Avalable onlne www.jocpr.com Journal of Chemcal and harmaceutcal Research, 2013, 5(12):113-117 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCRC5 A new segmentaton algorthm for medcal volume mage based on K-means clusterng L Xnwu Electronc Busness department, Jangx Unversty of Fnance and Economcs, Nanchang, Jangx, Chna ABSTRACT K-means algorthm s wldly used n medcal mage segmentaton for ts powerful fuzzy nformaton process ablty but the algorthm has some shortages such as low effcency n calculaton whch lmted the usage of the algorthm. Some measures are advanced to overcome the shortages of orgnal K-means algorthm and a new medcal volume mage segmentaton algorthm s presented. Frstly, accordng to the physcal means of the medcal data, the volume data feld s preprocessed to speed up succeed clusterng processng; Secondly, the mproved K-means algorthm s deduced and analyzed through mprovng cluster seed selecton method and calculaton flow and redesgnng pxel processng and operatonal prncple of orgnal K-means algorthm. Fnally, the expermental results show that the algorthm has hgh accuracy when used to segment 3D medcal mages and can mprove calculaton speed greatly. Key words: Medcal mage segmentaton, Volume segmentaton, K-means algorthm, Clusterng processng INTRODUCTION The segmentaton of 3D medcal data feld has always been an extremely challengng subject due to magng prncple, fuzzy tssue and other factors. In the past more than 20 years, people had addressed a large number of segmentaton algorthms. However, the complexty of human body structure, rregularty of tssue organs as well as dfference among dfferent ndvduals maes the segmentaton of medcal data feld no common theory so far. Although the segmentaton of 3D medcal data feld s very dffcult, t s one of the ey technologes for data feld processng and system analyss and understandng, and an extremely mportant step of data feld vsualzaton. Only can accurate segmentaton of the data feld obtan reasonable models for subsequent renderngs. It can be sad that the realzaton of 3D vsualzaton of the medcal data feld s to carry on correct and reasonable segmentaton of the mage data at frst [1]. Haralc and Shapra regard mage segmentaton as a clusterng process [2]. The clusterng means mathematcally that a large number of d -dmensonal data samples ( n unts) are clustered nto classes ( << n ) so as to maxmze the smlarty of the samples n same class and mnmze the smlarty of the samples n dfferent class. The clusterng process s to mae contnuous classfcaton of the data objects contanng several attrbutes by the clusterng algorthm automatcally, and the data s cut nto several classes by the dentfcaton of the data characterstcs. Therefore, the algorthms can be explored by the clusterng rules and the clusterng bass of varous targets found, and then based on whch, the mage s dentfed and segmented[3]. K-means algorthm s a basc dvson method n the clusterng methods and has better scalablty, so t s wdely used Cheng [4]. In addton, whle ths algorthm that taes error square and crteron functon as the clusterng crteron functon nvolves the clusterng result nto local soluton easly and mae t dependent on the ntal value, a large amount of 3D medcal mage data causes bad algorthm tmelness. In vew of these K-means algorthm shortages, a newly mproved K-means algorthm of medcal mage volume segmentaton s provded on the bass of the thnng of seeng the optmal ntal value and mprovng algorthm s procedure. 113
Data feld pretreatment Each voxel s gray value (or color value) s gven accordng to the people s habts or the users requrements, and not owned by substances. Therefore, the dfference of adjacent data has a certan meanng whle the absolute value of each data s of no mportance n the data feld. Ths algorthm suggests that the functon values of orgnal 3D data feld s wthn the range of 0-255 n the normalzaton ntegraton, and processed data replaces orgnal data to gve the gray level value so as to provde a gray level feld for the feature extracton, decrease the post-treatment memory demand and mprove the post-treatment speed. Although t s not smple for such problems as the tme consumpton that the data feld turns 16-bt and 12-bt gray level mages nto 8-bt under the premse of eepng up the ey nformaton of the mages n the process of the normalzaton pretreatment, the process s over n data format converson of the pretreatment and any data feld wll be treated only once so as not to affect the effcency of the whole algorthm. Algorthm Desgn K-means algorthm prncple Steps for K-means clusterng algorthm can be lsted as follows [5]. (1) Select n objects as the ntal cluster seeds on prncple; (2) Repeat (3) and (4) untl no change n each cluster; (3)Reassgn each object to the