseased part. We propose a ovel method of segmetatio, de-oisig usig Statioary Wavelet Trasform ad progressive trasmissio of segmeted diseased MRI images. The paper proposes a scheme for detectio of diseased lesios ad progressive trasmissio of MRI images. Here i this paper we deal with multi-modal MRI images. Our goal is to separate the diseased part from the o diseased part of a MRI image ad the we propose a way to perform progressive trasmissio of the segmeted image. I our techique we segregate the image based o levels of itesity, because diseased portio of the MRI image will have a differet itesity value with that of a o diseased multimodal MRI image. We perform etropy maximizatio usig PSO algorithm to get a threshold value which segregates the diseased cells from o diseased cells of the MRI image. This gets us the regio of iterest (ROI). We Mauscript received April 5, 2011 Mauscript revised April 20, 2011

2 160 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April 2011 perform de-oisig of the ROI usig multi-resolutio wavelet aalysis ad get the fial segmeted MRI image usig the variable mask. We perform DCT of the already segmeted MRI image ad the use varyig percetages of the DCT coefficiets to perform progressive trasmissio of the MRI image. k-meas clusterig is used for aalysis of the trasmitted image. This paper is orgaized as follows-ext sectio deals with the process of data acquisitio, sectio III deals with the proposed algorithm, sectio IV deals with results ad discussios, sectio V is the coclusio ad the last sectio is for the refereces. 2. MRI Data acquisitio ad roi We have take a set of slices of huma brai of patiets for testig purposes. We have tested our method i a umber of patiets. The patiets iclude those who are curretly udergoig chemotherapy ad also those who are cured of the brai lesios. We have acquired a set of 2-D slices of huma brai of patiets for testig purposes. The images are viewed usig cetricity dicom viewer provided by GE Medical. Differet MRI views are as follows FSE Axial T2, AxFlairFast, O-Ax T1 SE S. All the examiatios were doe o the same 1.5-T MRI imagig device. The thickess of each slice is 5.0 mm ad 1.5 mm gap betwee two slices. 3. Proposed algorithm 3.1 Previous Work Doe o Bi-ModalImage Figure 3. a) Origial Image b) Segmetatio usig Otsu method c)segmetatio usig Yu Qiao method Referece [11] presets a o-parametric ad usupervised method of automatic threshold selectio for segmetatio of image. A optimal threshold is selected by the discrimiat criteria which tries to maximize the separability of the resultat classes of the gray level i the image. The zeroth ad first-order cumulative momets of the gray level histogram is utilized makig the procedure very simple. Fig. 3 is a sythetic image which cotais a white rectagular box i a black backgroud. There is a smooth variatio of itesities from the obect ad backgroud. The Otsu method misses the valley ad sets the optimum threshold somewhere ear the middle of the backgroud. Whereas Yu Qiao method was able to properly segmet the sythetic image. Referece [1] proposed a criteria that combies the withiclass variace ad the itesity cotrast, J( λ, T) = (1 λ) σw( T) λ mo( T) mb( T) (1) where m o (Τ ) ad m b (T ) are mea itesities of the obect ad backgroud, respectively. σ w (T) is the square root of withi-class variace, Figure 1. The histogram of uiformly distributed backgroud ad obect σ ( T) = P( T) σ ( T) + P( T) σ ( T) (2) w b b o o Figure 2. image The histogram of a backgroud ad obect multimodal where P b (T ) ad Po(T ) are probabilities of the backgroud ad obect, σ b 2 (T) ad σ o 2 (T) are correspodig variaces of the backgroud ad obect, respectively (see Ref. [11] for their calculatio). I this criterio, the withi-class variace measures the itesity homogeeity withi the obect ad backgroud while itesity cotrast captures the itesity differece betwee them. The parameter λ is a weight that balaces their cotributios. Whe λ = 0, the criterio degeerates to the withi-class variace. If λ = 1, thresholdig is determied oly by the itesity cotrast, which may yield the threshold at the largest itesity of the image. Therefore, the weight should be i the rage of [0, 1]. The optimum threshold T* is selected by miimizig the criterio.

