Caractérisation de cas atypiques de la maladie de parkinson

INSTITUT DE LA FRANCOPHONIE POUR LINFORMATIQUE LABORATOIRE LORRAIN DE RECHERCHE EN INFORMATIQUE ET SES APPLICATIONS UMR 7503 Caractộrisation de cas atypiques de la maladie de Parkinson Mộmoire de fin dộtudes Master dInformatique Etudiant : NGUYEN Huu Giao Encadrants : M Bertrand Kerautret Maợtre de confộrences Universitộ Henri Poincarộ, IUT St Diộ Mme Isabelle Debled-Rennesson Habilitation Diriger des Recherches Universitộ Henri Poincarộ Aoỷt 2008 54506 Vandoeuvre-lốs-Nancy Cedex - France Table des matiốres Introduction 1.1 Problộmatique 1.2 Motivation 1.3 Objectifs initiaux du sujet 1.4 Contexte mộdical et contribution 1.5 Environnement de stage 1 3 Estimateurs de courbure 2.1 Couverture tangentielle et espace de tangente 2.2 Couverture tangentielle et segments flous 2.3 Calcul de la courbure par optimisation 2.4 Analyse et Comparaison 5 10 10 10 15 16 16 17 18 Extraction du contour partir de la forme de rộfộrence 3.1 Construction de la liste des candidats potentiels 3.1.1 Extraction du chemin passant entre deux points 3.1.2 Mộthode de la construction des candidats potentiels 3.2 Sộlection du meilleur contour 3.2.1 Contrainte du minimum local dộnergie 3.2.2 Contraintes sur la longueur du contour 3.2.3 Contraintes sur la courbure Expộrimentation & Application 19 Conclusion 25 A Publication la confộrence international 28 i Table des figures 1.1 1.2 Limage exemple du cerveau humain Illustration du rộsultat de la segmentation de la zone associộe au tronc cộrộbral 2.1 2.2 2.3 2.4 2.5 Illustration de couverture tangentielle(a) et des pentes (b) Illustration du vecteur des points dappui de lenveloppe convexe Illustration des diffộrentes configurations Illustration de la tangente estimộe Les rộsultats et comparaison de lestimateur GMC avec lestimateur de courbure discrốte basộ sur le cercle circonscrit La comparaison des estimateurs GMC et NDC 9 Illustration de lalgorithme de recherche de frontiốres Illustration des images gradients Un cas exemple du besoin de la construction de la liste de candidats Illustration de la liste des candidats potentialitộs Illustration dune courbe de lộnergie de tous les candidats de (a) et des contours des candidats (b) Illustration des plusieurs contours avec la mờme courbure Illustration des contours diffộrences de la liste de candidats avec les deux premiers contraintes sur une image noise de cercle (R = 61) 11 12 15 15 La construction du cercle R = 61 dans une image bruite Le rộsultat a obtenu sur une autre image bruitộe qui contient deux cercles bruitộes avec un rayon R1 = 88 et R2 = 65 Un exemple de re positionnement automatique des points rộfộrences.(R=88) Limage de cas rộfộrence pour le but de obtenir la courbure rộfộrence Cref Lextraction de la zone associộe au tronc cộrộbral du patient1 Lextraction de la zone associộe au tronc cộrộbral du patient2 Un exemple complete des extractions du tronc cộrộbral du patient2 19 2.6 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.1 4.2 4.3 4.4 4.5 4.6 4.7 ii 16 17 18 20 21 22 23 23 24 Liste des tableaux 4.1 4.2 4.3 4.4 4.5 4.6 Les rộsultats dexpộrimentation dun cercle R = 61 dans la Fig 4.1(b) Les rộsultats dexpộrimentation dun cercle R = 61 avec la mauvais initialisation des points rộfộrences dans la Fig 4.1(c) Les rộsultats dexpộrimentation du plus grand cercle R = 88 dans la Fig 4.2(b) Les rộsultats dexpộrimentation du petit cercle R = 65 dans la Fig 4.2(c) Les rộsultats dexpộrimentation avec MRI du patient1 et du patient2 Les rộsultats dun exemple complete des extractions avec MRI du patient2 iii 20 20 21 21 23 24 Remerciements Je voudrais tout dabord exprimer ma profonde reconnaissance M.Bertrand Kerautret et Mme.Isabelle Debled-Rennesson, mes responsables de stage, qui ont dirigộ mon travail Ses conseils et ses commentaires prộcieux mont permis de surmonter mes difficultộs et de progresser dans mes ộtudes Je tiens remercier tous les membres de lộquipe ADAGIo, LORIA Nancy pour leur accueil, leur sympathie ainsi que leurs idộes constructives Je remercie aussi tous les professeurs pour les connaissances quils mont transmises dans annộes de lIFI Je remercie mes parents, ma famille, mes amis pour leur soutien constant lors de mes ộtudes Enfin, merci ma petite amie, Uyen.Luong pour ta patience iv Rộsumộ Un estimateur robuste de la courbure discrốte a ộtộ proposộ rộcemment par Kerautret et al [1] Dans ce document, nous exploitons la prộcision et la stabilitộ de cet estimateur afin de dộfinir une mộthode dextraction des contours pour analyser les caractộristiques gộomộtriques Nous proposons dutiliser une fonction courbure de rộfộrence pour lextraction de la frontiốre dune forme dans une image en niveaux de gris La frontiốre dextraction se fait en utilisant des informations gộomộtriques reprộsentộes par la courbure de rộfộrence et en utilisant aussi des informations gradients de limage source Lapplication de ce travail est accomplie dans une application mộdicale, qui concerne la contribution la caractộrisation des formes atypiques de la maladie de Parkinson Nous proposons une technique de mesure sur latrophie du tronc cộrộbral en mesurant la courbure dans le domaine discret La premiốre partie de ce travail a ộtộ consacrộe analyser le problốme principal et la motivation du sujet de stage La deuxiốme partie