Texture Analysis and Modified Level Set Method for Automatic Detection of Bone Boundaries in Hand Radiographs

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1 Texture Analyss and Modfed Level Set Method for Automatc Detecton of Bone Boundares n Hand Radographs Syaful Anam Graduate School of Scence and Engneerng Yamaguch Unversty Yamaguch, Japan Department of Mathematcs Unversty of Brawjaya Malang, Indonesa Ej Uchno Graduate School of Scence and Engneerng Yamaguch Unversty Yamaguch, Japan Fuzzy Logc Systems Insttute Izuka, Japan Hdeak Msawa Department of Electrcal Engneerng Ube Natonal College of Technology Ube, Japan Norak Suetake Graduate School of Scence and Engneerng Yamaguch Unversty Yamaguch, Japan Abstract Rheumatod Arthrts (RA) s a chronc nflammatory jont dsease characterzed by a dstnctve pattern of bone and jont destructon. To gve an RA dagnoss, hand bone radographs are taken and analyzed. A hand bone radograph analyss starts wth the bone boundary detecton. It s however an extremely exhaustng and tme consumng task for radologsts. An automatc bone boundary detecton n hand radographs s thus strongly requred. Garca et al. have proposed a method for automatc bone boundary detecton n hand radographs by usng an adaptve snake method, but t doesn t work for those affected by RA. The level set method has advantages over the snake method. It however often leads to ether a complete breakdown or a premature termnaton of the curve evoluton process, resultng n unsatsfactory results. For those reasons, we propose a modfed level set method for detectng bone boundares n hand radographs affected by RA. Texture analyss s also appled for dstngushng the hand bones and other areas. Evaluatng the experments usng a partcular set of hand bone radographs, the effectveness of the proposed method has been proved. Keywords hand bones radograph; boundary detecton; modfed level set method; dffuson flter I. INTRODUCTION Rheumatod Arthrts (RA) s a chronc and systemc nflammatory dsorder that may affect many tssues and organs, but prncpally attacks synoval jonts. RA affects about 1% of the populaton worldwde and causes premature mortalt dsablt and compromsed qualty of lfe [1]. It has been demonstrated that early treatment sgnfcantly delays jont destructon, dsease actvt and functonal dsablty. Changes n the early stages of a dsease are thus extremely mportant. To gve an RA dagnoss, a radograph of patent s hand s taken as shown n Fg. 1(a), and hand bones are analyzed to detect eroson caused by RA as shown n Fg. 1(b). The boundares of the hand bones frstly need to be detected for the hand bone radograph analyss. However, t s an extremely exhaustng and tme consumng task for radologsts because the precson requred for correct dagnoss s very hgh. Therefore, an automatc bone boundary detecton n the hand radographs are to be establshed frst. Boundary detecton s a fundamental task n computer vson wth wde applcatons n areas such as feature extracton, object recognton and mage segmentaton [2]. The boundary detecton problem s the problem of fndng lnes separatng homogeneous regons. Actve contour models have been extensvely appled for detectng an mage boundary [3, 4, 5, 6, 7, 8, 9, 10]. The actve contour models have several desrable advantages over classcal mage segmentaton methods, e.g., edge detecton, thresholdng, and regon growth. The frst advantage of the actve contour model s that t can acheve sub-pxel accuracy of the object boundares [3]. The second s that t can be easly formulated under a prncpled energy mnmzaton framework, and allows ncorporaton of varous pror knowledge, such as shape and ntensty dstrbuton, for a robust segmentaton [8]. The thrd advantage s that t can gve smooth and closed contours as a segmentaton result, whch are necessary and can be readly used n further processng, such as shape analyss and recognton. Garca et al. [11] have proposed a fully automatc algorthm for detectng the boundares of bones n hand radographs by usng an adaptve snake method. However, t does not work well on hand radographs affected by RA, because n ths method several ntal contours must be decded frst and a lnear nterpolaton method s used as shown n Fg. 2. The snake method wth a certan ntal contour fals to detect the bone boundary as shown n Fg P a g e

