We address content-based retrieval of complete 3D object models by a probabilistic generative description of local shape properties. The proposed shape description framework characterizes a 3D object with sampled multivariate probability density functions of its local surface features. This density-based descriptor can be efficiently computed via kernel density estimation (KDE) coupled with fast Gauss transform. The non-parametric KDE technique allows reliable characterization of a diverse set of shapes and yields descriptors which remain relatively insensitive to small shape perturbations and mesh resolution. Density-based characterization also induces a permutation property which can be used to guarantee invariance at the shape matching stage. As proven by extensive retrieval experiments on several 3D databases, our framework provides state-of-the-art discrimination over a broad and heterogeneous set of shape categories.

We describe in this paper a method for 3D shape indexing and retrieval that we apply on three data collections of the SHREC - SHape Retrieval Contest 2008: Stability on watertight, CAD and Generic 3D models. The method is based on a set of 2D multi-views after a pose and scale normalization of the models using Continuous PCA and the enclosing sphere. In all views we extract the models silhouettes and compare them pairwise. To compute the similitude measure we consider the external contour of the silhouettes, we extract their convexities and concavities at different scale levels and we build a multiscale representation. The pairs of contours are then compared by elastic matching achieved by using dynamic programming.

This paper presents an evaluation of the stability of the augmented multiresolution Reeb graph (aMRG) for shape retrieval of 3D watertight models. The method is based on a Reeb graph construction which is a well-known topology based shape descriptor. Using multiresolution property and additive geometrical and topological informations, aMRG has shown its efficiency and robustness to retrieve high quality 3D models. The SHREC - SHape REtrieval Contest 2008 Stability on Watertight Models Track data collection B is composed of 1500 models: 15 classes of 100 models. Each class contains original models and models with noise. We propose to evaluate the robustness of the aMRG with embedded topological features with regards to the following perturbations: Gaussian noise, uneven re-sampling, small protrusions, and topological noise.

This paper presents a new technique to reduce the storage cost of high quality 3D video. In 3D video, a sequence of 3D objects represents scenes in motion. Every frame is composed by one or several accurate 3D meshes with attached high fidelity properties such as color and texture. Each frame is acquired at video rate. The entire video sequence requires a huge amount of free disk space. To overcome this issue, we propose an original approach using Reeb graphs, which are well-known topology based shape descriptors. In particular, we take advantage of the augmented multiresolution Reeb graph properties to store the relevant information of the 3D model of each frame. This graph structure has shown its efficiency as a motion descriptor, being able to track similar nodes all along the 3D video sequence. Therefore we can describe and reconstruct the 3D models of all frames with a very low-cost data size. The algorithm has been implemented as a fully automatic 3D video compression system. Our experiments show the robustness and accuracy of the proposed technique by comparing reconstructed sequences against challenging real ones.

We address the 3D object retrieval problem using multivariate density-based shape descriptors. Considering the fusion of first and second order local surface information, we construct multivariate features up to five dimensions and process them by the kernel density estimation methodology to obtain descriptor vectors. We can compute these descriptors very efficiently using the fast Gauss transform algorithm. We also make use of descriptor level information fusion by concatenating descriptor vectors to increase their discrimination power further. To render the resulting descriptors storage-wise efficient, we develop two analytical tools, marginalization and probability density suppression, for descriptor dimensionality reduction. The experiments on two different databases, Princeton Shape Benchmark and Sculpteur, show that, boosted with both feature level and descriptor level information fusion, and powered with fast computational schemes, the density-based shape description framework enables effective and efficient 3D object retrieval.

This work presents an improved method of 3D mesh models indexing for content-based retrieval in database with shape similarity and appearance queries. The approach is based on the multiresolutional Reeb graph matching presented by Hilaga et al. (2001). The original method only takes into account topological information what is often not sufficient for effective matchings. Therefore we proposed to augment this graph with geometrical attributes. We also provide a new topological coherence condition to improve the graph matching. Moreover 2D appearance attributes and 3D features are extracted and merged to improve the estimation of the similarity between models. Besides, all these new attributes are user-dependent as they can be weighted by variable terms. We obtain a flexible multiresolutional and multicriteria representation called augmented Reeb graph (ARG). Good preliminary results have been obtained in a shape-based matching framework compared to existing methods based only on statistical measures. In addition, our study lead us to an innovative part matching scheme based on the same approach as our augmented Reeb graph matching.

Spectral decomposition of mesh geometry has first been introduced by Taubin for geometry processing purposes. It has been extended to address transmission issues by Kami & Gotsman. Such decompositions give rise to pseudofrequential information of the geometry defined over the mesh connectivity. For large meshes a piecewise decomposition has to be applied in order to restrict the complexity of the transform. In this paper, we propose to introduce overlap for its spectral representation. We show visual gains obtained in compression and progressive transmission of mesh geometry.

We present a multilevel representation scheme adapted to storage, progressive transmission, and rendering of dense data sampled on the surface of real objects. Geometry and object attributes, such as color and normal, are encoded in terms of surface particles associated to a hierarchical space partitioning based on an octree. Appropriate ordering of surface particles results in a compact multilevel representation without increasing the size of the uniresolution model corresponding to the highest level of detail. This compact representation can progressively be decoded by the viewer and transformed by a fast direct triangulation technique into a sequence of triangle meshes with increasing levels of detail. The representation requires approximately 5 bits per particle (2.5 bits per triangle) to encode the basic geometrical structure. The vertex positions can then be refined by means of additional precision bits, resulting in 5 to 9 bits per triangle for representing a 12-bit quantized geometry. The proposed representation scheme is demonstrated with the surface data of various real objects.

