I. Partie and . Chapitre4, Unmodle tridimensionnel de la bifurcation de l'artrecarotide est

L. Bifurcations and R. , 42 4.1.2.1 Les bifurcations et la ponction bronchique, p.42

C. Des-notions, Une information chographique se rfrant une topologie d'embranchement, p.44

I. Partie and . Chapitre3, Passage d'une chographie 2D une chographie 3D 3.3 La localisation spatiale d'un pixel d'une image

.. Exprimentation-en-vueun-pixel-image, 90 3.3.4.1 Description thorique du protocole exprimental, p.96

.. Forces-et-faiblesses-de-ce-systme-d-'acquisition, 97 3.4.1 Les points forts du systme d'acquisition 97 3.4.1.1 L'intrt d'une haute frquence d'acquisition . . . 97 3.4.1.2 Un point fort mthodologique : l'indpendance des processus d'acquisition permet une acquisition optimale, p.97

.. Un-point-fort-technologique, la numrisation des images par l'chographe permet une acquisition chographique lev e, p.97

F. Ses-points, 98 3.4.2.1 Le systme n'est pas temps rel

.. Un-paramtrage-planaire-univoque, Conceptualisation 122 1.1.4.1 La notion de squelette externe merge de considrations physiques sur les coulements çuides au sein des bifurcations, p.122

.. Contraintes-imposes-sur-le-squelette-externe, 140 1.4.3.1 Elimination des points d'inçexions du squelette externe, p.140

.. Le-vecteur-unitaire-vvtt, 154 1.5.4 L'amplitude bbtt, p.155

. Dans-ce-chapitre, j'ai prsent des modles dformables classiques Bien que diçrentes topologies puissent tre envisages au sein de mme modlisation, celle de la bifurcation ne l

. Faisant-rfrence-ces-travaux, je prsente maintenant une mise en correspondance du modle dvelopp avec des donnes de la bifurcation de l'artre carotide Je rappelle rapidement, au lecteur, le plan de la suite de ce second chapitre : Obtention des donnes ; Dçnition d'une fonctionnelle nergtique ; Minimisation de cette fonctionnelle

I. Partie and . Chapitre2, Mise en correspondancedumodle avec les donnes lecteur que la ralisation de ce simple concept n'est pas si triviale

L. Diçcult-de-cet-chantillonnage-rside-dans, directe" entre l'chantillonnage du domaine de paramtrage, et celui de la surface. La discrtisation de la surface est obtenue par un chantillonnage du domaine en t; v : N pt subdivisions de l'intervalle ë,1; 1ë

P. J. Besl, S. Benayoun, C. Nastar, and N. Ayache, Dense non-rigid motion estimation in sequence of 3d images using diçerential constraints. CVRMed, 1995. ëCC92ë L.D. Cohen and I. Cohen. Deformable Models for 3D Medical Images using Finite Element and Balloons Parametric two-dimensional b-spline, representation of vein and artery from 2.5d echography used to aid virtual echography. CVRMed-MRCAS'97-LNCS, Proc. IEEE IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR'922, pp.9366-958, 1988.

T. F. Cootes, A. Hill, C. J. Taylor, and J. Haslam, The use of active shape models for locating structures in medical images, Image and Vision Computing, vol.12266, p.3555366, 1994.

T. F. Cootes, G. J. Page, C. B. Jackson, C. J. Taylor, T. F. Cootes et al., Statistical grey-level models for object location and identiçcation Modelling object appearance using the grey-level surface, Proc. British Machine Vision ConferencePycockk BMVAPr ess Proc. British Machine Vision Conference, pp.5333542-4799488, 1994.

T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, Training models of shape from sets of examples, Proc. British Machine Vision Conference, p.9918, 1992.

T. F. Cootes, C. J. Taylor, and A. Lanitis, Active shape model : Evaluation of amulti-resolution methos for improving image search Euclidean distance mapping Building a Complete Surface Model from Sparse Data Using Stati stical Shape Models : Application to Computer Assisted Knee Surgery, Proc. British Machine Vision Conference W. M. Wells, A. Colchester, and S. Delp, pp.32773362277248-207, 1980.

