Hybrid Method of Biomedical Image Segmentation

Transcription

1 Hybrd Method of Bomedcal Image Segmentaton Mng Hng Hng Department of Electrcal Engneerng and Compter Scence, Case Western Reserve Unversty, Cleveland, OH, Emal: Abstract In ths paper we present a general frame work for axon segmentaton n retnal mage and cont the nmber of axons. The algorthm contans three phases. Frst phase s preprocessng. The goal of ths phase s to get a bnary mage wth cell obects n t. In ths secton, we se two dfferent thresholdng methods one s FCM clsterng and the other s Ots s Method and I also compare the reslts of both methods. The next phase s separate cell obects from the bnary mage we get after phase. Here we separate the obects based on ts sze and shape. To separate obects by shape, we se V/H scan lne shape detecton to check the smoothness of obects. The last phase s to cont the nmber of obect n a bnary mage. II. ALGORITHM PHASE : Preprocessng Step : Image Enhancement Fgre s the npt mage for the algorthm to be developed. From the mage, we can observe that ths mage s contamnated by some rpples and some bondares of cells are very clear bt some are very ambgos. Ths, the frst step s to perform hstogram eqalzaton and enhance the contrast. The antcpated reslt s to make the ntensty dstrbton s bmodal. I. INTRODUCTION Optcal fnds assessment s wdely sed n medcal commnty for many reasons, sch as the optcal sensor s more senstve than hman eyes especal gray scale. For hman vson, on an average, we only can tell the dfference between gray levels s more than 0 0 (on 0 55). Bt for hghly senstve sensors, t can tell p to bt (abot 4 mllon) gray levels. Ths a machne vson can see more detals. Another reason we se optcal fnds assessment s to redce processng tme. Lke we are tryng to do n ths paper (to cont the nmber of axons or cells), there may be several ten thosands of axons n optcal nerve mage. If we cont all of them by orselves, t may take several days to do t. In ths paper, or goal s to locate and cont closed bndles n an optcal nerve mage. To acheve ths, frst we need to separate the obects we want from the mage. Thresholdng s a fndamental approach to segmentaton and when the ntensty of obects and backgrond are dffer enogh t can acheve pretty well reslts. Unfortnately, that s not the case n or npt mage. Ths we need to se dfferent knds of mage segmentaton technqes to separate axons from the mage. Fgre. Step : Thresholdng In ths step, we wll se thresholdng technqes to separate backgrond and cell s bondary from the mage. Two thresholdng methods wll be ntrodced. Fzzy C Mean (FCM) Clsterng Method The man process of FCM [] s performed nder featre space. To get the featre space, we se the ntensty of dfferent color layer from npt mage (Fgre ) as the 3 D featre space. Snce the ntensty of the same pxels n dfferent color layer are dffer. Also, n ths paper we se a spervsed FCM. The dea s try to make the reslt more relable wth the help of defnng pxels characterstc of each class type (bondary and back grond) by a hman

2 expert. Fgre s tranng set n featre space, and crcle markers are the center of each class Featre Space Backgrond Bondary ˆ = / x v N c k= / x v Fnally, we wll get a set of smlarty map (probablty map) for each class []. Fgre 3 shows the reslt. k Ble ntensty P( Backgrond Z ) P( Bondary Z ) 00 Green ntensty Red ntesty Fgre. Tranng set n featre space 40 To begn the FCM algorthm, we set membershp to each class as and class center as v (class centers come from the tranng set). Where s the classes and the pxel nmber, x s a vector of the gray levels n the mages. Second, set a cost fncton J as J = Nc N = = x v The otpts of the FCM algorthm are probablty maps for eac h tsse. We then assgn each pxel to the most probable class; ths wold get a bnary mage of each class (Fgre 4.). Bondary Image Fgre 3. Probablty maps Backgrond Image Where N s the sm on the pxels and Nc s the sm on the classes. Frst we need to calclate v. The formla to compte the clster centers v s: N x = vˆ = N () = For the pxel s of class, =. Otherwse, = 0. Ths to calclate the center of each class, eqaton () can redce to st calclatng the mean of ponts of each class. The next step s to mnmze the cost fncton J. To mnmze J wth respect to we have Fgre 4. Localzed Ots s Thresholdng Method Ots s method chooses the threshold to mnmze the ntra class varance of the black and whte pxels. It treats normalzed hstogram as a dscrete probablty densty fncton, as n