Over the last 20 years, several efforts have been devoted to the application of image processing and digital imaging techniques to art research in a context of close collaboration between the Centre de Recherche et de Restauration des Muse/spl acute/es de France (C2RMF) and the Ecole Nationale Superieure des Telecommunications (ENST). These efforts often found developments within National or European projects and were only made possible by the strong support of many partners throughout Europe. This set of projects and some of its results are presented, covering acquisition of information (from photos, or directly from paintings or objects), as well as storage management, database consulting, and image processing for pattern recognition and feature extraction.

We have developed an automatic system for 3D color reconstruction of real objects from 2D image sequences captured with a calibrated camera. The surface model is carved in an octree structure by using a shape from silhouette approach. The resulting 3D triangle mesh is obtained by a marching cube technique followed by a mesh decimation. The color related tasks of the whole system, such as object extraction and texture mapping, are addressed in the paper. We present a texture mapping strategy based on surface particles, It improves the texture quality by proper selection of the original color images yielding smooth color texture transitions both at triangle boundaries and within triangles. A particular care has been taken for the highlight removal problem. Reconstruction results demonstrate the attained quality.

The authors propose an edge-based method for the automatic construction of CAD models from range images of a prototype object. First, surface discontinuities of C/sup 0/ and C/sup 1/ types and the curves of surface curvature extrema are extracted from the range images. Then, a piecewise G/sup 1/-continuous surface description with triangular Gregory-Be/spl acute/zier patches is constructed to embed these extracted surface characteristics. The construction of this description is adaptive in the sense that an initially rough approximation is progressively refined at the locations where the approximation accuracy does not meet the requirements.>

A split-and-merge algorithm is proposed for the segmentation of the digitized surface of a range image into planar regions. The geometric data structure used is a triangular tessellation of image domain. This data structure, combined with an adaptive surface approximation technique, allows a better adaptation of the range image segmentation to the surface boundaries. It also provides an efficient neighborhood referencing mechanism, thus resulting in a fast algorithm.>

An adaptive surface fitting algorithm is proposed for modelling the digitized surface of a real object described by an array of 3D points sampled on a rectangular mesh and stored in the form of a range image. A G1 -piecewise approximation of the data is obtained by using an adaptive top-down method which combines the Delaunay triangulation technique with a triangular Gregory-Bezier patch model (tGB). The method begins with a rough approximation of the surface and progressively refines it in successive steps in the regions where the accuracy requirement of the approximation is not satisfied. The method, therefore, is essentially a local process. An optimization approach is used to obtain a G '-continuous piecewise approximation where each tGB patch is as smooth and regular as possible. Some experimental results are given to demonstrate the potential usefulness of this approach for the geometric modelling from range image data.

We propose here a pre-processing of 3D shapes which allows to give greater importance to the match between some parts of the surface of one object and some parts of the surface of the other object during the matching of the two objects. The method is working with objects defined on a digital grid and consists in a segmentation step to separate the main components of the shapes, and in a distance computation step to determine matching weights to be assigned to the surface points. Several new algorithms are developed: a 3D segmentation algorithm based on mathematical morphology, a fast method to compute geodesic distances on a 3D surface, a simple sphere creation algorithm on a digital grid. The method has been applied to chemical molecules.

In this paper, we introduce three types of shape control parmeters (tension, bias, and continuity) into the modelling of free-form surfaces composed of bicubic Bernstein-Bezier patches. This is an extension to surfaces of the three control parameters introduced in the local interpolatory spline curves by Kochanck and Bartels [12]. We first analyze the general conditions for guaranteeing the G' continuity of the surface at corners where three, four, or five patches meet. The analysis of the continuity constraints reveals the remaining degrees of freedom which can be exploited for the control of the surface shape. The shape control parameters arc then introduced. Experimental results are provided. They show the efficiency of these parameters for an easy and intuitive control of the surface shape.

A method is developed for surface-fitting from sampled data. Surface-fitting is the process of constructing a compact representation to model the surface of an object based on a fairly large number of given data points. In our case, the data is obtained from a real object using an automatic three-dimensional digitizing system. The method is based on an adaptive subdivision approach, a technique previously used for the design and display of free-form curved surface objects. Our approach begins with a rough approximating surface and progressively refines it in successive steps in regions where the data is poorly approximated. The method has been implemented using a parametric piecewise bicubic Bernstein-Bézier surface possessing G1 geometric continuity. An advantage of this approach is that the refinement is essentially local reducing the computational requirements which permits the processing of large databases. Furthermore, the method is simple in concept, yet realizes efficient data compression. Some experimental results are given which show that the representation constructed by this method is faithful to the original database.

In an experiment to determine the map of periodic tidal currents, aerial photographs have been taken of numerous floats spread over the surface of a scale model of the coast. These photographs allow an automatic measurement of the orientation, the magnitude and the direction of the flow of water.