Shape gradients, shape warping and medical application to facial expression analysis. (Déformation de courbes et de surfaces, gradients généralisés et application à l'analyse d'expressions faciales chez des patients épileptiques)

Cette these porte sur le domaine des statistiques de formes. Une forme peut etre une courbe plane en 2D ou une surface en 3D. Afin de pouvoir definir ces statistiques (moyenne, modes de variation), nous avons etudie plus precisement, dans une premiere partie plutot theorique, le recalage et la mise en correspondance de deux formes entre elle. Cela consiste a developper des moyens de deformer une forme sur une autre. Des distances sont definies entre deux formes et une descente de gradient est effectuee pour deformer la premiere en la seconde. Nous avons donc defini la notion de gradient sur l'espace des formes et generalise cette definition pour definir des champs de deformations qui ne derivent plus d'un gradient. Cette notion a ete appliquee pour construire une methode permettant de deformer une courbe en une autre en etant guide par des points d'amers definissant des correspondances entre ces deux courbes. Dans une seconde partie, nous presentons une application de ces methodes a l'analyse d'expressions faciales de patients epileptiques en collaboration avec l'equipe du Professeur Patrick Chauvel a l'hopital de La Timone a Marseille. Nous avons developpe des techniques pour quantifier ces expressions faciales, et ainsi pouvoir les comparer entre elles. Nous avons ensuite etudie un moyen de mettre en relation ces expressions faciales (enregistrees pendant des crises d'epilepsies) avec le signal electrique enregistre simultanement dans le cerveau des patients. Cette mise en relation repond a une demande de l'equipe medicale qui se sert de cette information parmi d'autres pour affiner leur diagnostic.

[1]  Olivier D. Faugeras,et al.  Reconciling Distance Functions and Level Sets , 1999, Scale-Space.

[2]  Vladimir Kolmogorov,et al.  Computing geodesics and minimal surfaces via graph cuts , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[3]  Alain Trouvé,et al.  Diffeomorphisms Groups and Pattern Matching in Image Analysis , 1998, International Journal of Computer Vision.

[4]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[5]  Niels Chr. Overgaard,et al.  A Geometric Formulation of Gradient Descent for Variational Problems with Moving Surfaces , 2005, Scale-Space.

[6]  H. Karcher.  Riemannian center of mass and mollifier smoothing , 1977 .

[7]  R. Gur,et al.  Automated video-based facial expression analysis of neuropsychiatric disorders , 2008, Journal of Neuroscience Methods.

[8]  Stanley T. Birchfield,et al.  Elliptical head tracking using intensity gradients and color histograms , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[9]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[10]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[11]  S. Osher,et al.  Geometric Level Set Methods in Imaging, Vision, and Graphics , 2011, Springer New York.

[12]  Sabine Moisan,et al.  Managing complex processing of medical image sequences by program supervision techniques , 1997, Medical Imaging.

[13]  Fadi Dornaika,et al.  Fast and reliable active appearance model search for 3-D face tracking , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  M. Delfour,et al.  Shape Analysis via Oriented Distance Functions , 1994 .

[15]  C. Darwin.  The Expression of the Emotions in Man and Animals , .

[16]  M. Mandal,et al.  Facial expressions of emotions and schizophrenia: a review. , 1998, Schizophrenia bulletin.

[17]  T. Gustavsson,et al.  Flame front matching and tracking in PLIF images using geodesic paths and level sets , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

[18]  Alan L. Yuille,et al.  Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Olivier D. Faugeras,et al.  How to deal with point correspondences and tangential velocities in the level set framework , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[20]  A. Dervieux,et al.  A finite element method for the simulation of a Rayleigh-Taylor instability , 1980 .

[21]  Niels Chr. Overgaard,et al.  An Analysis of Variational Alignment of Curves in Images , 2005, Scale-Space.

[22]  Ulf Grenander,et al.  Lectures in pattern theory , 1978 .

[23]  Laurent D. Cohen,et al.  Global Minimum for Active Contour Models: A Minimal Path Approach , 1997, International Journal of Computer Vision.