3 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April J ( λ, T ) = mi J ( λ, T ) T (3) Eq. (3) actually tries to decrease the withi-class variace ad icrease the itesity cotrast simultaeously. I this way, the itesity cotrast becomes a explicit factor for determiig the optimum threshold. 3.2 Proposed Criteria of Segmetatio for Multimodal Images Oe of the basic disadvatages of the above system is that it caot segregate a image based o the itesity levels i case of Multimodal images (MRI images). MRI image has a multimodal histogram (Fig. 2) i.e it may have umber of valleys istead of a sigle valley i case of bimodal histogram. We use the Etropy maximizatio techique ad the correspodig optimizatio of the fuctio H (Shao Etropy) for the threshold gray level rage at which the diseased cells differ from that of o diseased cells. Now the threshold value of segregatio is tha modified to get a exact value at which the diseased ad odiseased cells are completely segregated. 1) Etropy maximizatio usig PSO Algorithm to get the ROI: First we compute the ormalized histogram h() for a gray image f(x,y). P = h( ) = f / N, = 0,1,2, (4) Where f is the observed frequecy of gray level (or f is the umber of pixel that havig gray level ) ad N is the total umber of pixels i the picture. For multimodal image we wat to divide the total image ito (k+1) umber of homogeeous zoes ad for that we cosider the threshold gray levels at t 1, t 2, t 3,...t k. Shao Etropy is defied as t1 t l 1 2l 2... kl k = 0 = t1+ 1 = t+ 1 (5) H = P P P P P P Where t1 1 / = 0 t2 2 / = t1 + 1 P = P P for 0 t 1 P = P P for t 1 < t P = P / P for t k < 255 k = tk + 1 We have obtaied the fuctio H for the threshold gray level t 1 to t k usig PSO (Particle Swarm optimizatio) algorithm. Now we apply this expert kowledge that the gray level of diseased zoe of a MRI image vary from rage say Tx to Ty. Usig this expert kowledge, we apply our cocept of variable low pass filter mask after optimizig the threshold rage usig PSO which is explaied i subsequet sectio. 2) Optimizatio usig PSO algorithm: We optimize the basis fuctios obtaied usig Etropy maximizatio techique usig the cocept of PSO algorithm. PSO algorithm as applied to our techique: To maximize fuctio f ( X ) with () l ( u) X X X () l ( u) Where X ad X deote the lower ad upper bouds o X. PSO works as follows: 1 Assume the size of the swarm (umber of particles) is N. 2 Geerate the iitial positio of X i the rage ( u) ad X radomly as X1, X2... X N. () l X 3 Velocity is assiged for each particle as V1, V2... V N. 4 Evaluate obective fuctio values correspodig to the particles. Iitially all the particle velocities are assumed to be zero ad set the iteratio umber as i=1. 5 I i th iteratio fid the followig two parameters. Calculate the historical best value of X () i called P best,. Also fid G best, the highest value of obective fuctio ecoutered i all the previous iteratios by ay of the N particles. 6 Update the velocity as follows V( i) = θv( i 1) + c11 r[ Pbest, X ( i 1) (6) + cr 2 2[ Gbest X ( i 1)]; = 1, 2... N. 7 Update the positio of the particle as X ( i) = X ( i 1) + V ( i); = 1,2... N (7) 8 Check the covergece of the curret solutio. If the covergece criteria is ot satisfied the repeat steps 5, 6,7 The PSO algorithm is used for optimizig the iitial value of threshold to be used for segmetig the MRI image usig variable mask.

