Classification topologique locale d'images 3D

L'objectif de ce travail est de proposer une méthode d'analyse locale des formes des objets contenus dans une image 3D. Nous nous intéressons plus particulièrement aux formes de type cylindre ou plaque. Notre approche est basée sur l'analyse des points du squelette 3D et se déroule en deux étapes. Premièrement, 4 types de points du squelette sont identifiés : régulier, arc, bord et multiple. Un point du squelette est classé en fonction des propriétés topologique d'une région d'intérêt locale autour de ce point. La taille de cette région est réglée en fonction de l'épaisseur locale de la structure en ce point. Ensuite, la réversibilité du squelette est utilisée pour en déduire une classification du volume entier. Après avoir obtenu des résultats sur des images simulées 3D, nous présentons une application de la méthode dans l'identification des structures osseuses à partir d'images tomographiques hautes- résolution 3D

Reconstruction with Voronoi Centered Radial Basis Functions

The dinosaur model is courtesy of Cyberware, other models being courtesy of the AIM@SHAPE shape repositoryWe consider the problem of reconstructing a surface from scattered points sampled on a physical shape. The sampled shape is approximated as the zero level set of a function. This function is defined as a linear combination of compactly supported radial basis functions. We depart from previous work by using as centers of basis functions a set of points located on an estimate of the medial axis, instead of the input data points. Those centers are selected among the vertices of the Voronoi diagram of the sample data points. Being a Voronoi vertex, each center is associated with a maximal empty ball. We use the radius of this ball to adapt the support of each radial basis function. Our method can fit a user-defined budget of centers: The selected subset of Voronoi vertices is filtered using the notion of lambda medial axis, then clustered to fit the allocated budget

Discrete Scale Axis Representations for 3D Geometry

This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a spatially adaptive classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape representations. Our method combines scaling operations of medial balls for geometric simplification with filtrations of the medial axis and provably good conversion steps to and from union of balls, to enable efficient processing of a wide variety shape representations including polygon meshes, 3D images, implicit surfaces, and point clouds. We demonstrate the robustness and versatility of our algorithm with an extensive validation on hundreds of shapes including complex geometries consisting of millions of triangles

Medial Axis Approximation and Regularization

Medial axis is a classical shape descriptor. Among many good properties, medial axis is thin, centered in the shape, and topology preserving. Therefore, it is constantly sought after by researchers and practitioners in their respective domains. However, two barriers remain that hinder wide adoption of medial axis. First, exact computation of medial axis is very difficult. Hence, in practice medial axis is approximated discretely. Though abundant approximation methods exist, they are either limited in scalability, insufficient in theoretical soundness, or susceptible to numerical issues. Second, medial axis is easily disturbed by small noises on its defining shape. A majority of current works define a significance measure to prune noises on medial axis. Among them, local measures are widely available due to their efficiency, but can be either too aggressive or conservative. While global measures outperform local ones in differentiating noises from features, they are rarely well-defined or efficient to compute. In this dissertation, we attempt to address these issues with sound, robust and efficient solutions. In Chapter 2, we propose a novel medial axis approximation called voxel core. We show voxel core is topologically and geometrically convergent to the true medial axis. We then describe a straightforward implementation as a result of our simple definition. In a variety of experiments, our method is shown to be efficient and robust in delivering topological promises on a wide range of shapes. In Chapter 3, we present Erosion Thickness (ET) to regularize instability. ET is the first global measure in 3D that is well-defined and efficient to compute. To demonstrate its usefulness, we utilize ET to generate a family of shape revealing and topology preserving skeletons. Finally, we point out future directions, and potential applications of our works in real world problems

Skeletal representations of orthogonal shapes

Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric. The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods

MIMESIS, un environnement de conception et de simulation de modèles physiques particulaires masses-interactions CORDIS-ANIMA pour l'animation : du mouvement généré à l'image du mouvement

This thesis deals with the design of a computer framework dedicaced to animation by the physical mass-interaction CORDIS-ANIMA networks. Genericity and modularity of CORDIS-ANIMA having been still largely proved, the design and the implementation of such framework have to face with other theorical and practical problems that are discussed here in order to include every function that are required for an interactive creation of models and the communication inside a global chain of production of animated pictures. This thesis ends on the report of various situation of use in pedagogical, research and creation contexts.Cette thèse a pour objet la conception d’un environnement pour l’animation à l’aide de réseaux masses–interactions CORDIS-ANIMA. La généricité et la modularité de CORDIS-ANIMA ayant largement prouvé leur intérêt pour l’animation depuis 25 ans, la conception et l’implantation d’un environnement de conception de tels modèles doivent faire face à d’autres problématiques théoriques et pratiques qui seront discutées dans ce manuscrit, dans le but d’inclure dans cet environnement toutes les fonctionnalités requises pour une création interactive de modèles de mouvement et leur insertion dans une chaîne globale de production d’images animées. Cette thèse se terminera par le compte-rendu de situations d’utilisation dans un cadre pédagogique, de recherche et de création