A. Hill, T. F. Cootes, C. J. Taylor, A. Hill, C. J. Taylor et al., A generic system for image interpretation using çexible templates Object recognition by çexible template matching using genetic algorithms Geometrical modelling of abdominal aortic aneurysms Adder : a snake-based segmentation approach for intravascular ultrasound images : Techniques and application Deformable models in medical image analysis : a survey, Partie III . Bibliographie Medical Image Computing and Computer-Assisted Intervention-MICCAI'98 Proc. British Machine Vision Conference Proc. European Conference on Computer Vision G.Sandini. Ed.., pages 8522856 Proceedings of the 2nd conferenceo n Digital Image Computing ëMG95ë A. Moreau-Gaudry. Dea de mathmatiques appliques : segmentation automatique d'images dynamiques chographiques. 1995. ëMGCB98ë A. Moreau-Gaudry,P . Cinquin, and J.P. Baguet. A new branching model : Application to carotid ultrasonic data Thse : spcialit Mathmatiques, pp.8800887-2766285, 1992.

+. , B. Nazarian, V. Juhan, K. Malkani, R. Bulot et al., Modlisation tridimensionnelle des anvrismes aortiques Generalized image matching : Statistical learning of physically-based deformations Generalized matching for recognition and retrieval in an image database Numerical recipies in c : Second edition. ëPW89ë A. Pentland and J. Williams. Good Vibrations : Modal Dynamics for Graphics and Animation Recovery of parametric models from range images. The case of superquadrics with global deformations, Proceedings of the Fourth European Conference on Computer Vision ECCV'96 ëNMP96bë C. Nastar, B. Moghaddam, and A. Pentland Proceedings of the Third International Conference : Communicating by Image and Multimedia Computer Graphics SIGGRAPH'899, pp.431144121552221311146-214, 1989.

E. Une-comparaison, modle actif" et "extraction puis ajustement", p.214

P. Cinquin, C. Goret, I. Marque, S. Lavallee, R. W. Conners et al., Morphoscopie et modelisation continue d'images 3D A theoretical comparison of textures algorithm, Actes Congres AFCET RFIA 87 Proceedings of MARI, p.4399450119, 1980.

R. C. Ëder87ë-rachid-deriche, . Gonzalez, and R. E. Woods, Using Canny's Criteria to Derive a Recursively Implemented Optimal Edge Detector Digital Image Processing.A ddison-Wesley Publishing Company, 1993. ëHM93ë R. Horaud and O. Monga. Vision par Ordinateur. Hermes, Paris, 1993. ëHNG92ë I. Herlin, C. Nguyen, and C. Graçgne. A Deformable Region Model using Stochastic Processes Applied to Echocardiographic Images, CVPR, 1992. ëHu62ë M.K. Hu. Visual pattern recognition by momentinvariants. IRE Transactions on Information Therory, pp.1677187-181799187, 1962.

M. T. Hueckel, S. Y. Lu, and K. S. Fu, 18 :1133125, 1971. ëIon98ë I. Ionescu. Segmentation et recalage d'images chographiques par utilisation de connaissances physiologiques et morphologiques Joseph Fourier -Grenoble I, 1998. ëKir71ë R. Kirsh. Computer determination of the consistent structure of biological images A syntactic approach to texture analysis, ëMBO92ë O. Monga, S. Benayoun, and Faugeras O.D. From partials derivatives of 3D density images to ridge lines IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR'922, pp.31553283033330-3544359, 1971.

I. Partie, A. Bibliographie, P. Moreau-gaudry, J. P. Cinquin, and . Baguet, Active model based carotid ultrasonic data segmentation, p.1766183, 1999.

D. Marr, E. Hildreth, A. H. Mir, M. Hanmandlu, and S. N. Tandon, Theory of edge detection Texture analysis of ct images, ëPap65ë A. Papoulis. Probability, Random Variables, and Stochastic Processes, pp.187-217, 1965.