most smlar cluster n terms of the value of the cluster seeds; (4)Update the cluster seeds,.e., recompute the mean value of the object n each cluster, and tae the mean value ponts of the objects as new cluster seeds. Improvement of cluster seed selecton When calculatng the K turn of clusterng seeds wth the mproved algorthm, those data n the cluster havng a great smlarty to the K-1 category seeds should be adopted to calculate ther mean ponts (geometrcal center) as the clusterng seed of the K turn and the specfc calculaton method s below. (1) For the cluster c( 1) obtaned through the K-1 turn of clusterng, the mnmum smlarty sm _ mn of the ( 1) data n the cluster to the clusterng seed s ( 1) of the cluster s calculated; (2) The data n the cluster ( 1) clusterng seed ( 1) c s calculated that has a smlarty of more than *(1 sm_ mn ) 1 ( 1) β to the s (among, β s a constant between (0-1), and the data set s recorded as cn ( 1) ; cn are calculated as the clusterng seed of the K turn. (3) The mean ponts of the data n ( 1) (a) (b) (c) Fg.1: Comparng pctures of orgnal and mproved K-means algorthm In Fg.1, (a) shows cluster of the K-1 turn and ts seeds, (b) shows cluster of the K turn and the new seeds (ntal algorthm), and cluster of the K turn and the new seeds (mproved algorthm). Indcaton of the symbols n Fg 1 can be lsted as follows: means data pont n the cluster, means seed of the cluster n the K-1 114
turn, means new seed the cluster n the K turn, means range are used to calculate the new seeds. other data ponts, means the ponts wthn ts As seen n Fg. 1, the new clusterng seeds are obvously movng toward the data ntensve zone. The mproved algorthm could acheve a good clusterng effect on the cluster sets contanng solated ponts. For the processng of bg sets, ths mproved algorthm, as same as -means algorthm, s relatvely flexble and hgh-effectve. Its tme complexty s O (nt), of whch, n s the number of all objects, s the number of the clusters, whle t s the teraton number of the algorthm, and generally, and t. n Improvement of algorthm flow The general K-means algorthm s a gradent ascent teraton algorthm, each tme of teraton could cause the correspondng ncrease of the target functon values, and the teraton mght be ended n the lmted steps. However, such an algorthm also has some dsadvantages, for example, the algorthm s easly trapped n the local maxmum soluton and such a soluton depends on the selecton of ntal partton. Therefore, the means algorthm s used as local searchng process to be nlad n the local search structure of the teraton n order to obtan better clusterng results through the relatonshp between balancng the renforcement of the local search and extendng the searchng range. In the mage clusterng problems, D neghborhood of a partton refers to the partton obtaned through randomly selectng D dfferent clusters n a certan partton and redstrbutng them nto other clusters. In other words, the neghborhood of the current partton means the partton obtaned through randomly selectng one cluster and redstrbutng t nto other cluster. The calculaton flow of the K-means-based teraton clusterng algorthm of local searchng clusters s dsplayed n the followng. Input: the number of the results clusters, contanng the data set of N clusters. Output: clusters, ensurng that the clusters n all clusters are smlar or correlated. Step 1 Randomly select an ntal partton = C, C,... C } and calculate the correspondng concept n { 1 2 vector c( C ), = 1,2,..., then ntalze the current maxmum target functon value fopt and determne the endng condtons of the algorthm, the parameter value ε ( ε f 0) recevng the condtons and the maxmum teratng tmes n that the target functon value s not mproved any more [6]. Step 2 Repeat. Step 3 erform the local search on target functon value fopt and ts correspondng partton. Step 4 If fopt f fopt mproved any more, and the teraton tmes t := 0. wth the means cluster clusterng algorthm to obtan a local maxmum, the current best partton s Step 5 Repeat Step 6 Randomly generate a cluster ( 1,2,... N) = ', fopt = fopt x = and repeat the followng processes[7]., the current partton s not (1) If x s beyond the tabu lst, t wll be redstrbuted nto other cluster to calculate the ncrease f of the target functon value and the tmes of teraton wthout mprovement s t : t = t + 1; whle f x s n the tabu lst, Step 6 wll be repeated. (2) If f f ε, s the partton of redstrbuton, the target functon value s nto the tabu lst, and the tabu length of other tabu objects s deducted 1. f opt = fopt + f, x s added (3) If fopt f fopt, fopt = fopt, = ', and the tmes of teraton s t := 0. 115