4 162 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April Multi-resolutio Wavelet De-Noisig of ROI usig Statioary Wavelet ad Soft Thresholdig : I sigal aalysis we ca perform several fuctios to traslate the sigal ito differet forms so that it becomes suitable for differet applicatios. The Fourier Trasform coverts a sigal from time versus amplitude to frequecy versus amplitude, that is it trasforms a time domai sigal to frequecy domai sigal. The resultat trasform is useful for may applicatios but it is ot based i time. Also the Fourier trasform for a statioary ad o-statioary sigal is the same. Thus we have to keep resolutio across the etire sigal ad still be based i time. This led to the use of Wavelet trasform which has frequecy ad time domai iformatio. Discrete Wavelet Trasform (DWT) is ot a timeivariat Trasform. This meas that eve with periodic sigal extesio, the DWT of a traslated versio of a sigal Y is ot i geeral the traslated versio of the DWT of Y. The Statioary Wavelet Trasform (SWT) is a wavelet trasform algorithm desiged to overcome the lack of traslatio-ivariace of Discrete Wavelet Trasform (DWT). Traslatio ivariace is achieved by removig the dow-samplers ad up-samplers i the DWT ad up-samplig the filter coefficiets by a factor of 2(-1) i the th level of the algorithm. The mai applicatio of SWT is de-oisig. There is however a restrictio that SWT is defied oly for sigals of legth divisible by 2J, where J is the maximum decompositio level. Fig.4 gives the filter bak of Statioary Wavelet Trasform. We have used a geeral wavelet based approach [19] for de-oisig the image. We have used Statioary Wavelet Trasform (SWT) ad Iverse Statioary Wavelet Trasform for the de-oisig purpose. We have doe level 2 decompositio of the ROI of diseased MRI image. We have used Daubechies wavelets because they have good compressio property for wavelet coefficiets but ot for approximatio coefficiets. Daubechies wavelets are fully parameterized ad have straightforward procedure for calculatio of their aalysis filters. The threshold selected for Soft thresholdig for detail coefficiets is The output of de-oisig the ROI of the diseased MRI image is show i Fig.5(c). Usig a variable mask we get the fial segmeted MRI image as explaied i the ext sub-sectio. 3.4Cocept of variable mask: We start with a 3 3 mask. All the pixel positios havig a value more tha the threshold value obtaied usig Etropy maximizatio forms the ROI. The mask is moved over the de-oised ROI, if the eighborhood pixels display a similar value we icrease the size of the mask. The mask is grow i all the four directios depedig o the similarities of the pixel values. If the eighborhood pixels have differet value the we agai start afresh i the ew regio of the ROI. After executio of this procedure we get a segregated image cotaiig the diseased cells of the MRI image. The result of this step is show i Fig.5(d). 3.5 Progressive Trasmissio of MRI images usig DCT coefficiets For large amouts of data ad i our case 2-D MRI data poses problems i etwork trasmissios. Durig progressive viewig at the recipiet ode if the evolvig trasmissios idicate that the obect is desirable tha we cotiue trasmissio else drop the trasmissio. We take a set of 20 MRI images i the Axial T2 view which maily gives the pathology of the disease. Each slice is havig a resolutio of We deote this digital 19 obect as {( ys, N S)} s= 0, where y 0 < y 1 < y 2 < < y 20 provide orderig of the slices, from top to bottom of the head ad N s are matrices. A very simple scheme for progressive trasmissio at the trasmitter ed ca be takig each slice oe at a time ad get the segmeted MRI image usig Etropy maximizatio usig PSO algorithm ad variable mask as discussed i subsectio B-1,2,3,4 of sectio III. After gettig the segmeted image of each slice of MRI image we perform Discrete Cosie Trasform[20] of the segmeted MRI slice. The origial slice ad segmeted MRI image slice are displayed i Figure 5(a) ad Figure 5(d). After gettig the