2 (a) Fg. 3. An example of the faled detecton boundary result by a snake method wth a certan ntal contour. Hand bone eroson (a) (b) Fg. 1. Rheumatod arthrts. (a) Rheumatod arthrts photographed n the hand bone radograph. (b) The hand bone eroson s caused by rheumatod arthrts. Intal contour (b) Fg. 4. The level set method problems. (a) A premature termnaton problem. (b) A complete breakdown problem. : Seed ponts Fg. 2. Seed ponts of the adaptve snake method [11]. The ntal contours are defned smply by creatng a small contour around each seed pont. Exstng actve contour models can be categorzed nto two types. Those are a snake method and a level set method. The level set method, s a hghly robust and accurate method for trackng nterfaces movng under complex motons. It has been wdely and successfully used for mage segmentaton. The advantages of the level set method over the classcal snake 118 P a g e

3 method are that the curves break or merge naturally durng an evoluton process, and ther topologcal changes are thus automatcally handled. The level set method however doesn t work well on mages wth nose. It often leads to ether a complete breakdown or a premature termnaton n the curve evoluton process, resultng n unsatsfactory results as shown n Fg. 4. Ths s because the speed functon cannot properly detect the boundary and ts detected boundary s dull even after flterng. To avod a premature termnaton or a complete breakdown n the level set method, we propose a new modfed level set method. Two ponts n the level set method are modfed. The frst pont s on the flterng and the second pont s on the speed functon. In the standard level set method, the Gaussan flter s used for reducng nose. However, there s a hgh possblty that the mage boundary becomes dull after applyng the Gaussan flter. Therefore, the frst modfcaton pont s that the Perona Malk Dffuson (PMD) flter [12] s employed to substtute the Gaussan flter. The PMD flter not only reduces nose but also effectvely enhances the mage boundares. The second pont s that the speed functon of the level set method s modfed to mprove the moton of the level set contour. The modfed speed functon controls the moton of level set contour, and thus the zero level curve of the level set stops around the boundary areas and moves quckly n other areas. In hand bone radographs, the bone boundary detecton s very dffcult because the pxel ntenstes of bones and other areas are smlar n some parts, and the hand bone has nonunform llumnaton. To solve ths problem, we employ an entropy method as a preprocessng, whch s one of the texture analyss methods, to dstngush the hand bones and other areas. The effectveness of the proposed method s verfed through the experments by applyng t to the real hand bone radographs. II. RHEUMATOID ARTHRITIS AND HAND BONE RADIOGRAPHS Arthrts s a general term used to descrbe more than 100 chronc dseases of the jonts, bones and muscles. One type of arthrts s Rheumatod Arthrts (RA) whch s a chronc nflammatory jont dsease characterzed by a dstnctve pattern of bone and jont destructon. RA affects jonts n hands, hps, spne, knees and feet. Commonl the hand and wrst radographs are a source of mportant clncal nformaton wth regard to very prevalent musculoskeletal dseases. X-ray or radograph s the gold standard for an assessment of jont damage n RA. The hand bone radograph of Fg. 1(a) s used not only for the ntal dagnoss but also for the montorng of dsease progresson and assessment of the therapeutc effect of varous drugs. Fg. 1(b) shows the bone eroson whch s caused as a result of RA. Radographs depct the tme-ntegrated cumulatve record of jont damage. Its advantages are low costs, hgh avalablt