University of Erlangen-Nuremberg. Cauerstrae 7, Erlangen, Germany. and edges. Each node is labeled by a feature vector that characterizes

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1 Deformable Templates for the Localzaton of Anatomcal Structures n Radologc Images Wolfgang Sorgel and Bernd Grod Telecommuncatons Laboratory Unversty of Erlangen-Nuremberg Cauerstrae 7, Erlangen, Germany fwsoergel,grodg@nt.e-technk.un-erlangen.de Abstract. Ths paper descrbes a method for non-rgd regstraton of a model template wth the correspondng anatomc structure n a radologc mage. The model template s a graph consstng of labeled nodes and edges. Each node s labeled by a feature vector that characterzes the sought structures n ts vcnty. The edges connect the nodes n accordance wth anatomcal topology. The features whch descrbe possble node postons are computed by lterng the mage wth a set of Gabor lters and comparng the lter responses wth those from the model. The nal node postons are determned by mnmzng a deformaton energy term assocated wth the template. We show results for dgtzed lm orthopantomograms of the jaw whch ndcate good performance at modest computatonal eort for such artfact-rch mages. The results are used for localzaton of bone lesons relatve to anatomc structures. Keywords: Deformable Templates, Gabor Flters, Anatomy Localzaton, Non-rgd Regstraton 1 Introducton In the analyss of medcal mages t s often desrable to detect the poston of typcal anatomcal structures. One way to acheve ths s to regster the mage to a model or atlas mage of the depcted structure. In ths case, the shape, sze and locaton n the mage of the sought structure s roughly known but one needs to apply a non-rgd coordnate transformaton for regstraton. The method proposed n ths paper s smlar to the one ntroduced by Amt [1] based on a decomposable graph of landmarks matched to the mage by local operators and dscrete optmzaton, whch we have combned wth feature computaton by Gabor lterng as used for face recognton [2, 3]. The approach s based on a deformable template net consstng of nodes placed on anatomcal landmarks and edges connectng these nodes. Fgure 1 shows an example of a net that has been manually adapted to a schematc drawng of the facal skeleton. The nodes are labeled wth features descrbng how the mage should look lke n the vcnty of each node. These features are compared wth the respectve features for each mage coordnate pont to dentfy possble locatons of each node. The nal poston of each node s then determned by mnmzng a deformaton energy

2 Fg. 1. Model mesh wth nodes and edges manually adapted to a schematc drawng of the facal skeleton. assocated wth the net. Based on the poston of the nodes of the deformed net a non-rgd coordnate transform between model and mage can be appled. 2 Image Feature Computaton The localzaton of derent structures n the mages s based on Gabor lterng. These lters have found wdespread use n texture analyss [4] and varous computer vson tasks [2, 3]. They allow detecton of localzed structures, are senstve to orentaton and spatal frequency whle beng tolerant aganst brghtness varatons and can easly be ncorporated nto mult-scale approaches. One such complex, zero mean lter kernel s gven by (x; y) = k2 4 2 exp k 2 (x 2 + y 2 ) 8 2 e j(x cos +y sn ) e 22 : (1) It has the shape of a plane wave respondng best at the spatal frequency or scale k = and orentaton, restrcted by a Gaussan envelope. By lnear lterng wth lter kernels of derent scales and orentatons, one obtans a complex feature vector J(x; y) = J 1 (x; y) J 2 (x; y) : : : J n (x; y) T wth elements of the form J = a exp(j' ) for each pxel locaton (x; y) n the mage. For the anatomy detecton applcaton on panoramc X-ray mages we use 4 scales 2 f0; 1; 2; 3g and 4 orentatons 2 f0 o ; 45 o ; 90 o ; 135 o g resultng n 16-dmensonal feature vectors.

3 Based on these feature vectors we now determne smlarty of ponts n a gven mage I to those n another model mage I 0. Whle the ampltudes a are spatally smooth, the phase components vary wth approxmately the characterstc spatal frequency of the kernel. We use P S(J; J 0 ) = a a 0 P pp 1 + a a 0 cos(' ' 0) pp (2) a2 P a02 a2 P a02 as a smlarty crteron functon, resultng n hgh smlarty where ampltude and phase are both smlar. Compared to usng ampltude only we so get better results. The smlarty functon s evaluated for each node of the mesh. Usng one or more model mages wth known poston of the node we obtan a smlarty value from (2) for ths node at every pxel wthn the search area n the mage. A number of pont postons most smlar to the model s chosen as canddate ponts for possble postons of the node n the deformed net. 3 Deformaton of the Mesh The nal poston of the nodes n the mage s now determned by mnmzng a deformaton energy assocated wth the net. Ths energy E = E dstance + E angle s composed of a dstance term and an angle term. The dstance term E dstance models the edges of the net as lnear sprngs, normalzed by the model edge length. Dstance energy s used for keepng the proportons of the model. The second term E angle s derved from the derence of the angles between the edges at each node from the actual net mage to the model net. Ths term controls local deformatons. Snce we do not allow ntersectng edges we further use a penalty term whch ncreases the energy by a large, xed amount for each ntersecton. In the next step the model net s adapted to the mage by mnmzng an energy-lke objectve functon. Energy mnmzaton s ntalzed by placng each node on one of ts canddate ponts. Then a greedy algorthm [5], movng nodes n turn among canddate ponts, s utlzed to nd the nal poston of the nodes by mnmzng E. Actual mnmzaton s done n three steps, usng only E dstance rst, then E angle and nally the complete energy. Usng 5 canddate ponts for each node, 4 to 6 teratons over all node ponts are needed for convergence of each step. Note that feature smlarty (2) s not used for energy mnmzaton, only for the selecton of the canddate ponts whch are then treated equally. Thus there s no need to trade o mesh deformaton aganst feature smlarty. 4 Results and Applcatons We apply the proposed algorthm to a collecton of 233 dgtzed orthopantomographs of the jaws, orgnatng from derent sources and wth varable qualty. The structure s well recognzed n all cases. Well vsble anatomcal landmarks, lke ponts at the outer contour of the mandble are correctly found n over 95 % of all mages. On average 75 % of the 30 node ponts we use on these mages

