Locating Brain Tumors from MR Imagery Using Symmetry

Transcription

1 ocating rain Tumor from M magery Uing Symmetry Nilanjan ay aidya Nath Saha and Matthew obert Graham rown {nray1 baidya mbrown}@cualbertaca epartment of Computing Science Univerity of lberta Canada btract Tumor/abnormality egmentation from magnetic reonance imagery M can play a ignificant role in cancer reearch and clinical practice lthough accurate tumor egmentation by radiologit i ideal it i extremely tediou Experience how that for M databae indexing purpoe approximate egmentation can be adequate n thi paper we propoe a traightforward real-time technique to find a bounding box around the brain abnormality in an M image Our algorithm exploit left-to-right ymmetry of the brain tructure The propoed detection algorithm can play a ueful role in indexing and torage of bulk M data a well a provide an initial tep or eed to ait algorithm deigned to find accurate tumor boundarie NTOUCTON Currently the large databae of brain tumor magnetic reonance M image maintained by mot clinic are not indexed and cannot be earched baed on clinically relevant tumor characteritic uch a location and ize On the one hand manual tumor egmentation i extremely laboriou and tediou given the heer volume of M data On the other hand reliable and fat automated off-the-helf tumor egmentation algorithm are equally hard to obtain reently available automatic brain tumor egmentation algorithm that attempt to egment the tumor exactly do not perform a reliably a it i deired even from the databae indexing purpoe ntead we propoe in thi paper an algorithm that find a le exact egmentation but doe o reliably and in real-time Exact automatic egmentation of tumor/edema from brain M i a difficult and unolved problem For a nice account of thi topic from an image analyi and machine learning perpective ee [7] The potential road block eem to come from incorporating domain pecific knowledge into the algorithm Voxel-wie claification algorithm uch a thoe via upport vector machine are typically dependent on the locally computed feature computed within a window around a voxel On the other hand incorporation of global region-baed feature i non-trivial and computationally intenive [2] [5] Thee algorithm typically require regitration of M image tandardization of image intenitie and noie removal [7] Moreover many advanced algorithm can be low and unuitable for databae indexing purpoe Keeping thee view in conideration we propoe here a fat method for locating brain tumor in magnetic reonance M image Specifically the algorithm define bounding boxe around abnormal region caued by primary brain tumor in typical M canning modalitie including T1 T1 with gadolinium T2 and F [7] We believe that our algorithm ha at leat the following two direct application in the treatment of brain cancer Clinical center currently maintain large amount of archived brain tumor M data that i not indexed for eay retrieval according to image propertie atabae indexing baed on automated tumor location would allow a clinician to retrieve hitorical cae relevant to the diagnoi and treatment of new patient cancer n addition our propoed automated tumor location algorithm could be ued to eed or contrain an automated brain tumor egmentation ytem The key obervation underlying our approach i that normal brain tructure i roughly ymmetric: the left part and the right part can be divided by an axi of ymmetry Tumor/edema typically diturb thi ymmetry We utilize thi property to deign a real-time algorithm to locate bounding boxe The propoed algorithm ue only a ingle M image and avoid the non-trivial iue of image regitration and intenity tandardization Our bounding box finding algorithm i unupervied and require no prior training t ue only two uer-tuned parameter Empirical tudie with our algorithm how that thee two parameter can be conveniently et by a uer to run on a large amount of data OOSE TECHNQUE We cat the problem of finding a bounding box around brain abnormalitie from M a a change detection problem [6] We aume that the region of abnormality i located in one of the two halve of the brain Thu in the M one half of the brain act a a reference image and the other half a a tet image We need to compare the tet image with the reference image to find out the region of abnormality To formulate thi change detection problem let u conider the etting hown in Fig 1a where we how two image and Here i the tet image and i the reference image The tak i to find the anomalou region on that i not preent in Often traightforward method uch a taking the point-wie ubtraction image - fail to identify the