concerne les notions principales de "Estimateur robuste de courbures par optimisation globale" (GMC) dans un travail prộcộdent travail Dans la troisiốme partie de ce document, nous proposons une stratộgie pour dộfinir une liste des contours pour lanalyse les caractộristiques gộomộtriques et pour extraire ces contours Les rộsultats de cette approche est une application de comparer les courbes des cas pathologiques et des cas normales de la maladie de Parkinson sur les IRMs du cerveau de patients de la rộgion Guadeloupe et quelques expộriences sur les autres types dimages sont prộsentộes dans la derniốre partie v Abstract A robust discrete curvature estimator was recently proposed by Kerautret and al [1] In this master thesis, we exploit the precision and stability of this estimator in order to define a contour extraction method for analysing geometric features We propose to use a reference curvature function for extracting the frontier of a shape in a gray level image The frontier extraction is done by using both geometric information represented by the curvature of reference and by using gradient information contained in the source image The application of this work is done in a medical application, which concerns the contribution to the characterization of atypical forms of Parkinsons disease We introduce a technical measure on the atrophy of the brain stem measuring in the domain of discreet curvature The first part of this work has been devoted to analyse the problem pricipal and the motivation of the sujet de stage.The second part concerns to some main notions of the robust estimator of curvature along digital contours with global optimization algorithm (GMC) of previous work In the third part of this document, we propose a strategy to define a list of contours for analysing geometric feature and to extract these contours The results is a application to compare the curves of pathological cases and normals cases of the Parkinsons disease on the MRIs(Magnetic resonance imaging) brains of patients in the region Guadeloupe and some experiments on several others types of images are presented in the last part vi Chapitre Introduction 1.1 Problộmatique Lextraction des caractộristiques gộomộtriques des objets discrets est une ộtape importante dans le domaine de lanalyse dimage Lapplication de ce domaine est vaste comme dans limagerie mộdicale ou larchộologie Les estimateurs de laire, le pộrimốtre ou la courbure sont utilisộs pour caractộriser les objets discrets dintộrờt Le rộsultat de la mesure des informations gộomộtriques prộcis nest pas toujours une tõche facile, parce que la mesure des informations gộomộtriques dộpend de lestimateur gộomộtrique utilisộ mais aussi dộpend de la technique fournissant les contours discrets Lidộe principale de ce travail est de proposer une mộthode pour retrouver la forme du contour directement par lextraction de la frontiốre partir de contraintes gộomộtriques Les contraintes gộomộtriques seront dộfinies par la courbure fonction permettant dobtenir une solution initialisộe par lutilisateur Il existe des diffộrentes approches robustes quont ộtộ proposộes dans le domaine de la segmentation dimage En gộnộral, les composantes de limage comme le contour ou la rộgion sont extraites partir dinformations a priori Cette information peut ờtre dộfinie, par exemple, comme un modốle gộomộtrique de rộfộrence, les contraints ou linteraction avec lutilisateur Un exemple bien connu est lapproche de minimisation dộnergie telles que les "snake" ou contours actifs [2, 3, 4] Une autre approche appelộe Active Shape Model (ASM) [5, 6, 7] a utilisộ un modốle paramộtrique pour lextraction des formes Ils ont utilisộ les informations statistiques pour dộfinir des paramốtres Une autre technique bien connue pour la segmentation discrốte interactive est lalgorithme intelligent scissors [8] Cette technique permet lutilisateur de dộfinir les contours par limage gradient et de calculer le coỷt minimal entre points dộfinis par lutilisateur Il a ộtộ utilisộ souvent dans les applications mộdicales pour mesurer les formes [9, 10] Dautres techniques exploitent cette idộe (lazy snaping [11],enhanced lane [12] or grabcut [13]) Lexploitation directe de la courbure quantitative ộvolution na pas ộtộ encore appliquộe pour donner des contraintes a priori sur le contour extraire Mờme si Schoenemann et Cremers ont prộsentộ un estimateur de courbure pour dộterminer une solution optimale [14], mais leur approche nutilise pas la courbure comme un modốle de rộfộrence Un autre travail de Farber et al.