(4) If x s tested throughout all clusters and the tmes of teraton wthout mprovement s repeated. t p n, Step 6 wll be Step 7 Untl t = n means there s no mproved partton generated n the successve n tmes of teraton. Step 8 Randomly select several clusters from partton. and redstrbute them nto other clusters to obtan the new Step 9 Untl the endng condtons are met. xel processng and operatonal prncple of the algorthm In order to qucen the effcency and the ablty of the algorthm to process the large-scale data feld, the pxel operaton and processng have to comply wth the several followng prncples. (1)re-segment the data feld n the phase of the data feld segmentaton pretreatment,.e. use the methods of manual nteracton and model gudance. (2)Accordng to pror nowledge of the structure shape and the poston that medcal data feld dssected the tssue, gve the nteractve defnton to several seed ponts and tae these seed ponts as the ntal samples. (3)Accordng to the probablty dstrbuton of an establshed characterstc, drectly classfy the pxel ponts that the selected obvous characterstc belonged to a seed pont, namely the ponts that have the obvous characterstcs and defntely belong to a class wll be mared as a class drectly, and not be calculated. (4)Calculate the ponts that have no obvous characterstcs and are classfed strctly through mathematcal algorthm, namely the ponts that are possble to belong to dfferent classes only for the edge regon or the edge transtonal regon carry on the algorthm operaton and segmentaton. (5)As for these ponts to be calculated, use the dot nterlaced samplng to carry on the samplng calculaton n the space. Namely mae the samplng to calculate whether a pont belongs to A class from the surrounded seed pont A. When the calculaton of the n pont fnshes, next pont to be calculated wll be selected as n+2 but not n+1 accordng to the space order f the n pont belongs to A class; f the calculaton result s that the n+2 pont belongs to A class, the n+1 pont wll be fallen nto A class drectly; f the calculaton result s that the n+2 pont does not belong to A class, the attrbute that the n+1 pont drects towards A class wll be calculated repeatedly. Such ths reduces the blndness of the defned ntal sample ponts greatly so as to enhance the accuracy of the segmentaton, and also reduces the data quantty calculated by the algorthm greatly to enhance the algorthm effcency. Experment Confrmaton The algorthm performs the experment on C. C confguratons are 4 1.8G CU and 512M memory. In ths paper, the algorthm s smulated n the utlzaton of the data sets wth dfferent szes and varous dstrbutons. Due to the lmted space, the followng only ntroduces the segmentaton results of actual data felds measurement for a group of complex medcal organzaton MRI data feld. The date feld sze s128 128 128. The experment result shows the comparson wth general K-means algorthm[5]. (1) for segmentaton effect (see Fg. 2). Fg. 2 (a) s orgnal mage, Fg.2 (b) clustered and segmented by general K-means algorthm lacs many detals obvously, and Fg.2 (c) segmented by ths paper s algorthm has hgh segmentaton precson and good vsual effects; (2) ths paper s algorthm s also mproved sgnfcantly from the algorthm effcency (see Tab. 1). CONCLUSION General K-means clusterng algorthm s vulnerable to the local soluton n practcal applcaton, so ths paper fully utlzes pror nowledge of the segmentaton object to perform several pretreatments n the course of detaled computaton by the thnng of seeng the optmal ntal value n several samplngs and one clusterng as well as the mproved K-means clusterng algorthm procedure. As a result, large reducton of the processng unts and great mprovement of the algorthm ant-nterference mae the algorthm mprove not merely convergence speed but also segmentaton accuracy. Besdes, the practcal applcaton of K-means clusterng segmentaton algorthm s greatly mproved n 3D medcal data feld segmentaton. 116
(a) (b) (c) Fg.2: Orgnal mage and segmentaton effect mage wth dfferent algorthms Tab. 1 Segmentaton effcency and accuracy of dfferent algorthm Algorthm Ths paper s algorthm General K-means algorthm Tme consumpton (s) 17 96 Segmentaton accuracy 94.78% 77.58% Acnowledgement Ths wor s supported by the Natonal Natural Scence Foundaton of Chna under the grant No.6126034. REFERENCES [1] Bradley aul Sweet, Managasaran Shapor. Journal of Global Optmzaton. 2010, (1):23-32. [2] Haralc R.M, Shapro L. G. Computer Graphcs and Image rocessng. 2009,(4):100-132. [3] Jao Chunln, Gao Maotang, et al. Computer Engneerng and Applcaton. 2010, (20):93-96. [4] Yang Cheng, Fan Huang. Journal of Computer Vsualzaton. 2012, (11):259-272. [5] Tang Johnson, Brynjolsfson Rong et al. Journal of Computer Engneerng. 2013, (1):69-71. [6] Y Smth. IEEE Computers. 2012,(3):45-54. [7] Zhang Yangfu, Mao Jnln. Journal of Computer Applcaton, 2012,(8):31-43. 117