Search

Efficient representation of articulated objects such as human bodies is an important problem in computer vision and graphics. To efficiently simulate deformation, existing approaches represent 3D objects using polygonal meshes and deform them using skinning techniques. This paper introduces neural articulated shape approximation (NASA), an alternative framework that enables representation of articulated deformable objects using neural indicator functions that are conditioned on pose. Occupancy testing using NASA is straightforward, circumventing the complexity of meshes and the issue of water-tightness. We demonstrate the effectiveness of NASA for 3D tracking applications, and discuss other potential extensions.

International audience; We are interested in geometric approximation by parameterization of two-dimensional multiple-component shapes, in particular when the number of components is a priori unknown. Starting a standard method based on successive shape deformations with a one-component initial shape in order to approximate a multiple-component target shape usually leads the deformation flow to make the boundary evolve until it surrounds all the components of the target shape. This classical phenomenon tends to create double points on the boundary of the approximated shape. In order to improve the approximation of multiple-component shapes (without any knowledge on the number of components in advance), we use in this paper a piecewise Bézier parameterization and we consider two procedures called intersecting control polygons detection and flip procedure. The first one allows to prevent potential collisions between two parts of the boundary of the approximated shape, and the second one permits to change its topology by dividing a one-component shape into a two-component shape. For an experimental purpose, we include these two processes in a basic geometrical shape optimization algorithm and test it on the classical inverse obstacle problem. This new approach allows to obtain a numerical approximation of the unknown inclusion, detecting both the topology (i.e. the number of connected components) and the shape of the obstacle. Several numerical simulations are performed.

Many computer graphics applications use simpler yet faithful approximations of complex shapes to conduct reliably part of their computations. Some tasks, such as physical simulation, collision detection, occlusion queries or free-form deformation, require the simpler proxy to strictly enclose the input shape. While there are algorithms that can output such bounding proxies on simple input shapes, most of them fail at generating a proper coarse approximant on real-world complex shapes, which may contain multiple components and have a high genus. We advocate that, before reducing the number of primitives to describe a shape, one needs to regularize it while maintaining the strict enclosing property, to avoid any geometric aliasing that makes the decimation unreliable. Depending on the scale of the desired approximation, the topology of the shape itself may indeed have to be first simplified, to let the subsequent geometric optimization be free from topological locks. We propose a new bounding shape approximation algorithm which takes as input an arbitrary surface mesh, with potentially complex multi-component structures, and generates automatically a bounding proxy which is tightened on the input and can match even the coarsest levels of approximation. To sustain the nonlinear approximation process that may eventually abstract both geometry and topology, we propose to use an intermediate regularized representation in the form of a shape closing, computed in real time using a new fast morphological framework designed for efficient parallel execution. Once the desired level of approximation is reached in the shape closing, a coarse, tight and bounding polygonization of the proxy geometry is extracted using an adaptive meshing scheme. Our underlying representation is both geometry- and topology-adaptive and can be optionally controlled accurately by a user, through sizing and orientation fields, yielding an intuitive brush metaphor within an interactive proxy design environment. We provide extensive experiments on various kinds of input meshes and illustrate the potential applications of our method in scenarios that benefit greatly from coarse, tight bounding substitutes to the actual high resolution geometry of the original 3D model, including freeform deformation, physical simulation and level of detail generation for rendering.

International audience; Performance capture systems can be used to acquire high-quality animated 3D surfaces, usually in form of a dense 3D triangle mesh. Extracting a more compact, yet faithful representation is often desirable, but existing solutions for animated sequences are surface-based, which leads to a limited approximation power in the case of extreme simplification. We introduce animated sphere-meshes, which are meshes indexing a set of animated spheres. Our solution is the first to output an animated volumetric structure to approximate animated 3D surfaces and optimizes for the sphere approximation, connectivity, and temporal coherence. The result of our algorithm is a multi-resolution structure from which the user can choose the wanted level of simplification in real-time. We demonstrate the use of animated sphere-meshes for low-cost approximate collision detection. Additionally, we propose a skinning decomposition, which automatically rigs the input mesh to the chosen level of detail. The resulting set of weights are smooth, compress the animation, and enable easy edits.