[9] proposent une technique utilisant lalgorithme du livewire et qui se basent sur lassociation des structures de chaque images Dans ce cas, la courbure est seulement utilisộe comme un paramốtre pour le contour dassociation Notre principal objectif dans ce mộmoire est lutilisation des descriptions quantitatives de la forme de la courbure afin dextraire prộcisộment les informations gộomộtriques des contours de faỗon semi-automatiques Notre approche est basộe sur le Global Min-Curvature(GMC) estimateur introduit dans [1] et sur lalgorithme du plus court chemin dộfini sur la mộthode Live-Wire Lavantage principal de lestimateur GMC est la robustesse au bruit et la stabilitộ qui permet dextraire directement linformation gộomộtrique 1.2 Motivation La motivation de ce sujet est le dộveloppement dune application mộdicale qui utilise les techniques efficaces de la segmentation des objets discrets pour le but de la caractộrisation de formes atypiques de la maladie de Parkinson La Maladie de Parkinson [15, 16, 17] Laperỗu : La maladie de Parkinson est une maladie du systốme nerveux qui entraợne une perte du contrụle des muscles Elle affecte environ 0,4% des personnes õgộes de plus de 40 ans et 1% de celles qui ont plus de 65 ans Bien que lõge moyen dapparition de la maladie de Parkinson soit 57 ans, il arrive que la maladie dộbute pendant lenfance Les causes : Bien que les cellules du cerveau qui rốglent les mouvements (neurones moteurs) soient situộes dans la partie supộrieure du cerveau, elles ont besoin dune substance chimique appelộe dopamine, qui est produite dans le tronc cộrộbral (noyaux gris centraux) Une des causes de la maladie de Parkinson est la dộformation du tronc cộrộbral Fig 1.1 Limage exemple du cerveau humain Le tronc cộrộbral est la partie du systốme nerveux central situộe lintộrieur du crõne (encộphale), entre le cerveau proprement dit et la moelle ộpiniốre au-dessous Il sert de passage aux nerfs qui vont vers le cerveau et ceux qui en partent : ce sont les voies de la sensibilitộ et de la motricitộ (faisceau pyramidal et extra-pyramidal) Lanatomie : Le tronc cộrộbral est situộ entre la moelle ộpiniốre et le cerveau Il comprend de bas en haut : Le bulbe rachidien (jonction avec la moelle ộpiniốre cervicale) La protubộrance annulaire Les pộdoncules cộrộbraux (connectộs aux hộmisphốres cộrộbraux) Le tronc cộrộbral Fig 1.1 est accolộ en arriốre au cervelet par les pộdoncules cộrộbelleux Il est divisộ en trois parties et contient des fragments de substance grise (les noyaux), consti2 tuant lorigine des nerfs crõniens Une cavitộ remplie de liquide cộphalorachidien, le quatriốme ventricule cộrộbral, est contenue dans le tronc cộrộbral et dans le cervelet qui dộlimite les cavitộs 1.3 Objectifs initiaux du sujet Lidộe de ce sujet est de proposer une technique de mesure sur latrophie du tronc cộrộbral en mesurant dans le domaine discret la courbure de celui-ci sur une vue sagittale et sur sa surface supộrieure Cette technique est composộ des trois ộtapes principales suivantes : Segmenter la zone associộe au tronc cộrộbral Cette ộtude pourra sappuyer sur des techniques de segmentation en rộgions associộes au tronc cộrộbral par le mode dinteraction avec lutilisateur et pourra proposer une stratộgie pour sộlectionner la meilleure solution parmi lensemble des rộsultats de segmentations Fig 1.2 Illustration du rộsultat de la segmentation de la zone associộe au tronc cộrộbral Extraire la courbure du tronc cộrộbral Cette ộtude pourra sappuyer sur des estimateurs connus comme lestimateur discret introduit dans [18] Il sera aussi important de mesurer linfluence du traitement des images sources par rapport la technique de la mesure de la courbure utilisộe En particulier, la prise en compte du bruit dans les techniques destimation de la courbure [19], [20] pourrait permettre damộliorer certains rộsultats Dộtecter les cas pathologiques Cette ộtude pourra proposer une stratộgie pour la comparaison les courbures des cas pathologiques et des cas normaux 1.4 Contexte mộdical et contribution Ce sujet contribue la caractộrisation de formes atypiques de la maladie de Parkinson spộcifiques la Guadeloupe qui induisent en quelques annộes un handicap moteur sộvốre et pour lesquelles aucun traitement rộellement efficace nest connu Ces formes de la maladie pourraient toucher approximativement 1% de la population de plus de soixante-cinq ans, soit 1000 personnes pour la rộgion Guadeloupe En Guadeloupe, selon une ộtude clinique prospective au sein des parkinsoniens atypiques, formes ont ộtộ identifiộes, parmi lesquelles deux formes sont majoritaires : le Complexe La derniốre expộrimentation de cette approche est prộsentộe dans la Fig 4.7 Cest une expộrimentation complốte de lextraction des zones associộes au tronc cộrộbral Avec cet expộrimentation, on doit initialiser ensembles des valeurs de rộfộrence qui sont obtenus par dautres expộrimentations et sont prộsentes par les quatre premiốres colonnes du tableau 4.6 Le tableau 4.6 reprộsente aussi les informations des rộsultats de lextraction dimage du patient2 Dans la deuxiốme ligne de cette tableau, le signe de la courbure rộfộrence et de la courbure rộsultat de lextraction est nộgatif, parce que le sens de linitialisation est diffộrente (a) patient (2) (b)curvature value C=0.0601736 (c) curvature value C=-0.186659 (d)curvature value C=0.0845255 Fig 4.7 Un exemple complete des extractions du tronc cộrộbral du patient2 Image b c d Cref 0.0549 -0.15 0.087 Errperi 0.5 CM ax 0.05 -0.1 0.06 CM in 0.1 -0.2 0.1 CResult 0.0601736 -0.186659 0.0845255 Nall 128 25 70 Nest 80 19 32 time(ms) 3153 170 671 Tab 4.6 Les rộsultats dun exemple complete des extractions avec MRI du patient2 24 Chapitre Conclusion Dans ce document, nous avons proposộ une nouvelle approche pour lextraction du contour dune image par lanalyse des informations gộomộtriques des objets discrets Ce travail est basộ sur un estimateur robuste de la courbure discrốte et sur les informations gradients dimage pour la construction le plus court chemin La sộlection du contour a utilisộ des contraintes gộomộtriques et photomộtriques