3 n p (r q r q ) =, q = 0,,, L n Where n s the total nmber of pxels n the mage, n s th e nmber of pxels that have ntensty level r q, and L s the total nmber of possble ntensty levels n the mage Ots s method chooses the threshold vale k that maxmzes the between class varance []. In or case, f we apply the Ots s method on the entre mage the reslt wll not well. Snce the ntensty of cell s bondary s dffer n dfferent area of the mage. And I also apply a 4x4 Medan Flter to get rd of some nosy de to the reflecton of the fld. Fgre 5 s a magnfed mage of Fgre after applyng Ots s method wth/wthot mage dvson. Clearly from ths mage, Ots s method wth dvson and medan has better reslt (cell won t mx p wth bondary). q. magnfcaton rate, resolton of the sensor and the sze of cell we are lookng for. Fgre 6 shows the reslts before/after segmentaton by sze. Step : Segment Image by Shape (H/V Scan Lne Shape Detecton) The reslt from prevos ste p (rght mage of Fgre 6) stll contans many backgrond obects. Ths, we wll frther remove t based on ts shape characterstc. It s reasonable to assme the shape of the cell s rond and smooth. Hence, we can detect the smoothness of each obect n the mage. Before Removng Obects By Sze After Removng Obects By Sze Ots Method wth dvson & Medan Flter Ots Method wthot dvson Fgre 6. Fgre 5. To detect the smoothness, we se a horzontal and a vertcal scan lne passng throgh all obects. If the bondary of the obect has more than for dsont ntersecton ponts wth the H/V scan lne (Fgre 8), we catalog the obect as backgrond. Becase we are dealng wth the mage n dscrete doman, we need to do some extra detecton to avod followng staton. PHASE : Image Segmentaton In ths secton, we wll perform mage segmentaton based on the pror knowledge of the characterstc of obects we are nterest n. Step : Segment Image by Sze From the reslt after above steps, we wll have bnary mage contan cell (or cell s bondary) and backgrond obects n t (see Fgre 4). Usally the sze of backgrond s bgger than cell. Ths, we can delete those obects whose sze greater than the predefned threshold. We can easly determne the threshold by knowng Fgre 7. Fgre 8. Fgre 7 and 8 are magnfed mages of cell s bondary. When horzontal scan lne passng throgh the area crcled n red, we wll get more than for contnes ntersecton ponts. Wth ot any posteror process, the system wll regard ths obect as backgrond (actally t s a cell). To avod ths knd of msdgment, we need to