J. M. Prewitt, Object enhancement and extraction, PictureP r ocessing and psychopictorics, p.755149, 1970.

L. G. Roberts and S. N. Shir, Machine perception of three-dimensional solids Multiresolution 3d image processing and graphics, Optical and Electro-Optical Information Processing Multiresolution Image Processing and Analysis, pp.1599197-2244236, 1965.

F. Tomita, Y. Shirai, and S. Tsuji, Description of texture by a structural analysisPAMI-4422 :1833191, 1982. ëVV93ë L.J. Van Vliet. Grey-scale measurement in multi-dimensional digitized images, IEEE Trans. Pattern Anal. Mach. Intell, 1993.

W. Wechsler, Texture analysis ??? a survey, Signal Process, p.2711280, 1980.
DOI : 10.1016/0165-1684(80)90024-9

. Dans-ce-chapitre, je propose des solutions des diçcults prcdemment identiçes et prcise des points non encore abords dans les chapitres prcdents. Il me permet ainsi de faire l

. Dans-un-premier and . Temps, je dcris la construction d'une nouvelle surface trois trous partir du modle prcdemment dvelopp Cette surface , plus conforme l'ide de bifurcation, me permet de rpondre aux diçcults de dformations rencontres par le processus actif au niveau de la partie mdiale infrieure du modle. Je proçte aussi de ce paragraphe pour prsenter une rçexion sur les paramtres du modle

I. Partie and . Chapitre1, Possibles amliorations de la modlisation 1.3 Introduction d'une nouvelle information a priori, pp.5-6

I. Dans-le-troisime-chapitre-de-la-partie, inadquation partielle de la modlisation entreprise avec l'objectif recherch. En eçet, une bifurcation se prsente comme une surface trois trous

. Elle-est-simple, En reprenant la modlisation entreprise, je ne considre maintenant que la partie de la surface situe au dessus du plan P cut Ce dernier 1. Comme je l'ai prcdemment soulign, des interfrences entre le paramtre d'chelle S et les paramtres a 1 ; a 2 et a 3 du squelette peuvent exister. Açn de rsoudre ce problme, une premire solution peut consister çxer, pour chaque patient

C. Qu, illustre la çgure 1.3. Cette constatation tant souligne, une modlisation des contours de la bifurcation, tenant compte de l'angle d'incidence des ultrasons par rapport l'interface, constitue une nouvelle et prcieuse information a priori sur le contour recherch

A. Gauche, Pour chaque angle , j'extrais, l'aide d'une interpolation trilinaire, les proçls de niveau de gris centrs sur le contour

. Adroite, Image rsultat de l'extraction des proçls de niveau de gris

. Le-troisime-point-abord-traitait-de-l, injection d'une troisime information a priori de type contour dans le modle, sous la forme d'une modlisation statistique des niveaux de gris des contours. Sa construction m'a amen repenser les principes de l'acquisition chographique. Modlise par l'introduction de l'angle entre la direction d'incidence des ultrasons et la normale au contour recherch, cette nouvelle information a priori me renseigne sur l'aspect du contour recherch ainsi que sur la conçance accorder aux dplacements locaux Comme prcdemment

T. F. Ençn, G. J. Cootes, C. B. Page, C. J. Jackson, and . Taylor, sur la faisabilit d'une surface plus souple, partir d'un squelette surfacique dformable Ce dernier sujet pourrait faire l'objet de travaux plus longs termes. ëBjo96ë A. Bjorck. Numerical Methods for Least Squares Problems Statistical grey-level models for object location and identiçcation, Proc. British Machine Vision Conference, p.5333542, 1995.

T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, Training models of shape from sets of examples, Proc. British Machine Vision Conference, p.9918, 1992.

C. Nastar, B. Moghaddam, and A. Pentland, Generalized matching for recognition and retrieval in an image database Metaxas. Dynamic 3D models with local and global deformations : Deformable superquadrics, Proceedings of the Third International Conference : Communicating by Image and Multimedia, p.7033714, 1991.