possblty of standardzaton together wth blnded centralzed readng, reasonable reproducblt and exstence of valdated assessment methods. Furthermore, radography s helpful n the dfferentaton of RA from other jont condtons ncludng osteoarthrts, psoratc arthrts and neoplasms [13]. III. IMAGE BOUNDARY DETECTION Image segmentaton s a process of parttonng a dgtal mage nto multple segments. Image segmentaton s typcally used to locate the objects and boundares n mages. The boundary of an mage can provde valuable nformaton for further mage analyss and nterpretaton tasks. A boundary s a contour n the mage plane that represents a change n pxel ownershp from one object or surface to another [14]. Images are characterzed by color, texture, and non-texture regons. Thus, boundares can arse due to the adjacency of any of these regons n natural mages. IV. TEXTURE ANALYSIS An mage texture s a property that represents the surface and structure of an mage. Generally speakng, the mage texture can be defned as a regular repetton of an element or a pattern on a surface. The mage texture s a complex vsual pattern composed of enttes or regons wth sub-patterns wth the characterstcs of brghtness, color, shape, sze, etc. An mage regon has a constant texture f a set of ts characterstcs are constant, slowly changng or approxmately perodc. The mage texture can be regarded as a smlarty groupng n an mage. Texture analyss s a major step n texture classfcaton, mage segmentaton and mage shape dentfcaton. Image segmentaton and shape dentfcaton are preprocessng steps for object recognton n an mage [15]. Texture analyss refers to a class of the mathematcal procedures and models that characterze the spatal varatons wthn magery by means of extractng nformaton. Approaches to the texture analyss are usually categorzed nto structural, statstcal, model-based and transform methods. Feature extracton s the frst stage of the mage texture analyss. The results obtaned from ths stage are used for texture dscrmnaton, texture classfcaton or object shape determnaton. One of the feature extracton methods s a hstogram based entropy method. The mage s assumed as a functon f ( y) of two space varables x and y, where x 0, 1,..., N 1 and y 0, 1,..., M 1. The functon f ( y) can take dscrete values of 0, 1,...,G 1, whch are the values of the ntensty n the mage. The ntensty-level hstogram s a functon showng the number of pxels n the whole mage, whch s defned by: 119 P a g e

4 N 1M 1 h( ) ( f ( y), ), (1) x0 y0 where ( j, ) s a followng Kronecker s delta functon: 1, j ( j, ) (2) 0, j. Dvdng the values h() by the total number of pxels n the mage, one obtans the approprate probablty densty of occurrence of the ntensty levels as follows: h( ) p ( ), 0, 1,..., G 1. (3) NM The entropy s defned by: G 1 0 E p( ) log ( p( )). (4) 2 The entropy method s also often used for characterzng the mage texture. V. ANISOTROPIC DIFFUSION FILTER The ansotropc dffuson flter was orgnally proposed by Perona and Malk [12] n order to preserve the edges of an mage. The basc dea behnd the Perona Malk Dffuson (PMD) process s to get an ncreasngly smoothed mage u( from an orgnal mage u 0 ( y), ndexed by a dffuson parameter t. Ths process can be nterpreted as an mage convoluton by a Gaussan kernel G( wth an ncreasng wdth as follows: I( I 0( y)* G(. (5) The ansotropc dffuson equaton s defned by: where I t I dv( c( I) t c( I c( I, (6) c( g( I ( ) (7) s a dffuson coeffcent. I denotes a gradent of an mage. g refers to an edge stoppng functon, whch s a decreasng functon of the gradent of an mage. The ntal condton s gven by: I 0) I ( y), (8) ( 0 and the dscrete verson of PMD s defned by: where s ( y) and p are the coordnates of the pxel of concern and ts neghborng pxels, respectvely. s an ntensty at s wth an teraton count n. represents the s dffuson drectons. s the number of pxels n the neghborng area. s a parameter. A monotoncally decreasng functon of the gradent of an mage s usually adopted as g. The gradent of