4 frther detect the contnty of those ntersecton ponts by checkng ts coordnates. Fgre 9 shows the reslt before/after segmentaton by shape. Before Removng Obects By Shape Fgre 9. After Removng Obects By Shape PHASE 3: Cont the Nmber of Cells To cont the nmber of obects n a bnary mage, we scan all pxels and check ts connectvty (In the bnary mage, vale represents obect and vale 0 represents backgrond). When we meet frst non zero vale, we gve that pxels a label vale start from. Next, when we meet another non zero val e, we check ts srrondng s label vale. If the srrondng label vales are all zero, we gve that pxel a label vale, otherwse, we gve the pxels t a label vale the same as srrondng label vale. Repeat above steps ntl all pxels are examned [3]. The obects nmber s then the maxmm label vale. Fgre 0 shows the reslt. In Fgre 0, cells are marked by red astersks and the nmber of the axons s 46. III. D ISCUSSION In phase, or am s to get a bnary mage whch contans as mch cell obects as possble. I tred two methods, one s FCM clsterng algorthm and the other s Ots s method. The reslt of FCM clsterng (Fgre 4.R) s not good (compared wth Ots s Method (Fgre 6.L)). In Fgre 4 many cells stll connect wth backgrond, especally n pper area. The performance of FCM depends on the mage yo choose to bld the featre space. In ths paper I se Red, Green and Ble ntensty of the orgnal mage to bld the featre space. Snce R,G and B mage come from the same mage, ther ntensty dstrbton shares the same characterstc. Ths, ths decreases the beneft of FCM algorthm. To overcome ths problem, we need more mages come from dfferent type of sensor, sch as nfrared rays, X ray or MRI mage etc, as npt mages to bld the f eatre space. Also, for a spervsed FCM, the tranng set defned by or self wll greatly nflence the reslt. To have a better reslt, the more tranng set ponts we choose the better reslt we ll get. And the tranng set ponts we choose for each class mst cover all statons as possble as we can. Fgre 0. The next thresholdng method I sed n ths paper s Ots s method. As mentoned n prevos secton, localzed Ots s method has better performance, bt we stll lose several cell obects after applyng Ots s method. That s becase the npt mage s hghly contamnated.

5 Another reason s the color of ncles s the same as the backgrond. Ths makes the recognton of small cells more dffclt. In phase, we are tryng to remove backgrond (nose) obects. The dea of removng obect by sze s very smple. Jst calclate the nmber of pxels of each obect. We have a sefl fncton BWLABEL n Matlab. Ths fncton can cont the nmber of obects and t also can label whch pxel belong to whch obect by the method I mentoned n prevos secton, and the otpt of the fncton contans two data, one s the nmber of obects and the other s an mage of npt n label doman. To calclate the th obect sze, we st cont the nmber of n label doman. The dffclty of phase s to remove obect by shape. At frst, I try to se sgnatre of the mage. Bt n the npt mage, cells have dfferent knds of shape. If we se sgnatre method, the detecton wll become very complex. Ths I se H/V scan lne to detect the shape. Fgre. Fgre s a bnary bondary mage. To detect the nmber of ntersecton ponts of bondary and V/H scan lne, we add the vales along colmns and rows. The reslts represent the nmber of ntersecton ponts. To frther determne dsont ntersecton ponts, we compare the dfference of ts coordnates. For example, n Fgre the y coordnates of ntersecton ponts of bondary and red lne are Y = [,, 3, 8]. Then we perform crclar shft of Y one element to the left, we get Y = [, 3, 8, ]. Next, we calclate Y Y = [,, 5, 7]. The nmber of non one elements s the nmber of dsont ntersecton ponts. In the example, the nmber of dsont ntersecton ponts s. Fgre. ` H/V scan lne shape detecton s smple and fast, bt t cannot deal wth the condton lke Fgre. Fgre 3 shows the reslt of over contng de to the falre of H/ V scan lne shape detecton. After Removng Obects By Shape Fgre 3. APPENDIX After Removng Obects By Shape In Appendx, fle FnalProect (Man).m s the man program. And FnalProect (FCM).m only performs spervsed FCM algorthm. The reslt of FnalProect (FCM).m wll store n the fle DataTmp.mat. Last, ExpertDef.m s fncton for spervsed Fzzy C Mean. REFERENCES. Bezdek, James C. Pattern Recognton wth Fzzy Obectve Fncton Algorthms. s.l. : Klwer Academc Pblshers, 98.. Rafael C. Gonzalez, Rchard E. Woods. Dgtal Image Processng nd. s.l. : Prentce Hall, Inc., Mlan Sonka, Vaclav Hlavac, Roger Boyle. Image Processng, Analyss, and Machne Vson. s.l. : Thomson Engneerng, 998( edton).