[24]  Dieter Schmidt,et al.  Modern management of epilepsy: A practical approach , 2008, Epilepsy & Behavior.

[25]  C. Goodall.  Procrustes methods in the statistical analysis of shape , 1991 .

[26]  Anthony J. Yezzi,et al.  Gradient flows and geometric active contour models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[27]  Michael I. Miller,et al.  Landmark Matching via Large Deformation Diffeomorphisms on the Sphere , 2004, Journal of Mathematical Imaging and Vision.

[28]  Laurent Younes,et al.  Computable Elastic Distances Between Shapes , 1998, SIAM J. Appl. Math..

[29]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[30]  Anand Rangarajan,et al.  Shape analysis using the Fisher-Rao Riemannian metric: unifying shape representation and deformation , 2006, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006..

[31]  Pascal Fua,et al.  Accurate face models from uncalibrated and ill-lit video sequences , 2004, CVPR 2004.

[32]  Jörgen Ahlberg,et al.  CANDIDE-3 - An Updated Parameterised Face , 2001 .

[33]  P. Ekman,et al.  Facial action coding system: a technique for the measurement of facial movement , 1978 .

[34]  R. Cattell,et al.  The Procrustes Program: Producing direct rotation to test a hypothesized factor structure. , 2007 .

[35]  Vladimir Kolmogorov,et al.  What energy functions can be minimized via graph cuts? , 2002, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Song Wang,et al.  Landmark-based shape deformation with topology-preserving constraints , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[37]  Paul M. Thompson,et al.  Linear and non-linear geometric object matching with implicit representation , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[38]  Matthew MacDonald,et al.  Shapes and Geometries , 1987 .

[39]  Thomas Vetter,et al.  A morphable model for the synthesis of 3D faces , 1999, SIGGRAPH.

[40]  S. Vadlamani.  On the Diffusion of Shape , 2007 .

[41]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[42]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[43]  A. Toga,et al.  Brain Warping Via Landmark Points and Curves with a Level Set Representation , 2004 .

[44]  Renaud Keriven,et al.  Shape Priors using Manifold Learning Techniques , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[45]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[46]  Anand Rangarajan,et al.  Non rigid registration of shapes via diffeomorphic point matching and clustering , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[47]  Olivier D. Faugeras,et al.  Statistical shape influence in geodesic active contours , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[48]  Yajie Tian,et al.  Handbook of face recognition , 2003 .

[49]  Guillermo Sapiro,et al.  New Possibilities with Sobolev Active Contours , 2007, International Journal of Computer Vision.

[50]  Rasmus Larsen,et al.  Functional 2D Procrustes Shape Analysis , 2005, SCIA.

[51]  Benjamin B. Kimia,et al.  Symmetry-Based Indexing of Image Databases , 1998, J. Vis. Commun. Image Represent..

[52]  Vladimir Kolmogorov,et al.  Multi-camera Scene Reconstruction via Graph Cuts , 2002, ECCV.

[53]  Rachid Deriche,et al.  Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[54]  F. Bookstein.  Landmark methods for forms without landmarks: localizing group differences in outline shape , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[55]  J Bancaud,et al.  Post‐Traumatic Epilepsies of Multiple Cortical Origin , 1970, Epilepsia.

[56]  Olivier D. Faugeras,et al.  Designing spatially coherent minimizing flows for variational problems based on active contours , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[57]  Stefano Soatto,et al.  Multi-view stereo beyond Lambert , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[58]  Laurent Younes,et al.  Optimal matching between shapes via elastic deformations , 1999, Image Vis. Comput..

[59]  Guillermo Sapiro,et al.  Variational Problems and Partial Differential Equations on Implicit Surfaces: Bye Bye Triangulated Surfaces? , 2003 .

[60]  Rachid Deriche,et al.  Geodesic active regions and level set methods for motion estimation and tracking , 2005, Comput. Vis. Image Underst..

[61]  R E Ramsay,et al.  Patterns of involvement of facial muscles during epileptic and nonepileptic events , 1996, Neurology.

