Master 2 Dauphine MATH, MATHEMATIQUES APPLIQUEES et THEORIQUES/ APPLIED AND THEORETICAL MATHEMATICS 2023/2024

Variational Methods, PDEs and geodesics for Image Analysis 

Laurent D. Cohen  

Directeur de Recherche au CNRS
CEREMADE, UMR CNRS 7534,
Université Paris Dauphine, PSL
Place du Marechal de Lattre de Tassigny
75775 Paris cedex 16, France
Tel. (33-1) 44 05 46 78 Fax (33-1) 44 05 45 99
Cohen @ ceremade.dauphine .fr
http://www.ceremade.dauphine.fr/~cohen

PhD : Open positions. Contact me.

 Résumé du Cours de Master

 

This course, after giving a short introduction to digital image processing, will present an overview of variational methods for Image segmentation. This will include deformable models, known as active contours, solved using finite differences, finite elements, level sets method, fast marching method. A large part of the course will be devoted to geodesic methods, where a contour is found as a shortest path between two points according to a relevant metric. This can be solved efficiently by fast marching methods for numerical solution of the Eikonal equation. We will present cases with metrics of different types (isotropic, anisotropic, Finsler) in different spaces. All the methods will be illustrated by various concrete applications, like in biomedical image applications.

Les articles indiqués ci-dessous permettent d'approfondir les notions vues en cours, mais il n'est évidemment pas obligatoire de lire tous ces articles.

Page de description et sources pour les TP: Numerical Tour

 

Schedule : wednesday 10:15-13:30

Where?: University Paris Dauphine, B110

Language :The course will be in English, except if all students speak French.

Overview of the Course (the matching between dates and thematics is approximative and can change).

• In order to receive information about this course, please register here

• 24 January 2024, 10h15: Presentation of the course
• 24 January 2024, 10h15-13h30: Introduction to Digital Image Processing
• 31 January 2024, 10h15-13h30: Reconstruction with Regularization, variational problems.
• 7 February 2024, 10h15-13h30: Reconstruction with Regularization, variational problems.
• 14 February 2024 10h15-13h30: Active Contours and Deformable models
• Article sur les contours actifs 2D et 3D: Differences Finies/Elements Finis/Ballon
• Article de synthese sur les modeles deformables
• Modèle de Ballon.
• Méthode des éléments finis, Spline Snakes
• Modèles déformables et contours actifs.
• Avoiding Local Minima for Deformable Curves in Image Analysis.    PDF
• Premier Article sur les contours actifs et Region
• Modèle Région. Énergie Chan Vese.
• Segmentation et Reconstruction avec Régularisation par level sets.
• Modèles Déformables par level sets, Contours actifs Géodésiques.

• La méthode des Level Sets/Ensembles de Niveau  

• Evolution des courbes planes et méthode des ensembles de niveau/ level sets.
• 28 February 2024 10h15-13h30: Minimal Paths/ Geodesic lines
  Article de synthese sur les chemins minimaux
  Article de base sur les chemins minimaux


• 6 March 2024 10h15-13h30 : Minimal Paths, Different metrics and spaces, Fast Marching and Voronoi
  • Chemins minimaux Livre de synthese
•  
  • Métriques isotropes et anisotropes. Fast marching sur des triangulations. Application au maillages d'images et de surfaces.
  • Geodesic re-meshing and parameterization using front propagation Similar paper in French
  • Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization. ,
  • Landmark-based Computation for Heuristically Driven Path Planning
  • Chemins minimaux et tubular Anisotropy
• 13 March 2023 10h15-13h30: Minimal Paths, Fast Marching/ QUIZZ at the end.
•  
• Article sur les chemins minimaux et l'endoscopie virtuelle
• Fast Constrained Surface Extraction by Minimal Paths Similar paper in French
• Fast extraction of tubular and tree 3D surfaces with front propagation methods.
• Generalized Voronoi Tesselations for Vector-Valued Image Segmentation Similar paper in French
• Fast 3D Brain Segmentation Using Dual-front Active Contours With Optional User-Interaction
• A new implicit method for surface segmentation by minimal paths in 3D images.
• Multiple Contour Finding and Perceptual Grouping as a set of Energy Minimizing Paths  Similar paper in French for RFIA'02
• Multiple contour finding and perceptual grouping using minimal paths
• Compléments sur les modèles déformables, Vote Géodésique et Métriques de Finsler
  • Chemins minimaux et Vote Geodesique
  • Chemins minimaux et Vote Geodesique suite
  • Métriques de FINSLER: méthodes géodésiques et pénalisation de la courbure
  • Métriques de FINSLER: méthodes géodésiques avec terme Région
  • From Active Contours to Minimal Geodesic Paths: New Solutions to Active Contours Problems by Eikonal Equations.
•  

 

Autres Articles sur ma page web
 

Un livre ancien en ligne d'introduction aux techniques de base de traitement d'image

Un livre en ligne d'introduction aux techniques de base de traitement d'image

VALIDATION du cours

A short QCM of 15mn at the end of the last class. Analysis of a research paper.