DCT of segmeted diseased MRI slice we perform iverse DCT of the segmeted MRI takig 10 % to 100% of the coefficiets may be i steps of 10. We use k- meas clusterig to get the clustered view of the each of the images obtaied. Progressive trasmissio of the MRI slice with 30%, 40% ad 50% of the coefficiets are displayed i Figure 6 a),b),c). The images obtaied are the trasmitted progressively for detectio of aomalies at the receiver s ed. 3.6Aalysis ad detectio of progressively redered diseased MRI images usig k-meas clusterig techique. Clusterig Aalysis is a fudametal but importat tool i statistical data aalysis. Clusterig techiques have bee widely applied i a variety of scietific areas as patter recogitio, iformatio retrieval, microbiology aalysis, ad so forth. k-meas clusterig [17],[18] has k umber of cluster ceters. K-meas clusterig aims to partitio N iputs (called data poits) x 1, x 2, x 3 x ito k clusters by assigig a iput x t

5 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April ito the th cluster if the idicator fuctio I(/x t ) = 1 holds with I(/x t )= { 1 if =argmi 1 r k x t m r 2 ;{ 0 otherwise (8) Here, m 1,m 2,..m k are called seed poits that ca be leared i a adaptive way as follows: Step 1: Pre-assig the umber k of clusters, ad k iitialize the seed poits {m } =. 1 Step 2: Give a iput x t, calculate I(/x t ) by (8). Step 3: Oly update the wiig seed poit m w, i.e., I(w/x t )=1, by ew old old m = m + η( x m ), (9) w w t w Where η is a small positive learig rate. The above step 2 ad step 3 are repeatedly implemeted for each iput util all seed poits coverge. We perform k-meas clusterig o the images that are obtaied by varyig the percetage of DCT coefficiets. The result of the clusterig helps us to aalyze the images. The clusterig results i predomiatly two clusters amely diseased cells ad the backgroud. The result of the clusterig is show i Fig.6(a),(b),(c). results clearly show that eve with 30% coefficiets the lesios are more or less visually clear as show i Figure 5(a). As the percetage of coefficiets icrease the images become progressively clearer. The method of progressive trasmissio of diseased MRI images proposed here is effective for detectio of diseases. Here we have proposed that k-meas algorithm ca be used to aalyze the progressively trasmitted images. 5. coclusio The proposed method is very useful for progressive trasmissio of diseased MRI images. The aalysis is doe usig k-meas algorithm but other methods of aalysis ca be devised. The proposed scheme is for 2D MRI slices. The proposed method ca be suitably modified for 3D progressive image trasmissio of ) diseased MRI images by retaiig iteral data or features. 4. Results ad Discussios I the case Figure. 5(a), we take te particles for each of three dimesioal spaces take, where each dimesio of space represets a threshold value. Usig PSO we get three threshold values 20,100, 157. Usig expert kowledge we observe that diseased cells of MRI image lie above the threshold value of 157 usig θ =0.9 to 0.4, c 1 =1 ad c 2 =2. Usig the threshold value we get the regio of iterest which cotais all diseased cells alog with small umber of o diseased cells, the results of the process is show i Figure 5(b). We de-oise the ROI usig Multi-resolutio Wavelet Aalysis. We use Statioary Wavelet Trasform ad the method of Soft thresholdig to get the de-oised ROI. The threshold used for Soft thresholdig is The results of de-oisig are show i Figure 5(c). The variable mask is applied i a regio growig maer o the ROI to get the fial segmeted MRI image as show i Figure 5(d). Discrete Cosie trasform of Figure 5(d) is carried out. The results of k-meas clusterig after performig Iverse Discrete Cosie Trasform by takig 30%, 40%, 50% of the DCT coefficiets for the purpose of progressive trasmissio are displayed i Figure 6. The Figure 4. SWT filter bak Figure 5. Diseased MRI Image b) ROI usig PSO Algorithm c) De-oised Image usig SWT ad Soft Thresholdig d) Segmeted Image usig variable mask.