an mage and the speed functon are gven by: and (9) (10) (11) where K s a parameter whch controls the strength of dffuson. I ( n1) s I s I g( I s s, p s I p I g takes large values at the regons where the ntensty gradents are low. On the contrar t takes low values at the regons where the ntensty gradents are hgh. VI. LEVEL SET METHOD The level set methods have been wdely and successfully used for detectng mage boundares. The basc dea of the level set method s that the contour s represented by the zero level set of a hgher dmensonal functon, called a level set functon. The moton of the contour s formulated based on the evoluton of the level set functon. Let us consder a dynamc parametrc contour C ( x( s,, y( s, ), the curve evoluton of whch s defned by: C / t FN, (12) where t s a set pont n tme, s s a curve parameter, N s an nward normal vector to the curve C. F s a speed functon that controls the moton of the contour. The curve evoluton of (12), n terms of a parameterzed contour, can be converted to a level set formulaton by embeddng the dynamc contour C as the zero level set of a tme dependent level set functon (. Assumng that the embeddng level set functon takes the negatve values nsde the zero level contour and the postve values outsde, the nward normal vector can be expressed as N /, where s a gradent operator. The curve evoluton of (12) s then converted to: s 1 g( z), 2 z 1 K s, p, ) I s, p, (n) I s 120 P a g e

5 / t F, (13) whch s referred to as a level set evoluton equaton. Curve evoluton that s used by the level set (x) s defned by: / t dv( d ( ) ) ( ) dv( g / ) g ( ), p (14) where s a drac delta functon and dv s a dvergence operator. g s a speed functon whch s gven by: (,j) Wndow g 1/(1 ( G * I ), (15) where G s a Gaussan flter and I s an mage [7]. VII. PROPOSED METHOD We modfy the level set method and apply t for bone boundary detecton n hand radographs. We further propose to employ an entropy method-based texture analyss as a preprocessng. Ths chapter s dvded nto two sectons. Those are bone texture extracton and modfed level set method. A. Bone Texture Extracton In the frst step, the hand bone radograph s cropped to get a regon of concern as of Fg. 5. In the second step, the cropped radograph s scanned as n Fg. 6 and the entropy s calculated for each wndow as follows: Fg. 6. Scan of the cropped radograph by usng a movng wndow (raster scan). E (, j) 255 k 0 p( k)log ( p( k)), 2 (16) where E(, j) s an entropy evaluated at the center of the wndow. Fg. 7. The entropy of an mage of Fg. 5. Fg. 5. The hand bone radograph to be processed. Fg. 8. The hand bone radograph after applyng the eroson morphologcal operaton to Fg P a g e

6 The entropy of an mage of Fg. 5 s shown n Fg. 7. From Fg. 7 t can be observed that the entropy can dstngush the bone areas and the other areas. The entropy has however a dsadvantage that t makes the bones be connected to each other even f they are separated actually. To overcome ths problem, t s recommended to employ the eroson morphology operaton before the entropy of an mage s evaluated. An eroson operaton s one of the most basc morphologcal operatons. It adds and/or removes pxels on the mage boundares. The number of pxels added and/or removed from the objects n an mage depends on the sze and the shape of the structurng element of the eroson morphology operaton. Fg. 9. The entropy of an mage of Fg. 8. Fg. 10. The result after applyng the PMD flter to Fg 9. Fg. 12. The values of the standard speed functon for Fg. 10. Fg. 11. The result after applyng the Gaussan flter to Fg 9. The wndow moves from the top left to the rght, then n the next row, untl the bottom rght of an mage. Ths s called a raster scannng. Fg. 13. The values of the modfed speed functon for Fg P a g e