qui sont initialisộes par une fonction de courbure de rộfộrence dộfinie par lutilisateur Comme perspectives, on va dộfinir une technique dinitialisation automatique de la fonction de courbure par dộtecter automatiquement les points de rộfộrence La mộthode danalyse en composant principales (ACP) est une des techniques convenables [5] Ce sujet se fait dans la cadre danalyser et dappliquer les estimateurs de la courbure discrốte de la thộmatique de ô gộomộtrie discrốte ằ de lộquipe ADAGIo Nous avons exploitộ la prộcision et la stabilitộ de lestimateur "Estimateur robuste de courbures par optimisation globale" GMC En fait, cette approche peut sadapter facilement avec des autres estimateurs On peut analyser et comparer lexactitude et la stabilitộ de ces estimateurs Dans le cadre de ce travail on a essayộ appliquer lestimateur NDC [26] Pour la perspective, on peut utiliser plusieurs estimateurs pour la sộlection des candidats du contour Ce travail a contribuộ la caractộrisation de formes atypiques de la maladie de Parkinson Une application de ce travail a bien contribuộe au dộveloppement dune application mộdicale de mesure sur latrophie du tronc cộrộbral des images MR du cerveau des patients Pour les travaux venir, on va ộtendre cette approache aux images en trois dimensions On va estimer non seulement la courbure de contour mais aussi va examiner la surface du tronc cộrộbral par appliquer la mộthode de 3D live-wire segmentation [31] et lestimateur de caractộristiques de courbure sur des surfaces bruitộes [32] 25 Bibliographie [1] Kerautret, B., Lachaud, J : Robust estimation of curvature along digital contours with global optimization In et al., C., ed : Proc of the Int Conf on DGCI Volume 4992 of LNCS., Springer (2008) 334345 [2] Kass, M., Witkin, A., Terzopoulos, D : Snakes : Active contour models International Journal of Computer Vision 1(4) (1988) 321331 [3] Caselles, V., Kimmel, R., Sapiro, G : Geodesic active contours In : ICCV (1995) 694699 [4] Lachaud, J.O., Vialard, A : Discrete deformable 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boulevard de lhụpital 75013 paris (2007) [31] Malmberg, F., Vidholm, E., Nystrửm, I : A 3d live-wire segmentation method for volume images using haptic interaction In : In Proc of the Int Conf on DGCI Volume 4245 of LNCS., Springer (2006) 663673 [32] Provot, L., Debled-Rennesson, I : Geometric feature estimators for noisy discrete surfaces In : In Coeurjolly et al., editor, Proc of the Int Conf on Discrete Geometry for Computer Imagery Volume 4992 of LNCS., Springer (2008) 275286 27 Annexe A Publication la confộrence international ISVC08 - Las Vegas, Nevada, USA http ://www.isvc.net/ 28 Discrete Contour Extraction from Reference Curvature Function H.G Nguyen1 , B Kerautret1 , and P Desbarats2 LORIA, Nancy-University 54506 Vanduvre -l`es-Nancy Cedex, France {kerautre,Huugiao.Nguyen}@loria.fr LaBRI, University of Bordeaux 351, cours de la Libration 33405 Talence, France desbarat@labri.fr Abstract A robust discrete curvature estimator was recently proposed by Kerautret et al [1] In this paper, we exploit the precision and stability of this estimator in order to define a contour extraction method for analysing geometric features We propose to use a reference curvature function for extracting the frontier of a shape in a gray level image The frontier extraction is done by using both geometric information represented by the curvature of reference and by using gradient information contained in the source image The application of this work is done in a medical application Introduction Extracting geometric characteristics of digital objects is an important step in the field of image analysis The application domain is large like in medical imaging or in archaeology Area, perimeter or curvature estimator can be used to characterize digital objects of interest Obtaining precise geometric measure is not always a simple task since it depends both on the geometric estimators and on the technique providing the digital contour The main idea of this work is to propose a method for recovering contour shape by directly extracting the frontier from geometric constraints The geometric constraints will be defined mainly by the curvature function allowing to obtain a solution from user initialisation even when several contours can be found (see figure above) Numbers of different approaches were proposed throughout the literature dealing with image segmentation Generally the image components are extracted from a contour or region approach which exploits additional an a priori information This information can be defined for example from smoothness constraints, geometric model of reference, or user interaction A well known example of Energy-minimizing approach including smoothness constraints are the snake or active contours [24] Another approach called Active Shape Model (ASM) [5] This work was partially funded by the ANR project GeoDIB Bertrand Kerautret was partially funded by a BQR project of Nancy University used a parametric model for extracting shapes They used statistical information to define parameters Another well known technique for discrete interactive segmentation is the intelligent scissors [6] This technique helps the user to define contours by computing image gradient and computing minimal path from user