6 164 IJCSNS Iteratioal Joural of Computer Sciece ad Network Security, VOL.11 No.4, April 2011 Figure 6. Progressive trasmissio of Figure.5(d). with a) 30 % coefficiets b) 40% coefficiets c) 50% coefficiets Refereces [1] Y. Qiao, Q. Hu, G. Qia, S. Luo, ad W. L. Nowiski, Thresholdig based o variace ad itesity cotrast, Patter Recogitio, vol. 40, pp , [2] J.M.S. Prewitt, ad M.L. Medelsoh, The aalysis of cell images, A. N. Y. Acad. Sci. vol. 128, o. 3, pp , [3] J.S. Weszka, ad A. Rosefeld, Histogram modificatio for threshold selectio, IEEE Trasactios o Systems, Ma ad Cyberetics, vol. 9, o. 1, pp , [4] J. Kittler, ad J. Illigworth, Miimum error thresholdig, Patter Recogitio, vol. 19, o. 1, pp , [5] S. Cho, R. Haralick ad S. Yi, Improvemet of Kittler ad Illigworth s miimum error thresholdig, Patter Recogitio, vol. 22,o.5,pp ,1989. [6] J.S. Lee ad M.C.K. Yag, Threshold selectio usig estimates from trucated ormal distributio, IEEE Tras. Syst. Ma Cyber.,vol. 19,o. 2,pp , [7] T. Pu, Etropic thresholdig: a ew approach, CVGIP: Graphical Models Image Process.,vol. 16,pp ,1981. [8] C.H. Li ad C.K. Lee, Miimum cross etropy thresholdig, Patter Recogitio, vol. 26,o. 4,pp ,1993. [9] H.D. Cheg, J.R. Che ad J.G. Li, Threshold selectio based o fuzzy c-partitio etropy approach, Patter Recogitio,vol. 31,o. 7, pp ,1998. [10] P.K. Saha ad J.K. Udupa, Optimum image thresholdig via class ucertaity ad regio homogeeity, IEEE Tras. Patter Aal. Mach. Itell.,vol. 23, o.7,pp ,2001. [11] N. Otsu, A thresholdig selectio method from graylevel histograms, IEEE Tras. Syst. Ma Cyber, vol.9,o. 1,pp.62 66,1979. [12] J. Kittler ad J. Illigworth, O threshold selectio usig clusterig criteria, IEEE Tras. Syst. Ma Cyber., vol. 15, o. 5, pp ,1985. [13] Q. Hu,Z. Hou ad W.L. Nowiski, Supervised ragecostraied thresholdig, IEEE Tras. Image Process,vol.15,o. 1,pp ,2006. [14] Y.Kabir, M.Doat, B.Scherrer, F.Forbes, C.Garbay, Multimodal MRI Segmetatatio of Ischemic Stroke lesios, Proceedigs of the 29 th Aual Iteratioal Coferece of the IEEE EMBS, Cite Iteratioale, Lyo Frace,August 23-26, [15] Zhu, H., Brow, R.A., Villaueva, R.J., Villaueva-Oller, J., Lauzo, M.L., Mitchell, J.R. ad Law, A.G., Progressive imagig: S-trasform order. ANZIAM J. v45 ie. C1002- C1016. [16] Aruava De, Raib Locha Das, Aup Kumar Bhattacharee, Deepak Sharma," Maskig based Segmetatio of diseased MRI images", Iteratioal Coferece o Iformatio Sciece ad Applicatios, ICISA 2010 proceedigs, IEEE Seoul chapter, Seoul,Korea,pp , /10 [17] MacQuee, J.B., "Some methods for classificatio ad aalysis of multivariate observatios", I: Proceedigs of 5 th Berkeley Symposium o Mathematical Statistics ad Probability, Uiversity of Califoria Press, Berkeley, CA,pp ,1967. [18] R.O. Duda, P. E. Hart, D.G. Stork,"Patter Classificatio",pp , Secod Editio, Joh Wiley ad Sos, [19] R.C. Gozalez, R.E. Woods, Digital Image Processig, pp.392, , Secod Editio, Pretice Hall Idia, [20] K.R. Rao ad P. Yip, Discrete Cosie Trasform: Algorithms, Advatages, Applicatios. New York:Academic, 1990