7 6) Calculate the contour evoluton by usng (14). 7) Calculate the new contour. 8) Repeat steps (v) and (v) untl t converges or the maxmum number of teratons s reached. Fg. 14. Randomly gven ntal contour of the level set. A structurng element of t s a matrx consstng of only 0's and 1's that can have any arbtrary shape and sze. The pxels wth values of 1 defne the neghborhood. In ths paper, the 90 degrees lne structure element s used. The length of the lne s set to be 11. The result of the eroson morphology appled to Fg. 5 s shown n Fg 8, and the entropy of an mage of Fg. 8 s shown n Fg. 9. Fg. 9 s used thereafter. B. Modfed Level Set Method In ths secton, the modfed level set method s descrbed, whch s appled to the entropy of an mage n secton VII. A. The procedure of the modfed level set method s summarzed as follows: 1) Apply the PMD flter to the entropy of an mage to smooth t. Ths PMD flter substtutes the Gaussan flter n the standard level set method. 2) Calculate the mage gradent magntude I( y). 3) Normalze I( y) n range [0,1] as follows: VIII. EXPERIMENTAL RESULTS The proposed method s appled to a set of the hand bone radographs. In the experments, four hand bone radographs are used. The bone boundary results by the proposed method are compared wth the boundares manually detected by an experenced medcal doctor. As descrbed n chapter VII, Fg. 5 s the nput mage to be processed. Fg. 8 s obtaned after applyng the eroson morphologcal operaton to Fg. 5. Fnally Fg. 9 s obtaned by computng the entropy of Fg. 8. It s seen that Fg. 9 has unform llumnaton and thus the bone areas and the other areas are softly dstngushed. Fgs. 10 and 11 show the entropy of an mage after applyng the PMD flter and the Gaussan flter to Fg. 9, respectvely. It s seen that the PMD flter works better than the Gaussan flter. The values of the standard speed functon and the values of the modfed speed functon for Fg. 10 are shown n Fgs. 12 and 13, respectvely. It can be seen that the modfed speed functon clearly show the bone boundares better than the standard speed functon. The modfed speed functon can thus avod a complete breakdown or a premature termnaton, whle the standard speed functon cannot. The parameters of the level set of (14) are emprcally assgned as Δt 10, 1, 0. 2 / Δt, 5, and Fg. 14 shows the randomly gven ntal contour of the level set. The contour of the level set moves gradually wth a speed functon g. The level set contour wth zero level moves from outsde to nsde, because the level set functon has G I( y) mn ( I( y) ). norm max( I( y) ) mn ( I( y) ) (17) 4) Calculate the modfed speed functon whch s defned by: g exp bg ) norm, (18) ( 2 where b s a constant whch controls the moton of the contour. 5) Gve the ntal contour of the level set. (a) 123 P a g e

8 (b) Fg. 15. The bone boundary detecton results for the left hand radograph. (a) The left hand bone radograph to be proccessed. (b) The red lnes and the green lnes show the boundares detected by the proposed method and those manually detected by an experenced medcal doctor, respectvely. negatve values nsde the zero level set contour and postve values outsde. The contour of the level set stops and converges on the boundary areas because the values of the speed functon g on the boundary areas are close to 0. Fg. 15(a) and Fg. 16(a) show the radographs for the left and rght hands to be processed, respectvely. Fg. 15(b) and Fg. 16(b) show the boundary detecton results for each hand. It s seen from those results that the red lned boundares manually detected by the proposed method are close to the green lned boundares by an experenced medcal doctor. The proposed method s effcent. (b) Fg. 16. The bone boundary detecton results for the rght hand radograph. (a) The rght hand bone radograph to be proccessed. (b) The red lnes and the green lnes show the boundares detected by the proposed method and those manually detected by an experenced medcal doctor, respectvely. TABLE I. NUMERICAL EVALUATION OF THE BONE BOUNDARY DETECTION RESULTS. (Pxels) Data Hand Image sze Hausdorff dstance Data 1 Data 2 Data 3 Data 4 Left Hand 1539 x Rght Hand 1500 x Left Hand 1347x Rght Hand 1341x Left Hand 1437x Rght Hand 1398x Left Hand 1449x Rght Hand 1425x Average 44.8 (a) (a) 124 P a g e