defined points It was frequently used in medical application for shapes measures as in [7, 8] Other more recent techniques exploit this idea (lazy snaping [9], enhanced lane [10] or grabcut [11]) Exploiting directly the quantitative curvature evolution was not yet applied to give a priori constraints for shape/contour extraction Even if recently Schoenemann and Cremers introduced curvature to determine globally an optimal solution [12], their approach does not use quantitatively the curvature as a reference model Another recent work from Făarber et al proposed a Live-wire based segmentation approach to associate corresponding image structures In that case, the curvature was only used as a parameter for the contour association [7] Our main objective is to use quantitative description of the shape from the curvature values in order to extract contours and to perform semi-automatics precise geometric measures The curvature will there guide the segmentation process Our approach is grounded on the Global Min-Curvature (GMC) estimator introduced in [1] and is using the shortest path algorithm defined on the live-wire method The main advantage of the GMC estimator is the robustness to noise and the stability which allows to extract directly geometric information as for example the points of local maxima/minima curvature The paper is organized as follows: some main notions of the curvature estimator of previous work are reviewed in the following section Then section introduces the proposed method used to construct and select a list of candidates for the contour between two reference points Finally, section is devoted to the medical application which validates our approach by some experiments on several types of normal and pathological MR images of human brain Curvature Estimator Global Min-Curvature estimator The main idea of the GMC estimator is first to take into account all the shapes having the same discretization and to select the more probable shape Using this approach we can expect to obtain a precise estimator with low resolution shape The second objective was to obtain precise results even with non perfect digitization processes inducing noisy contours Following the first objective, local bounds on tangent directions were defined from the maximal straight segments and then the curvature was computed by a global minimization approach (see Fig 1) More precisely, by denoting C the mapping which associates to an arc length s the direction of the tangent at point C(s) (C = (0x, C )), the curvature minimization is defined as follows: L = J[C] = C L (s)ds = 0 dC ds ds (1) upper leaning pts lower leaning pts minimum slope slope a/b maximum slope (a) (b) Fig (a): tangential cover of the boundary of a digitized shape, where each maximal segment is drawn as a black bounding box aligned with its slope (b): slope of a maximal segment and estimation of maximal and minimal slopes with leaning points where |C| stands for the euclidean length of C The shape of reference to O is the shape in F of boundary C which minimizes J[C] and which is digitized as O From the tangent bounds, the minimization is performed by a relaxation approach (more details can be found in [1]) To be resistant to noise (our second objective) we extend this approach by replacing discrete maximal segments with the maximal blurred segments proposed by Debled et al [13] The maximal blurred segments are defined from a width and allow us to have a multi-level adapted estimator Analyse of precision of discrete estimators The resulting curvature gives precise and stable results As illustrated in Fig 2, the precision given on a circle shows precise results compared for example to the estimator based on osculating circles [14] The column (c) illustrates the extraction of local minima/maxima on a generated font obtained at 300 dpi We can see that the GMC estimator gives good local minima/maxima compared to the GMC estimator The bad results of the CC estimator are due to the lack of stability since numerous oscillations appear even with large resolution Note that the local minima/maxima values were simply extracted from the curvature graph by a simple values quantification for a given precision Contrarily to other curvature estimators no post-processing is needed in order to exploit values and thus, there is no risk of degradation of the extracted geometric information Resistance to noise and comparisons Experiments and comparisons were applied on noisy shapes and obtained with others estimators The GMCB estimator was compared with the blurred version of CC estimator proposed by Nguyen and Debled [15] (called NDC estimator) As in the smooth case, the GMC estimators always show more precision and stability than NDC estimators Details and comparisons can be found in previous work [1] 0.050005 0.1 GMC estimator: grid step=0.1 0.05 GMC estimator: grid step=0.1 CC estimator: grid step=0.1 0.05 0.049995 0.04999 -0.05 0.049985 -0.1 0.04998 -0.15 0.049975 -0.2 0.04997 -0.25 0.049965 -0.3 20 40 60 80 (a) 100 120 140 160 180 20 40 60 80 100 120 140 160 (b) 180 (c) Fig Results and comparisons with the CC estimator on a circle of radius 20 with grid step =0.1 (graph (a) and (b)) Extraction of the local maxima/minima with GMC (top of column (c)) and CC estimators (bottom of column (c)) Dark (resp light) areas