4 are placed correctly. Most of the ponts not found are obscured by magng artfacts or poor lm exposure. Snce the topologcal structure of the net s not aected by msplaced ponts and the msplacement s typcally less than the average dstance between node ponts, ths rate s acceptable for our task. It could be further ncreased by addng another optmzaton step where the requrement that node ponts can only be placed on the canddate ponts determned n secton 2 s relaxed. The use of a mult-resoluton scheme whch can be ecently mplemented wthn the gven framework s another opton. Computatonal effort s modest wth an overall executon tme of a few mnutes on a desktop workstaton. Fgure 2 shows a typcal example of a net adapted to an mage of the jaw and an example for an artfact-rch mage wth some msplaced nodes. Note that the structure s recovered well nevertheless. The deformed template Fg. 2. Deformable net adapted to an X-ray mage of the facal skeleton. Upper mage: Typcal result. Lower mage: Dcult mage wth some msplaced nodes s then used to dene a non-rgd coordnate transform from the actual mage to the model. Ths transform can ether be based on a trangulaton of the net and ane transforms of the mage ponts wthn each trangle or radal bass functons dened n the node ponts. We use the proposed template matchng method wthn a system for characterzaton and dagnoss of bone lesons n the facal skeleton [6]. The goal s to

5 determne the poston of a gven regon wthn the jaws. For ths purpose, the coordnates of the contour of a leson are transformed to the model coordnates whch allows ntersectng t wth the predetermned anatomc labelng of the regons n the model. As a result we get a fuzzy membershp value for each regon whch enables us to compare the locaton of derent lesons. 5 Conclusons We have presented a method for non-rgd regstraton of template models wth anatomcal structure n radologcal mages. Based on a labeled mesh we can determne a coordnate transform from the actual mage to the model. The Gabor lters used as feature labels n the nodes allow detecton of local characterstc structures, senstve to scale and orentaton whle beng robust aganst brghtness and contrast varatons commonly found n X-ray mages. We acheve an overall rate of correct node localzaton of 75 %, wth better results for well vsble structures. For our applcaton of mappng leson postons to predetermned regons ths performance s sucent. Improvements by addtonal ne search, the use of a mult-resoluton framework or by the applcaton of heurstcs are under nvestgaton. The method s not bound to an mage modalty or applcaton, extensons to 3D datasets are possble. 6 Acknowledgments Ths work was supported n part by a grant from FRIATEC AG, Mannhem. We would lke to thank the Klnk und Polklnk fur Mund-,Kefer-,Geschtschrurge n Erlangen for ther competent advse. References 1. Yal Amt. Graphcal shape templates for automatc anatomy detecton wth applcatons to MRI bran scans. IEEE Transactons on Medcal Imagng, 16(1):28 { 40, February M. Lades, J.C. Vorbruggen, J. Buhmann, J. Lange, C. von der Malsburg, R. P. Wurtz, and W. Konen. Dstorton nvarant object recognton n the dynamc lnk archtecture. IEEE Transactons on Computers, 42(3):300 { 311, Laurenz Wskott, Jean-Marc Fellous, Norbert Kruger, and Chrstoph von der Malsburg. Face recognton and gender determnaton. In Proceedngs Intern. Workshop on Automatc Face- and Gesture Recognton, pages 92 { 97, Zurch, B. S. Manjunath and Y. W. Ma. Texture features for browsng and retreval of mage data. IEEE Transactons on Pattern Analyss and Machne Intellgence (PAMI), 18(8):837 { 841, August D.J. Wllams and M. Shah. A fast algorthm for actve contours and curvature estmaton. Computer Vson, Graphcs, Image Processng, 55:14 { 26, Wolfgang Sorgel, Sabne Grod, Martn Szummer, and Bernd Grod. Computer aded dagnoss of bone tumors n the facal skeleton. In Bldverarbetung fur de Medzn, pages 179 { 183. Sprnger, March 1998.