2 region difference correctly The reaon are variou; however the mot prominent one i that the left and right halve of a brain do not preciely match on a point-to-point bai even when we conider a normal brain without tumor/edema Noie i alo preent in the difference image n thi paper we ue a region-baed approach rather than a point-to-point comparion that mot of the change detection algorithm ue [6] To detect the region of abnormality on we conider a core function defined by the hattacharya coefficient C [4] We define our propoed core metric a follow Conider a horizontal dotted line drawn acro the image and in Fig 1a at a ditance from the top of the image We define two rectangle on the image domain [0w] [0] and [0w] [h] where w and h are repectively the width and the height of the image and Note that and repectively denote the image domain above and below the horizontal line We define the propoed core function a: E where are normalized gray level intenity hitogram probability ma function The ubcript on denote whether i contructed on the tet image or on the reference image The upercript of denote on which portion of the image domain i contructed For example denote the normalized intenity hitogram of image within Here Y X i the inner product of two vector X and Y Thu the core function i the difference of C between the image domain above and below the reference line at C i a number between 0 and 1 C between two probability ma function pmf i 1 when they are exactly equal f two pmf are very different eg with dijoint upport then their C value will be 0 From thi perpective our core metric eentially meaure: a how imilar are the two upper hitogram and b how diimilar are the two lower hitogram Thu when our core function ha a high value we expect the two upper hitogram to achieve a good match while the two lower hitogram are likely to have a poor match On the other hand a low value of E indicate a mimatch between the upper hitogram and a good match between the lower hitogram We claim that the core function help determine the location of in a very fat computation Our claim i expreed in Fig 1b which how that the core function hould firt increae then decreae and then increae again a increae from 0 to h The increaing and decreaing egment meet at l and u at the lower and upper bound of repectively So from a core plot we can locate the upper and lower bound for quickly To find the left and right bound of we imply rotate and by 90 degree and follow the ame procedure The following two propoition etablih thi claim along with the neceary aumption about the data ie and ropoition 1: E M + where and M + roof: Note that can be written a: + Uing the above decompoition for one can how: and + imilar et of two inequalitie hold for Combining thee four inequalitie yield the reult QE a b Fig 1: a Finding from image uing a reference image b typical core function plot

3 ropoition 2: f the following four condition viz i << ii << iii c and 1 iv c 2 hold where c 1 and c 2 are two contant then E i a increaing when 0 l b decreaing when l u and c increaing when u h roof: umption i and ii together with ropoition 1 imply: E Next applying iii and iv in the expreion for yield: c c 1 2 Now it i traightforward to verify that i increaing when 0 l decreaing when l u and again increaing when u h QE M mage a Score plot for vertical direction oundary and ine of Symmetry Score plot for horizontal direction c d Fig 2: a T1 weighted M with overlaid bounding found by the propoed method b kull boundary and line of ymmetry c E plot for vertical direction d E plot for horizontal direction To etablih the nature of E a illutrated in Fig 1b the aumption iii and iv can be relaxed One only need that the rate of area change with repect to occur fater than that of the C On the other hand the aumption i and ii mean that the abnormality portion of i different from the ret when compared with repect to a reference hitogram The ue of our computation i illutrated in Fig 2 n Fig 2a we how a brain M T1 weighted with gadolinium henceforth referred to a T1C in which the abnormality i oberved on the left ide of the image correponding to the patient right ide Firt we compute a gradient vector flow b nake [8] to find the kull boundary a hown in Fig 2b Next a vertical line i drawn through the centroid of the nake Thi vertical line erve a a line of ymmetry OS alo hown on Fig 2b For an image having coniderable rotation one can fit an ellipe to the nake and take the major axi of the ellipe a the OS Now the portion of M to the left of the OS erve a the tet image and the portion of M to the right of OS after taking a reflection erve a the reference image Note that we do not need to know a priori if the tumor i located on the left or the right ide fter finding the bounding box on one ide ay on the left ide we tet if the average intenity within the bounding on the left ide i greater than that on the right ide auming that tumor/edema will produce tronger ignal on T1C image core function plot for the vertical direction and another plot for the horizontal direction are hown repectively in Fig 2c and Fig 2d Finally to locate the bounding box we detect the extrema of the core plot a hown in Fig 2c and 2d The bounding box found i overlaid on Fig 2a Note that the core function ha a number of local extremum point lo note that our propoition cannot guarantee that the extremum point we are eeking are the global one n practice we find thee extremum point by the following algorithm lgorithm 1 Step 1: ocate all maxima and minima from a core plot Thee extrema are found within a neighborhood of ize N pixel a uer defined parameter we take N41 for all our experiment Step 2: Conider all the pair of conecutive extremum point: maxp minp where maxp i a maximum and minp i a minimum point From among all uch pair find the pair l u for which the difference E l E u i the maximum Note that in lgorithm 1 following the claim of ropoition 2 we are eentially looking for a pair of point compried of a conecutive maximum point and minimum point that repectively correpond to the upper and the lower bound of the bounding box The difference E l E u i the amount of decreae in core function between two conecutive extrema The neighborhood ize N limit the ize of the abnormal region we can find For example lgorithm 1 will be able to find bounding boxe with height larger than N ESUTS Thi ection illutrate the reult of applying our bounding box finding algorithm to brain M data n Fig 3 we how bounding boxe found by our algorithm on four T1C image n thee example the bounding boxe include the region of abnormality a intended The two parameter of the propoed bounding box finding algorithm i the number of hitogram bin which we take 64 for all our experiment and the neighborhood ize N that we take 41 pixel for all the experiment