represent local minima (resp maxima) (green (resp blue) ) In the following our main idea is to exploit the stability and the precision of the GMC estimator in order to define a robust new approach for shape segmentation Moreover the resistance to noise with the choice of the parameter associated to the width used for the analysis can contribute to new perspectives Contour Selection from Curvature Information We define by Ps , Pe the two reference points which need to be initialized by the user in respect to the reference curvature The reference geometric informations of segment Ps Pe are defined as constant From the initial reference shape, we compute the mean curvature value Cref of Ps Pe by using GMCB estimator with a specific width defined according noise level of the image We estimate a possible distance for a change of this curvature by two values : Cmax and Cmin The admissible ratio error of the perimeter Errperi of Ps Pe is also initialized 3.1 Construction of the list of the potential candidates Let us construct a shortest path map from a target point to all other points in the image The cumulative cost of a path from a target pixel was proposed by Mortensen et al in 1995 [6] The local cost of the image pixels is defined from the different edge features In this work, the Sobel operator was used to compute the gradient magnitude fG and the gradient direction fD of the source image The information of laplacian zero-crossing fZ and Edge Pixel Value fI are considered as the important components of the cost of the pixel To increase noise robustness, we chose the following function to determine the cost from a point p to a neighboring point q: l(p, q) = 0.7 fG + 0.1 fD + 0.1 fZ + 0.1 fI (2) After computing the local cost of the pixels, we use the shortest path algorithm [16] to construct the relation map from a reference point to all other points of the image We denote the shortest path from Ps and Pe by S(Ps , Pe ) which is easy to extract from the shortest path map of Ps The shortest path getting from point Ps to Pe through point pk is denoted by Sk : Sk = {S(Ps , pk ), S(pk , Pe )} In order to recover the closest contour to the ideal reference solution, we need to obtain a list of potential candidates For this purpose, we propose a method to construct a list of potential candidates A associated to the segment Ps Pe We denote by Ps and Pe the image of Ps and Pe obtained by a rotation of centered at M defined as the center of Ps Pe The list of potential candidates A associated to the angle is defined by: P2 pi M1,2 pk P1 A = {Qk |Qk < a x + b y + c < + and Qk M > Qk+1 M }; with: a , b , c associated to the straight segment defined by (Ps , Ps ) To increase the probability to obtain the best candidate list, we use three values of : 3 4 The , and The total list of candidate points A is then A = A A A construction of the potential candidates is illustrated with the previous floating figure 3.2 Selection through the possible candidates From the list of possible potential candidates, we propose the following three selection steps in order to select the best contour according the geometric and photometric image constraints Selection based on local minima value of energy : The first selection of candidates is based on its energy value in order to retain only the significant points and to reduce the number of candidates We compute the energy Ek defined for each point pk A by: Ek = G(Sk ) = G(S(Ps , pk )) + G(S(pk , Pe )) The function G gives the average value of a path coast and can be defined P i=0,l g(xi ) as: with g(x) giving the coast function of the discrete point x in the l shortest path algorithm Then, the new list of candidates A1 is selected by minimizing locally the energy Ek of all candidates of the list A 0.3 all candidates Energie function Min locaux selectioned candidates (local minima energy) 0.29 0.28 0.27 0.26 0.25 0.24 0.23 10 20 30 40 50 60 70 80 90 100 (a) (b) Fig Illustration of the energy curve associated to each candidate (computed on the segment Ps , Pe ) The candidates with local minimal energy are represented by a blue cross (a) The contours associated to each candidate are is represented in figure (b) The contour with local minimal energy are represented in blue with large line width Selection according length constraint After using the information of local energy to remove the weak candidates, we can bypass the particular ambiguous cases of candidate by using the length constraint It is particularly relevant because in some particular cases there can exist several contour solutions with the same curvature value The following figure on the right illustrates such a particular Pe case To avoid this ambiguity, we estimate the length Lk defined for each candidate pk A1 of Ps Pe as follows: d(xi , xi+1 ) where d(xi , xi+1 ) gives the distance from xi to the next neighbouring in the contour candidate xi+1 In order to get a sig- Ps nificant value of length for a candidate, we must detect special configurations where the contours overlap From the information of length Lk of contour, we select the new list of candidates A2 by the following constraint: A2 = {pk | |Lk Lref | Errperi }; Lref Fig 3.2 shows an example of candidate selection obtained from the initial list (a) representing all the initial candidates Adding curvature