[62]  O. Faugeras,et al.  Variational principles, surface evolution, PDE's, level set methods and the stereo problem , 1998, 5th IEEE EMBS International Summer School on Biomedical Imaging, 2002..

[63]  S. Osher,et al.  From Landmark Matching to Shape and Open Curve Matching : A Level Set Approach , 2002 .

[64]  Jean Gotman,et al.  EEG–fMRI of epileptic spikes: Concordance with EEG source localization and intracranial EEG , 2006, NeuroImage.

[65]  Ulf Grenander,et al.  Hands: A Pattern Theoretic Study of Biological Shapes , 1990 .

[66]  F. Wendling,et al.  Time-frequency matching of warped depth-EEG seizure observations , 1999, IEEE Transactions on Biomedical Engineering.

[67]  Marcus A. Magnor,et al.  Weighted Minimal Hypersurfaces and Their Applications in Computer Vision , 2004, ECCV.

[68]  D W Roberts,et al.  Intractable Seizures of Frontal Lobe Origin: Clinical Characteristics, Localizing Signs, and Results of Surgery , 2000, Epilepsia.

[69]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

[70]  Anthony J. Yezzi,et al.  Vessel Segmentation Using a Shape Driven Flow , 2004, MICCAI.

[71]  Nahum Kiryati,et al.  Unlevel-Sets: Geometry and Prior-Based Segmentation , 2004, ECCV.

[72]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[73]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[74]  Facundo Mémoli,et al.  Eurographics Symposium on Point-based Graphics (2007) on the Use of Gromov-hausdorff Distances for Shape Comparison , 2022 .

[75]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .

[76]  Nikos Paragios,et al.  Shape Priors for Level Set Representations , 2002, ECCV.

[77]  Guillermo Sapiro,et al.  Geodesic Active Contours , 1995, International Journal of Computer Vision.

[78]  Shaogang Gong,et al.  Tracking Facial Feature Points with Gabor Wavelets and Shape Models , 1997, AVBPA.

[79]  I. M. Glazman,et al.  Theory of linear operators in Hilbert space , 1961 .

[80]  A Biraben,et al.  Fear as the main feature of epileptic seizures , 2001, Journal of neurology, neurosurgery, and psychiatry.

[81]  John W. Fisher,et al.  Nonparametric methods for image segmentation using information theory and curve evolution , 2002, Proceedings. International Conference on Image Processing.

[82]  Paul M. Thompson,et al.  The role of image registration in brain mapping , 2001, Image Vis. Comput..

[83]  F. Bookstein.  Size and Shape Spaces for Landmark Data in Two Dimensions , 1986 .

[84]  Rasmus Larsen,et al.  L1 Generalized Procrustes 2D Shape Alignment , 2008, Journal of Mathematical Imaging and Vision.

[85]  Alain Trouvé,et al.  Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[86]  Facundo Mémoli,et al.  Gromov-Hausdorff distances in Euclidean spaces , 2008, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[87]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[88]  Stefano Soatto,et al.  Deformotion: Deforming Motion, Shape Average and the Joint Registration and Approximation of Structures in Images , 2003, International Journal of Computer Vision.

[89]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[90]  Renaud Keriven,et al.  3D model fitting for facial expression analysis under uncontrolled imaging conditions , 2008, 2008 19th International Conference on Pattern Recognition.

[91]  Ragini Verma,et al.  Quantifying Facial Expression Abnormality in Schizophrenia by Combining 2D and 3D Features , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[92]  Wendy Taylor,et al.  Online! The Book , 2003 .

[93]  François Brémond,et al.  Human Behaviour Visualisation and Simulation for Automatic Video Understanding , 2002, WSCG.

[94]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[95]  M.B. Shamsollahi,et al.  Representation of SEEG signals using time-frequency signatures , 1998, Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Vol.20 Biomedical Engineering Towards the Year 2000 and Beyond (Cat. No.98CH36286).

[96]  P. Lions,et al.  Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations. , 1984 .