4 ymmetry The technique ue a coring function that provide a meaure of the imilarity or difference between two region in term of the hattacharya coefficient computed on thoe region intenity hitogram We provide a mathematical bai of the behavior of thi coring function that eentially locate the bounding box Thi region-baed and image feature hitogram-baed approach can open new avenue of brain tumor boundary delineation Our approach ha everal advantage: a t exploit approximate left-right ymmetry of the brain b No preproceing uch a intenity tandardization or noie removal i required by our algorithm c t require no labeled image data nor any training d t doe not require image regitration e Only two uer defined parameter are ued f t can be implemented in real-time One limitation of our algorithm i that it aume the tumor/abnormality i confined to the left or right ide of the brain and doe not cro the OS lo when the tumor i fragmented into multiple part our algorithm tend to detect only the mot prominent region of abnormality n the future we would like to relax thee two limitation Fig 3: M image and bounding boxe around abnormal region For performance evaluation of our algorithm we conider 2 G S the ice coefficient C [3]: C where S i the G + S et of pixel within a bounding found by our algorithm and G i the et of pixel belonging to a bounding box computed around the tumor/edema boundary a drawn by a human expert radiologit The modulu ign in C denote the number of pixel belonging to a et The ideal value of C i 1 in which cae S G C value cloer to 1 implie a better egmentation Fig 4 how encouraging ice coefficient value for two et of brain M data taken from two patient n Fig 4 lice number refer to the axial lice taken at different height through the patient brain already mentioned other than providing a fat mean for databae indexing our algorithm can alo provide an initialization for other egmentation algorithm We elaborate thi view in Fig 5 n Fig 5a a bounding box i firt computed by our propoed method n Fig 5b we how egmentation by the Chan-Vee method [1] tarting with an initial contour from the bounding box of Fig 5a Fig 5b how the final boundary computed by the Chan-Vee algorithm n Fig 5c we how the Chan-Vee egmentation from a different initial curve a hrunk kull boundary in thi cae We oberve that puriou egmentation boundarie are generated in Fig 5c Thi example illutrate that our propoed bounding box algorithm can aid other algorithm to delineate the region of abnormality V FUTUE WOK N CONCUSONS We propoe a technique for computing bounding boxe around brain abnormality in tandard M image baed on Fig 4: ice coefficient for M image for two tudie a b c Fig 5: a ounding box b egmentation within bounding box c egmentation on the entire image nitial encouraging reult from a few patient tudie have prompted u to conduct extenive teting on the patient image databae maintained at the Cro Cancer ntitute on the Univerity of lberta campu We alo plan to couple thi bounding box finding algorithm with other in-houe egmentation algorithm viit: Extenion of the propoed algorithm to 3 are traightforward We are currently making thi effort at but

5 not the leat being a change detection algorithm we plan to extend the application area of our algorithm to other area uch a video urveillance EFEENCES [1] TF Chan and Vee ctive contour without edge EEE Tranaction on mage roceing vol10 no2 pp [2] Cobza N irkbeck M Schmidt M Jägerand Murtha 3 variational brain tumor egmentation uing a high dimenional feature et n Mathematical Method in iomedical mage nalyi a workhop in conjunction with nternational Conference on Computer Viion CCV 2007 io de Janeiro razil October 2007 [3] ice Meaure of the amount of ecologic aociation between pecie Ecology vol 26 pp [4] K Fukunaga ntroduction to tatitical pattern recognition cademic re 2 nd ed 1990 [5] C-H ee S Wang F Jiao Greiner Schuurman earning to model patial dependency: emi-upervied dicriminative random field Neural nformation roceing Sytem Vancouver C ecember 2006 [6] J adke S ndra O l-kofahi oyam mage Change etection lgorithm: Sytematic Survey EEE Tran mage roceing vol14 no3 pp March 2005 [7] M Schmidt utomatic brain tumor egmentation MSc Thei Univerity of lberta 2005 [8] C Xu and J rince Snake hape and gradient vector flow EEE Tranaction on mage roceing vol7 no3 pp