9 Hausdorff dstance between two curves s 44.8 pxels. Based on the defnton of the Hausdorff dstance, ths means that the maxmum error s 44.8 pxels. The proposed method could detect the bone boundares qute well for almost all the mages that were used. One faled result s shown n Fg. 17. It can be seen that the pxel ntenstes of the hand bone and the pxel ntenstes of the other areas are mostly smlar n some parts. Fg. 17(a) shows the entropy of the nput mage after PMD flterng. Fg. 17(b) shows a hand bone boundary detected by an experenced medcal doctor. Fg. 17(c) shows the bone boundary detected by the proposed method. Even for a case as dffcult as ths, the proposed method could somehow detect the bone boundary. (b) (c) Fg. 17. One faled result of the bone boundary detecton. (a) The entropy of the nput mage after applyng the PMD flter. (b) The bone boundary detected by an experenced medcal doctor. (c) The bone boundary detected by the proposed method. The bone boundary detecton results are numercally evaluated by Hausdorff dstance [16]. The Hausdorff dstance between the two curves s defned as the maxmum of the dstance to the closest pont between two curves as follows: e( A,B) max( max{ d( a,b)},max{ d( b, A)}), j j (19) where A { a 1, a 2,...,a m } and B { b 1,b 2,...,b m } represent the two curves. a and b j are the ordered pars of x and y coordnates of a pont on the curve. d( a, B) s the dstance to the closest pont for a to curve B defned by: d( a,b) mn b a. j j (20) The numercal evaluatons of the bone detecton results by Hausdorff dstance are gven n Table 1. The average of the IX. CONCLUSIONS We have proposed a modfed level set method for an automatc detecton of the bone boundares n hand radographs. The proposed method has shown a good detecton performance. The proposed method however could not work well for some cases when the pxel ntenstes of the bone and those of the other areas are smlar. In future works, the above problem needs to be further consdered. We am to develop a method whch s robust to a varety of mage ntenstes. Applcaton of the present method to other practcal cases and more comparatve dscussons wth other technques are left for the future studes. ACKNOWLEDGMENT Ths work was supported by the research fund from the Izuka Research and Development Organzaton under the project number Syaful Anam would also lke to thank DGHE postgraduate scholarshp of Indonesa for supportng hs stay at Yamaguch Unverst Japan. REFERENCES [1] B. Zelnsk, Hand radograph analyss and jont space locaton mprovement for mage nterpretaton, Schedae Informatcae, vol. 17/18, pp , [2] M. Leordeanu, R. Sukthankar and C. Smchsescu, Effcent closedform soluton to generalzed boundary detecton, European Conference on Computer Vson, LCNS, vol. 7575, pp , [3] L. He, S. Zheng and L. Wang, Integratng local dstrbuton nformaton wth level set for boundary detecton, Journal of Vsual Communcaton and Image Representaton, vol. 21, pp , [4] K. Horbert, K. Rematas and B. Lebe, Level-set person segmentaton and trackng wth mult-regon appearance models and top-down shape nformaton, In Proceedngs of Internatonal Conference on Computer Vson, pp , [5] M. L, C. He and Y. Zhan, Adaptve regularzed level set method for weak boundary object segmentaton, Mathematcal Problems n Engneerng, vol. 2012, pp. 1 16, [6] C. L, R. Huang, Z. Dng, J. C. Gatenb D. N. Metaxas and J. C. Gore, A level set method for mage segmentaton n the presence of ntensty nhomogenetes wth applcaton to MRI, IEEE Transactons on Image Processng, vol. 20, no. 7, pp , [7] C. L, C. Xu, C. Gu and M. D. Fo Dstance regularzed level set evoluton and ts applcaton to mage segmentaton, IEEE Transactons on Image Processng, vol. 19, pp , [8] P. U. Panchal and K. C. Jondhale, Image object detecton usng actve contours va level set evoluton for segmentaton, Journal of Sgnal and Image Processng, vol. 3, pp , P a g e

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