Franck Hétroy

Topological quadrangulations of closed triangulated surfaces using the Reeb graph

Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the construction of coarse topological quadrangulations of closed triangulated surfaces, based on Morse theory. In order to construct on the surface a quadrangulation of its canonical polygonal schema, we compute first a Reeb graph then a canonical set of generators embedded on the surface. Some results are shown on different surfaces.

An iterative algorithm for homology computation on simplicial shapes

We propose a new iterative algorithm for computing the homology of arbitrary shapes discretized through simplicial complexes. We demonstrate how the simplicial homology of a shape can be effectively expressed in terms of the homology of its sub-components. The proposed algorithm retrieves the complete homological information of an input shape including the Betti numbers, the torsion coefficients and the representative homology generators.To the best of our knowledge, this is the first algorithm based on the constructive Mayer-Vietoris sequence, which relates the homology of a topological space to the homologies of its sub-spaces, i.e. the sub-components of the input shape and their intersections. We demonstrate the validity of our approach through a specific shape decomposition, based only on topological properties, which minimizes the size of the intersections between the sub-components and increases the efficiency of the algorithm. Highlights? We present a new iterative algorithm for homology computation for simplicial shapes. ? It is the first algorithm based on the constructive Mayer-Vietoris sequence. ? The homology of a shape is expressed in terms of the homologies of its sub-components. ? The validity of our approach is demonstrated through a specific shape decomposition. ? We prove that our algorithm is a reasonable tool for computing the homology of a shape.

Mesh repair with user-friendly topology control

Limitations of current 3D acquisition technology often lead to polygonal meshes exhibiting a number of geometrical and topological defects which prevent them from widespread use. In this paper we present a new method for model repair which takes as input an arbitrary polygonal mesh and outputs a valid 2-manifold triangle mesh. Unlike previous work, our method allows users to quickly identify areas with potential topological errors and to choose how to fix them in a user-friendly manner. Key steps of our algorithm include the conversion of the input model into a set of voxels, the use of morphological operators to allow the user to modify the topology of the discrete model, and the conversion of the corrected voxel set back into a 2-manifold triangle mesh. Our experiments demonstrate that the proposed algorithm is suitable for repairing meshes of a large class of shapes.

Animating Quadrupeds: Methods and Applications

Films like Shrek, Madagascar, The Chronicles of Narnia and Charlottes web all have something in common: realistic quadruped animations. While the animation of animals has been popular for a long time, the technical challenges associated with creating highly realistic, computer generated creatures have been receiving increasing attention recently. The entertainment, education and medical industries have increased the demand for simulation of realistic animals in the computer graphics area. In order to achieve this, several challenges need to be overcome: gathering and processing data that embodies the natural motion of an animal – which is made more difficult by the fact that most animals cannot be easily motion‐captured; building accurate kinematic models for animals, with adapted animation skeletons in particular; and developing either kinematic or physically‐based animation methods, either by embedding some a priori knowledge about the way that quadrupeds locomote and/or adopting examples of real motion. In this paper, we present an overview of the common techniques used to date for realistic quadruped animation. This includes an outline of the various ways that realistic quadruped motion can be achieved, through video‐based acquisition, physics based models, inverse kinematics or some combination of the above.

Segmentation of temporal mesh sequences into rigidly moving components

In this paper is considered the segmentation of meshes into rigid components given temporal sequences of deforming meshes. We propose a fully automatic approach that identifies model parts that consistently move rigidly over time. This approach can handle meshes independently reconstructed at each time instant. It allows therefore for sequences of meshes with varying connectivities as well as varying topology. It incrementally adapts, merges and splits segments along a sequence based on the coherence of motion information within each segment. In order to provide tools for the evaluation of the approach, we also introduce new criteria to quantify a mesh segmentation. Results on both synthetic and real data as well as comparisons are provided in the paper.

Constriction Computation using Surface Curvature

This paper provides a curvature-based algorithm to compute locally shortest geodesics on closed triangulated surfaces. These curves, which are called ``constrictions, are useful for shape segmentation. The key idea of the algorithm is that constrictions are almost plane curves; it first finds well-located simple, plane, closed curves, and then slides them along the surface until a shortest geodesic is reached. An initial curve is defined as a connected component of the intersection between the surface and a plane going through an initial vertex. Initial vertices and planes are determined using approximations of surface curvature.

From a closed piecewise geodesic to a constriction on a closed triangulated surface

Constrictions on a surface are defined as simple closed curves whose length is locally minimal. In particular, constrictions are periodic geodesics. We use constrictions in order to segment objects. In [4], we proposed an approach based on progressive surface simplification and local geodesic computation. The drawback of this approach is that constrictions are approximated by closed piecewise geodesics which are not necessarily periodic geodesics. In this paper, we compute constrictions starting from the closed piecewise geodesics previously computed and moving them on the surface. We compare the location of the initial closed piecewise geodesics to the location of the constrictions. Finally, we define and compute different types of constrictions on a surface.

Classification of non-manifold singularities from transformations of 2-manifolds

Non-manifold models are frequently encountered in engineering simulations and design as well as in computer graphics. However, these models lack shape characterization for modelling and searching purposes. Topological properties act as a kernel for deriving key features of objects. Here we propose a classification for the non-manifold singularities of non-manifold objects through continuous shape transformations of 2-manifolds without boundary up to the creation of non-manifold singularities. As a result, the non-manifold objects thus created can be categorized and contribute to the definition of a general purpose taxonomy for non-manifold shapes.

Automatic localization and quantification of intracranial aneurysms

We discuss in this paper the problem of localizing and quantifying intracranial aneurysms. Assuming that the segmentation of medical images is done, and that a 3D representation of the vascular tree is available, we present a new automatic algorithm to extract vessels centerlines. Aneurysms are then automatically detected by studying variations of vessels diameters. Once an aneurysm is detected, we give measures that are important to decide its treatment. The name of the aneurysm-carrying vessel is computed using an inexact graph matching technique. The proposed approach is evaluated on segmented real images issued from Magnetic Resonance Angiography (MRA) and CT scan.

Topological Quadrangulations of Closed Triangulated Surfaces Using the Reeb Graph

Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method to construct coarse topological quadrangulations of closed triangulated surfaces, based on theoretical results about topological classification of surfaces and Morse theory. In order to compute a canonical set of generators, a Reeb graph is constructed on the surface using Dijkstras algorithm. Some results are shown on different surfaces.