[97]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[98]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[99]  O. Faugeras,et al.  Level set based segmentation with intensity and curvature priors , 2000, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis. MMBIA-2000 (Cat. No.PR00737).

[100]  D. Mumford,et al.  Riemannian Geometries on Spaces of Plane Curves , 2003, math/0312384.

[101]  Guillermo Sapiro,et al.  Dynamic Shapes Average , 2003 .

[102]  Michael I. Miller,et al.  Group Actions, Homeomorphisms, and Matching: A General Framework , 2004, International Journal of Computer Vision.

[103]  C. Elger,et al.  Epileptic Seizures and Epilepsy: Definitions Proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE) , 2005, Epilepsia.

[104]  Marcus A. Magnor,et al.  Space-time isosurface evolution for temporally coherent 3D reconstruction , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[105]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

[106]  Hong Qin,et al.  Shape Reconstruction from 3D and 2D Data Using PDE-Based Deformable Surfaces , 2004, ECCV.

[107]  Jean-Philippe Pons,et al.  Generalized Gradients: Priors on Minimization Flows , 2007, International Journal of Computer Vision.

[108]  Anthony J. Yezzi,et al.  Sobolev Active Contours , 2005, International Journal of Computer Vision.

[109]  D. Cremers,et al.  Diffusion-snakes: combining statistical shape knowledge and image information in a variational framework , 2001, Proceedings IEEE Workshop on Variational and Level Set Methods in Computer Vision.

[110]  Craig T. Lawrence,et al.  A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm , 2000, SIAM J. Optim..

[111]  J Bancaud,et al.  Clinical semiology of frontal lobe seizures. , 1992, Advances in neurology.

[112]  K. Mueser,et al.  Deficits in facial-affect recognition and schizophrenia. , 1988, Schizophrenia bulletin.

[113]  Nikos Paragios,et al.  Matching Distance Functions: A Shape-to-Area Variational Approach for Global-to-Local Registration , 2002, ECCV.

[114]  Beat Fasel,et al.  Automati Fa ial Expression Analysis: A Survey , 1999 .

[115]  J. Bellanger,et al.  Epileptic fast intracerebral EEG activity: evidence for spatial decorrelation at seizure onset. , 2003, Brain : a journal of neurology.

[116]  Olivier D. Faugeras,et al.  Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics , 2005, Found. Comput. Math..

[117]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[118]  Stanley Osher,et al.  New framework for object warping: semi-Lagrangian level set approach , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[119]  Simon K. Warfield,et al.  Landmark-Guided Surface Matching and Volumetric Warping for Improved Prostate Biopsy Targeting and Guidance , 2004, MICCAI.

[120]  Maja Pantic,et al.  Automatic Analysis of Facial Expressions: The State of the Art , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[121]  Rachid Deriche,et al.  Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation , 2002, International Journal of Computer Vision.

[122]  Ron Kikinis,et al.  Registration of 3D Intraoperative MR Images of the Brain Using a Finite Element Biomechanical Model , 2001, IEEE Trans. Medical Imaging.

[123]  Anthony J. Yezzi,et al.  A statistical approach to snakes for bimodal and trimodal imagery , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[124]  Alain Trouvé,et al.  Diffeomorphic Matching Problems in One Dimension: Designing and Minimizing Matching Functionals , 2000, ECCV.

[125]  Timothy F. Cootes,et al.  Active Appearance Models , 1998, ECCV.

[126]  Charles C. Taylor,et al.  Procrustes shape analysis of triangulations of a two coloured point pattern , 1999, Stat. Comput..

[127]  Olivier D. Faugeras,et al.  Reconciling Landmarks and Level Sets , 2006, 18th International Conference on Pattern Recognition (ICPR'06).

[128]  Stephen J. Maybank,et al.  The Fisher-Rao Metric for Projective Transformations of the Line , 2005, International Journal of Computer Vision.

[129]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[130]  Fred L. Bookstein,et al.  Principal Warps: Thin-Plate Splines and the Decomposition of Deformations , 1989, IEEE Trans. Pattern Anal. Mach. Intell..