P. .. Pulsatile, Sommaire 2.1 Intrts de l'information, pp.6-9

I. Partie and . Chapitre2, Une nouvelle information a priori : la pression pulsatile La premire se propage travers les vaisseaux artriels une vitesse de l'ordre de 8mès 6mès dans l'aorte, 10mès dans l'artre radiale Au cours de son trajet, elle distend les parois artrielles, Cette distension

. Si-de-plus, je peux modliser la relation pressionèrayon par une fonction, par exemplee, l'injection de cette relation dans une modlisation par contours actifs pourrait tre une nouvelle information a priori trs prcieuse. 2.2 Son acquisition

. Dans, ai prsent des premiers lments en vue d'une tude plus objective et reproductible de l'EIMAC. Deux grands axes de recherche ont t investigus : le premier, spciçque cette tude, consistait obtenir de donnes chographiques 3D de la bifurcation de l'artre carotide. A l'aide de briques lmentaires du laboratoire, j'ai dvelopp, en collaboration avec le service d'Hypertension Artrielle de l'hpital Michallon

K. S. Cette-mise-en-correspondance,-celle-ci-est-naturellement-et-eçcacement-approche-suite-bibliographie-Ëahb87ë, T. S. Arun, S. D. Huang, E. Blostein-Ëbai95ë, G. Bainville et al., Least-squares çtting of two 3-d point sets Athrosclrose et Hypertension artrielle Donnes de l'chographie carotidienne quantitative Dveloppement et validation d'un logiciel de mesure The localizer interface users's guide and reference manual Ultrasonic biopsy -a noninvasive screening technique to evaluate the cardiovascular risk and to follow up the progression and the regression of atherosclerosis Ultrasonic three-dimensional imaging and volume from series of arbitrary sector scans Reproducibility of measures of parietal thicknening and of carotid diameter by a ne w automatic analysis program, ëBes88ë P.J. Besl. Geometric modelling and computer vision. Proc. IEEE ëBjo96ë A. Bjorck. Numerical Methods for Least Squares Problems. SIAM 13th Scientiçc meeting of the American Society of Hypertension ëBMMG + 99ë J.P. Baguet, J.M. Mallion, A. Moreau-Gaudry, M. Pheoc, and J.P.Tremel, F.andSiche. Relationship between cardiovascular remodeling and the pulse pressure in never trea ted essential hypertension. 47th Annual scientiçc meeting of the Cardiac Society of Australia and New Ze aland, pp.40050-7811, 0273.

V. Partie, S. Bibliographie, C. Benayoun, N. Nastar, C. Ayache et al., Dense non-rigid motion estimation in sequence of 3d images using diçerential constraints. CVRMed, 1995. ëBri97ë I. Bricault. Endoscopie bronchique assistepar ordinateur Rsolution multiniveaux d'un problme d'optimisation scneèmodle Using 2.5D echography in computer assisted spine surgery, IEEE Engineering in Medicine and Biology Society Proceedings Computer assisted pericardial punctures : animal feasability study. CVRMed- MRCAS'97 ëCC92ë L.D. Cohen and I. Cohen. Deformable Models for 3D Medical Images using Finite Element and Balloons IEEE Computer Society Conferenceo n Computer Vision and Pattern Recognition CVPR'922, pp.1600161-2855294, 1992.

P. Cinquin, C. Goret, I. Marque, S. Lavallee, R. W. Conners et al., Morphoscopie et modelisation continue d'images 3D A theoretical comparison of textures algorithmP arametric two-dimensional b-spline, representation of vein and artery from 2.5d echography used to aid virtual echography. CVRMed-MRCAS'97-LNCS, Actes Congres AFCET RFIA, pp.4399450-2855294, 1980.

T. F. Cootes, A. Hill, C. J. Taylor, J. Haslam, G. John et al., The use of active shape models for locating structures in medical images A pentagonal surface patch for computer aided geometric design Experimental protocol for accuracy evaluation of 6-D localizer s for Computer Integrated Surgery : Application to four optical localizers Outcome in patients with asymptomatic neck bruits, MICCAI'98, pp.3555366-27772858600865, 1983.