In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper., {"references":["Pierre Alliez, David Cohen-Steiner, Olivier Devillers, Bruno Levy, and\nMathieu Desbrun. Anisotropic polygonal remeshing. ACM.Transactions\non Graphics, 22:485493, 2003.","Pierre Alliez, Eric Colin de Verdiere, Olivier Devillers, and Martin\nIsenburg. Isotropic surface remeshing. In M.S. Kim, editor, SMI03:\nProceedings of Shape Modeling International 2003, pages 4958, Los\nAlamitos, 2003. IEEE Computer Society.","P. Alliez, M. Meyer, and M. Desbrun. Interactive geometry remeshing.\nAcm Transactions on Graphics, 21(3):347354, 2002.","Mario Botsch and Leif Kobbelt. A remeshing approach to\nmultiresolution modeling. In R. Scopigno and D. Zorin, editors,\nProceedings of 2nd Eurographics Symposium on Geometry Processing,\npages 189196. Eurographics, 2004.","V. Kraevoy and A. Sheffer. Cross-parameterization and compatible\nremeshing of 3d models. Computer graphics proceedings, annual\nconference series: SIGGRAPH conference proceedings, 2004.","L. Kobbelt, J. Vorsatz, U. Labsik, and H.P. Seidel. A shrink wrapping\napproach to remeshing polygonal surfaces. Computer Graphics Forum,\n18:119130, 1999.","Emil Praun and Hugues Hoppe. Spherical parametrization and\nremeshing. Computer graphics proceedings, annual conference series:\nSIGGRAPH conference proceedings, pages 340349, 2003.","F. Fan, S. Lai, J.Wang, C. Huang, Y. Li, Mesh Clustering by\nApproximating Centroidal Voronoi Tessellation. Proc. 2009 SIAM/ACM\nJoint Conference on Geometric & Physical Modeling, 2009, pp.\n301-306.","Q. Du, V. Faber, and M. Gunzburger. Centroidal voronoi tessellations:\nApplications and algorithms. SIAM Rev., 41(4):637676, 1999.\n[10] Q. Du, M. D. Gunzburger, and L. Ju. Constrained centroidal voronoi\ntessellations for surfaces. SIAM J. Sci. Comput., 24(5):14881506, 2002.\n[11] A. W. M. Garland and P. S. Heckberty. Hierarchical face clustering on\npolygonal surfaces. In Proceedings of the Symposium on Interactive 3D\nGraphics, 2001.\n[12] S. Valette and J.-M. Chassery. Approximated centroidal voronoi\ndiagrams for uniform polygonal mesh coarsening. 23(3):381389, 2004.\n(Proc. Eurographics04).\n[13] S. Valette, J.-M. Chassery, and R. Prost. Generic remeshing\nof 3d triangular meshes with metric-dependent discrete voronoi\ndiagrams. IEEE Transactions on Visualization and Computer Graphics,\n10(2):369381, 2008."]}

When the same objects in different datasets have different positions and shapes, map alignment is necessary to minimise these geometric inconsistencies for successful map integration. In this paper, we propose a method to detect conjugate-point pairs for aligning two polygon datasets by matching the contours of corresponding polygons. This method comprises three processes, including identification of the corresponding polygon pairs, shape approximation with virtual corner-vertices and detection of conjugate-point pairs with our modified vertex-attributed-string-matching (VASM) algorithm. We applied this method to two distinct spatial datasets; a cadastral map and a topographical map of the same urban area. Then, the performance of our method was assessed visually and statistically. Both evaluations showed satisfactory results.

This paper presents a method of shape chartification suitable for surface approximation. The innovation of this approach lies on the definition of an iterative refinement of the shape into a set of patches that are automatically tiled and used to approximate the original shape up to a prescribed error. The coding of the patches is supported by the Reeb graph and contains the rules to properly tile, stitch them, and reconstruct the original shape while preserving its topology, using a technique which is also exploited for reconstructing an object from non-planar contours. The method is geometry-aware by definition, as the nodes of the Reeb graph are representative of the main shape features, which belong to the approximated shape already at the initial iteration steps. The points of the reconstructed shape belong to the original surface, their total number is highly reduced, and the original connectivity is replaced by a set of patches that preserves the global topology of the input shape.

Clothing computer design systems include three integrated parts: garment pattern design in 2D/3D, virtual try-on and realistic clothing simulation. Some important results have been obtained in pattern design and clothing simulation since the 1980s. However, in the area of virtual try-on, only limited methods have been proposed which are applicable to some defined garment styles or under restrictive sewing assumptions. This paper presents a series of new techniques from virtually sewing up complex garment patterns on human models to visualizing design effects through physical-based real-time simulation. We first employ an hierarchy of ellipsoids to approximate human models in which the bounding ellipsoids are optimized recursively. We also present a new scheme for including contact friction and resolving collisions. