Jean-Philippe Vandeborre

Topology driven 3D mesh hierarchical segmentation

In this paper, we propose to address the semantic- oriented 3D mesh hierarchical segmentation problem, using enhanced topological skeletons. This high level information drives both the feature boundary computation as well as the feature hierarchy definition. Proposed hierarchical scheme is based on the key idea that the topology of a feature is a more important decomposition criterion than its geometry. First, the enhanced topological skeleton of the input triangulated surface is constructed. Then it is used to delimit the core of the object and to identify junction areas. This second step results in a fine segmentation of the object. Finally, a fine to coarse strategy enables a semantic- oriented hierarchical composition of features, subdividing human limbs into arms and hands for example. Method performance is evaluated according to seven criteria enumerated in latest segmentation surveys [3]. Thanks to the high level description it uses as an input, presented approach results, with low computation times, in robust and meaningful compatible hierarchical decompositions.

A practical approach for 3D model indexing by combining local and global invariants

In this paper we present a three-dimensional model retrieval system. In our approach, a three-dimensional model is described by three invariant descriptors: a curvature index which consists of a histogram of the principal curvatures of each face of the mesh, a histogram of distances between the faces, and a histogram of the volumes based on each face. This work focuses on extracting these invariant descriptors from the three-dimensional models, and on combining these descriptors in order to improve retrieval performance. An experimental evaluation demonstrates the satisfactory performance of our approach on a fifty three-dimensional model database.

A New 3D-Matching Method of Nonrigid and Partially Similar Models Using Curve Analysis

The 3D-shape matching problem plays a crucial role in many applications, such as indexing or modeling, by example. Here, we present a novel approach to matching 3D objects in the presence of nonrigid transformation and partially similar models. In this paper, we use the representation of surfaces by 3D curves extracted around feature points. Indeed, surfaces are represented with a collection of closed curves, and tools from shape analysis of curves are applied to analyze and to compare curves. The belief functions are used to define a global distance between 3D objects. The experimental results obtained on the TOSCA and the SHREC07 data sets show that the system performs efficiently in retrieving similar 3D models.

Learning Boundary Edges for 3D-Mesh Segmentation

This paper presents a 3D‐mesh segmentation algorithm based on a learning approach. A large database of manually segmented 3D‐meshes is used to learn a boundary edge function. The function is learned using a classifier which automatically selects from a pool of geometric features the most relevant ones to detect candidate boundary edges. We propose a processing pipeline that produces smooth closed boundaries using this edge function. This pipeline successively selects a set of candidate boundary contours, closes them and optimizes them using a snake movement. Our algorithm was evaluated quantitatively using two different segmentation benchmarks and was shown to outperform most recent algorithms from the state‐of‐the‐art.

A framework for the objective evaluation of segmentation algorithms using a ground-truth of human segmented 3D-models

In this paper, we present an evaluation method of 3D-mesh segmentation algorithms based on a ground-truth corpus. This corpus is composed of a set of 3D-models grouped in different classes (animals, furnitures, etc.) associated with several manual segmentations produced by human observers. We define a measure that quantifies the consistency between two segmentations of a 3D-model, whatever their granularity. Finally, we propose an objective quality score for the automatic evaluation of 3D-mesh segmentation algorithms based on these measures and on the ground-truth corpus. Thus the quality of segmentations obtained by automatic algorithms is evaluated in a quantitative way thanks to the quality score, and on an objective basis thanks to the groundtruth corpus. Our approach is illustrated through the evaluation of two recent 3D-mesh segmentation methods.

Invariant High Level Reeb Graphs of 3D Polygonal Meshes

Many applications in computer graphics need high level shape descriptions, in order to benefit from a global understanding of shapes. Topological approaches enable pertinent surface decompositions, providing structural descriptions of 3D polygonal meshes; but in practice, their use raises several difficulties. In this paper, we present a novel method for the construction of invariant high level Reeb graphs, topological entities that give a good overview of the shape structure. With this aim, we propose an accurate and straightforward feature point extraction algorithm for the computation of an invariant and meaningful quotient function. Moreover, we propose a new graph construction algorithm, based on an analysis of the connectivity evolutions of discrete level lines. This algorithm brings a practical solution for the suppression of non-significant critical points over piecewise continuous functions, providing meaningful Reeb graphs. Presented method gives accurate results, with satisfactory execution times and without input parameter. The geometrical invariance of resulting graphs and their robustness to variation in model pose and mesh sampling make them good candidates for several applications, like shape deformation (experimented in this paper), recognition, compression, indexing, etc.

A comparative study of existing metrics for 3D-mesh segmentation evaluation

In this paper, we present an extensive experimental comparison of existing similarity metrics addressing the quality assessment problem of mesh segmentation. We introduce a new metric, named the 3D Normalized Probabilistic Rand Index (3D-NPRI), which outperforms the others in terms of properties and discriminative power. This comparative study includes a subjective experiment with human observers and is based on a corpus of manually segmented models. This corpus is an improved version of our previous one (Benhabiles et al. in IEEE International Conference on Shape Modeling and Application (SMI), 2009). It is composed of a set of 3D-mesh models grouped in different classes associated with several manual ground-truth segmentations. Finally the 3D-NPRI is applied to evaluate six recent segmentation algorithms using our corpus and the Chen et al.’s (ACM Trans. Graph. (SIGGRAPH), 28(3), 2009) corpus.

Enhancing 3D mesh topological skeletons with discrete contour constrictions

This paper describes a unified and fully automatic algorithm for Reeb graph construction and simplification as well as constriction approximation on triangulated surfaces.The key idea of the algorithm is that discrete contours – curves carried by the edges of the mesh and approximating the continuous contours of a mapping function – encode both topological and geometrical shape characteristics. Therefore, a new concise shape representation, enhanced topological skeletons, is proposed, encoding the contours’ topological and geometrical evolution.First, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Next, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes and constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, which we refer to as enhanced topological skeletons.Extensive experiments showed that, without any preprocessing stage, proposed algorithms are fast in practice, affine-invariant and robust to a variety of surface degradations (surface noise, mesh sampling and model pose variations). These properties make enhanced topological skeletons interesting shape abstractions for many computer graphics applications.

A Bayesian framework for 3D models retrieval based on characteristic views

The management of big databases of three-dimensional models (used in CAD applications, visualization, games, etc.) is a very important domain. The ability to characterize and easily retrieve models is a key issue for the designers and the final users. In this frame, two main approaches exist: search by example of a three-dimensional model, and search by a 2D view. We present a novel framework for the characterization of a 3D model by a set of views (called characteristic views), and an indexing process of these models with a Bayesian probabilistic approach using the characteristic views. The framework is independent from the descriptor used for the indexing. We illustrate our results using different descriptors on a collection of three-dimensional models supplied by Renault Group.

Reeb chart unfolding based 3D shape signatures

This paper presents a novel surface parameterization based technique that addresses the pose insensitive shape signature problem for surface models of arbitrary genus. It is based on the key idea that two surface models are similar if the canonical mappings of their sub-parts introduce similar distortions. First, a Reeb graph of the shape is computed so as to segment it into charts of controlled topology, denoted as Reeb charts, that have either disk or annulus topology. Next, we define for each Reeb chart a straightforward mapping to the canonical planar domain. Then, we compute a stretching signature of the canonical mapping based on an area distortion evaluation. Finally, the input shape is represented by the set of the stretching signatures. An application to pose-insensitive shape similarity is proposed by comparing the signatures of the different Reeb charts. Promising experimental results are presented and compared to state-of-the-art techniques. The gain provided by this new signature as well as its interest for partial shape similarity are demonstrated.