T. F. Cootes, G. J. Page, C. B. Jackson, and C. J. Taylor, Statistical grey-level models for object location and identiçcation, Proc. British Machine Vision Conference, pp.5333542-274, 1995.

+. , T. E. Craven, J. E. Ryu, M. A. Espeland, F. R. Khal et al., Evaluation of the associations between carotid artery atherosclerosis and coronary artery stenosis. a case control study Conversion of complex contour line deçnitions into polygonal element mosaics An evaluation of methods for imaging and quantifying coronary and carotid lumen stenosis and atherosclerosis. Circulation, 87 suppl. III :II177II33, 1993. ëCT94ë T.F. Cootes and C Modelling object appearance using the greylevel surface Training models of shape from sets of examples Active shape model : Evaluation of amulti-resolution methos for improving image search Risk factors for extracranial carotid artery atherosclerosis Euclidean distance mapping Extraction de composantes connexes base sur une dtection optimale Using Canny's Criteria to Derive a Recursively Implemented Optimal Edge Detector, Proc. British Machine Vision Conference Proc. British Machine Vision Conference Proc. British Machine Vision Conference Proceedings of MARI ëDD94ë A. Delcker and C. Diener. Quantiçcation of atherosclerotic plaques in carotid arteries by 3d ultrasound ëDes96ë V. Dessenne. GMCAO : applications a la ligamentoplastie et a la chirurgie orthognatique ëDGRL96ë J. Deng, J.E. Gardener, C.H. Rodeck, and W.R. Lees. Fetal echocardiography in 3-dimensions and 4-dimensions, pp.123001242-4799488, 1978.

V. Partie, C. Bibliographie, H. Emile, A. Fuchs, E. Stae et al., Building a Complete Surface Model from Sparse Data Using Stati stical Shape Models : Application to Computer Assisted Knee Surgery Towards performing ultrasound-guided needle biopsies from within a head-mounted display Anatomie humaine. Deux. e'd. Bruxelles : De Boeck Universite', 1993. ëGML + 93ë, and le groupe de prvention cardiovasculaire en mdecine du travail. Evidence for in vivo carotid and femoral wall thickening in human hypertension, Actualits Vasculaires Internationales : Perspectives Medical Image Computing and Computer-Assisted Intervention-MICCAI'98 ëGR93ë R.C. Gonzalez and Woods R.E. Digital Image Processing.A ddison, pp.18822-8800887, 1982.

+. , S. Glacov, E. Weisenberg, C. K. Zarins, R. Stankunavicius et al., Compensatory enlargementofhuman atherosclerosis coronary arteries A generic system for image interpretation using çexible templates Outils pour la modlisation de structures et la simulation d'examens chographiques, Proc. British Machine Vision Conference ëHNG92ë I. Herlin, C. Nguyen, and C. Graçgne. A Deformable Region Model using Stochastic Processes Applied to Echocardiographic Images CVPR, 1992. ëHTB96ë D. Henry,J.T roccaz, and J.L. Bosson. Virtual Echography : Simulation of ultrasonographic examinations, pp.137111375-2766285, 1987.

K. S. Hill, C. J. Taylor, T. Cootes, M. K. Hu, M. T. Hueckel et al., Object recognition by çexible template matching using genetic algorithms Visual pattern recognition by momentinvariants IT-18 :1799187 An operator which locates edges in digitalized pictures Segmentation et recalage d'images chographiques par utilisation de connaissances physiologiques et morphologiques Joseph Fourier -Grenoble I, 1998. ëJNM + 96ë Geometrical modelling of abdominal aortic aneurysms. CVRED-MRCAS Computer determination of the consistent structure of biological images Computer biomedical research, 4 :3155328, 1971. ëLD89ë C. Loop and T. DeRose. Am ultisided generalization of bzier surfaces Mathematics at a glance A syntactic approach to texture analysis Three-dimensional ultrasound imaging of the female breast and human fetus in utero : Preliminary results From partials derivatives of 3D density images to ridge lines Adder : a snake-based segmentation approach for intravascular ultrasound images : Techniques and application, Proc. European Conference on Computer Vision IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR'922 Proceedings of the 2nd conferenceo n Digital Image Computing ëMGCB98ë A. Moreau-Gaudry,P . Cinquin, and J.P. Baguet. A new branching model : Application to carotid ultrasonic data, pp.1766183-85228561133125, 1962.

V. Partie, A. Bibliographie, P. Moreau-gaudry, J. P. Cinquin, E. Marr et al., Active model based carotid ultrasonic data segmentation Theory of edge detection Texture analysis of ct images Correlation of the extent and severity of atherosclerosis in the coronary and cerebral arteries Relationship between arterial disease in diçerent sites. a study of the aorta and coronary, carotid and iliac arteries Deformable models in medical image analysis : a survey, Thse : spcialit Mathmatiques, pp.1766183187-217, 1962.

+. , B. Nazarian, V. Juhan, K. Malkani, R. Bulot et al., Modlisation tridimensionnelle des anvrismes aortiques, Innov. Techn. Biol. Med, p.177554311441, 1996.

+. , B. Nazarian, V. Juhan, K. Malkani, R. Bulot et al., Generalized matching for recognition and retrieval in an image database ëNor94aë Northern Digital Inc. OPTOTRAK :Collect GuideèGlossaryèDisplay Guide ëNor94bë Northern Digital Inc. OPTOTRAK :Getting Started Guide ëNor94cë Northern Digital Inc. OPTOTRAK :System Guide on behalf of the CHS collaborative research group Savage Distribution and correlates of 278 V. sonographically detected carotid artery disease in the cardiovascular health study Directional çltering in edge detection APRIL 1998. ëPer96ë O. Peria. Fusion d'images morphologiques et fonctionnelles par l'utilisation de capteur intermediaire Fetal face visualization using threedimensional ultrasonography Object enhancement and extraction PictureP r ocessing and psychopictorics Numerical recipies in c : Second edition. ëPW89ë A. Pentland and J. Williams. Good Vibrations : Modal Dynamics for Graphics and Animation. Computer Graphics SIGGRAPH'899, 23333 :2155222 Three-dimensional ultrasound : accuracy of distance and volume measurements Machine perception of three-dimensional solids Design of an n-sided surface patch from hermite boundary data Recovery of parametric models from range images. The case of superquadrics with global deformations Boundary çnding with parametrically deformable model Model-based deformable surface çnding for medical images Three-dimensional ultrasound imaging of carotid artery plaques Multiresolution 3d image processing and graphics. Multiresolution Image Processing and Analysis Three-dimensional reconstruction of kidney from ultrasonic images Determinant of carotid intima-media thickness : a population-based ultrasonography study in easten çnnish men Ultrasound b-mode imaging in observational studies of atherosclerosis progressionA therosclerosis in a deçned population : an autopsy survey in malmo, sweden Dynamic 3D models with local and global deformations : Deformable superquadrics Use of monitoring software to improve the measurement of carotid wall thickness by b-mode imaging Description of texture by a structural analysis Texture analysis -a survey, Modlisation tridimensionnelle des anvrismes aortiques. Innov. Techn Generalized image matching : Statistical learning of physically-based deformations. Proceedings of the Fourth European Conference on Computer Vision ECCV'96 Proceedings of the Third International Conference : Communicating by Image and Multimedia ëPap65ë A. Papoulis. Probability, Random Variables, and Stochastic Processes Optical and Electro-Optical Information ProcessingIII :II566II65, 1993. ëSte68ë N.H. Sternby Signal Process The quantiçcation od atherosclerosis iii : the extent of corrrelation of degrees of atherosclerosis within ans between the coronary and cerebral vascular beds, pp.431144117522176061116153499-356, 1960.