constraints : When the second selection of candidates is done, we use GMCB estimator to measure the curvature value Cki of the points i in the candidate list pk A2 of Ps Pe Since the curvature estimator is stable enough, the curvature values are useful to evaluate these remaining candidates and to select the best candidate of an interval Ps Pe The average value of curvatures Ck of candidate k is defined as Ck = P i=0,n n (Cki ) where n is the number of points for this candidate The smallest list (a) (b) (c) Errperi < 10% (d) Errperi < 5% Fig Illustration of the candidates obtained on a noisy circle (R = 61) Four points on the top, bottom, left, right of the circle are used to build the list of four segments Ps Pe Image (a) represents all potential candidates Image (b) shows the contours of (a) which have the minimal local energy and without the overlapping contours The two images (c) and (d) show the selected candidates which satisfy the length constraint Errperi of candidate A3 will be selected by a constraint to limit the range of curvature : A3 = {pk |CMin Ck CMax }; We calculate the value quadratic error between the average curvature of candidate pk A3 and the curvature of its reference which is defined as : Errquad = (Ck Cref )2 The minimal value of Errquad is used to determine the best contour of interval Ps Pe Experiments and application Our first experiment (Fig 5) illustrates the results obtained on a damaged circular test shape The reconstruction was obtained from a constant curvature value of 0.0163 and the length error constraint was set to 20% All of candidats are represented in green The contours were well recovered in white, even with a non precise initialisation (c), the global contour is correct Note that initial points could be easily adjusted in a post processing step The illustration images of the introduction shows the results on noisy images obtained with several reference curvature values The main objective of our approach is to use quantitative description of the shape from the curvature values in order to extract contours An application of the use of these curvature values is to make an early diagnostic of a particular Parkinsons disease syndrome Progressive Supranuclear Palsy (PSP) is an atypical degenerative parkinsonian syndrome [17] It leads to postural instability with falls up to subcortical dementia Its diagnostic can be established by clinicians using conventional MRI exams However, the differentiation between different parkinsonian syndromes is not easy and often leads to erroneous diagnostics [18] Furthermore this differentiation is only qualitative and very difficult (a) (b) (c) Fig Results obtained on a test image (a) The curvature of reference was set to 0.0163 Image (c) shows the result with a non perfect initialisation to achieve in the earlier stages of the syndrome, when medical treatment is still able to slow down the degenerative process It is thus important to develop a quantitative method to make an earlier diagnostic for this particular syndrome PSP can be spotted in MR images as an atrophy of the mid-brain part of the brain stem This atrophy leads to a curvature changing on the upper surface of the mid-brain The images used in the following experimentation were undertaken on a Philips Medical Systems 1.5 Tesla Intera MR acquisition system using a T1 SE (Spin Echo) scanning sequence Fig shows the result obtained on two cases extracted from MR images which were used to diagnose PSP The results shown on the first row were obtained from a set of reference values (Cref = 0.0549, Errperi = 1, CMin = 0.05, CMax = 0.1) The contours were correctly extracted with the curvature value C1 = 0.0540354 Since the curvature result of the healthy patient is close with the Cref of , we continued to used the for the comparison with the others MR images The image in the second row seems to be a suspected case of PSP The curvature value of the best contour was C2 = 0.0605799 The distance between the obtained curvature value to the reference value Cref is used to discriminate the images and to diagnose pathological cases Our last experiment for this approach is depicted in the third row of Fig which shows the contour extraction of three parts of the brain stem of MR image Here, we must use three sets of reference value Note that the curvature sign of (c) is negative since we consider the initialisation order The tabular in figure Fig 6(j) shows timing measures with the number of candidates needed by the optimization process, where Nall and Nest are respectively the total number of candidates and the number of candidates which have been evaluated This measures were obtained on a 1.5GHz Intel Celeron M processor with MR images of resolution 300 ì 300 pixels Conclusion The main contribution of this work was a proposition of a new simple way for extracting image contours by using predefined curvature informations The ex- (a) patient (1) (b) all candidates (c)curvature value C=0.0540354 (d) patient (2) (e) all candidates (f)curvature value C=0.0605799 (g) (h) (i) Image g1 g2 g3 Cref Errperi 0.0549 -0.15 0.5 0.087 CM ax 0.05 -0.1 0.06 CM in CResult Nall 0.1 0.0601736 128 -0.2 -0.186659 25 0.1 0.0845255 70 Nest time(ms) 80 3153 19 170 32 671 (j) Fig Results and comparisons on two MR images (first and second row) Images (b,e) illustrate all the candidates used for the solution selection and the selected contours are shown in (c,f) The third row show other contours extraction obtained with other curvature parameters Tabular (j) shows parameter values and time measures 10 traction was based on a robust curvature estimator and on the construction of shortest paths from image gradient informations The application to medical application appears promising and future work will deal with the medical validation in the context of the parkinsons atypical disease Another future work will deal with the extension of this approach to 3D images References Kerautret, B., Lachaud, J.: Robust estimation of 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I.: Curvature estimation in noisy curves In: CAIP Volume 4673 of LNCS., Springer (2007) 474481 16 Dijkstra, E.: A note on two problems in connexion with graphs Numerische Mathematik (1959) 269271 17 Savoiardo, M.: Differential diagnosis of parkinsons disease and atypical parkinsonian disorders by mangnetic resonance imaging Neurol Sci 24 (2003) 3537 18 Schrag, A., Good, C., Miszriel, K., Morris, H., Mathias, C., Lees, A., Quinn, N.: Differentiation of atypical parkinsonian syndromes with routine mri Neurology 54(3) (2002) 697707 [...]... les cas particuliers du syndrome de la maladie Parkinson La paralysie supra nuclộaire progressive (PSP)(appelộe aussi maladie de Steele-RichardsonOslewski) est un syndrome atypique du parkinsonien dộgộnộratif [16] Elle dộbute obligatoirement aprốs lõge de 40 ans et est lorigine de 10 15 % des syndromes parkinsoniens Il sagit dun syndrome parkinsonien relativement symộtrique prộdominant sur la musculature... Alors, la fonction de coỷt fG de la partie de gradient magnitude est : fG (p) = 1 G(p) Gmin Gmax Gmin Laplacian Zero-Crossing fZ : Laplacien est une dộrivation au deuxiốme ordre : L(x, y) = 2I 2I + x2 y 2 Dans le cas dune image, il nexiste pas une dộrivộe seconde unique mais quatre dộrivộes partielles En pratique, on lốve cette ambiguùtộ en ayant recours opộrateur laplacien qui fait la somme des deux... concernant le bruit dans la dộrivộe premiốre sont encore plus importantes dans les calculs de dộrivộe seconde On utilise donc couramment une combinaison de lissage et laplacien ce qui correspond au laplacien dune gaussienne Lestimation de la dộrivộe seconde ộtant trốs sensible aux bruits, il convient de filtrer trốs fortement limage avant den mesurer le laplacien La matrice est de convolution : 1 1... 4.4 Limage de cas rộfộrence pour le but de obtenir la courbure rộfộrence Cref En fait, la dộtermination de lensemble des valeurs de rộfộrence = {Cref , Errperi , CM in , CM ax } doit ờtre dộfinie en fonction de la forme de rộfộrence Lutilisateur doit identifier la valeur de courbure rộfộrence Cref Ici, on a lancộ cette expộrimentation plusieurs fois avec des images 22 IRM diffộrentes de diffộrents... le cadre de ce travail on a essayộ appliquer lestimateur NDC [26] Pour la perspective, on peut utiliser plusieurs estimateurs pour la sộlection des candidats du contour Ce travail a contribuộ la caractộrisation de formes atypiques de la maladie de Parkinson Une application de ce travail a bien contribuộe au dộveloppement dune application mộdicale de mesure sur latrophie du tronc cộrộbral des images... les candidats de 2 avec Errperi < 5% Fig 3.7 Illustration des contours diffộrences de la liste de candidats avec les deux premiers contraintes sur une image noise de cercle (R = 61) 3.2.3 Contraintes sur la courbure Lorsque la deuxiốme sộlection des candidats a ộtộ faite, nous utilisonslestimateur GMCB pour mesurer la valeur de courbure Ck des candidats k dans la liste un candidat 2 de lintervalle... classification claire 1.5 Environnement de stage Ce travail sinscrit la fois dans la thộmatique ô gộomộtrie discrốte ằ de lộquipe ADAGIo et travers une collaboration avec M.Pascal Desbarats de lUniversitộ de Bordeaux 1 et 2 ADAGIo est une ộquipe du LORIA crộộe depuis janvier 2006 suite la restructuration des anciennes ộquipes Adage et Modbio La thộmatique directrice de cette ộquipe porte sur lalgorithmique... 1 1 1 Alors, la fonction de coỷt fZ de la partie de Laplacian Zero-Crossing est : fZ (p) = 0 si IL (p) = 0 1 si IL (p) = 0 Gradient Direction fD : Le gradient de direction ou dorientation ajoute une contrainte smoothness la frontiốre des images gradients par association de la relation entre les grands coỷts et leur directions dans la frontiốre La direction du gradient est simplement la direction du... On a obtenu la valeur de courbure des candidats dans la liste 2 ( ộtape 3 de la sộlection des candidats) On a choisi une valeur optimale par la main Grace la premiốre expộrimentation, on a obtenu un ensemble des valeurs de rộfộrence 1 = {0.0549, 1, 0.05, 0.1} pour les autres expộrimentations Les deux cas significatifs de plusieurs images IRM des patients qui ont appliquộ par cette mộthode, sont prộsentộs... comme la diffộrence de la direction ou de lorientation est minimisộe L(p, q) = 1 pq p q si D (p).(p q) 0 q p si D (p).(p q) < 0 Edge Pixel Value fP : Edge Pixel Value est une value de niveau de gray dun pixel dans limage origine Alors, la fonction de coỷt fP de la partie de Edge Pixel Value : fP = 1 I(p) 255 14 3.1.2 Mộthode de la construction des candidats potentiels On note Ps et Pe sont les deux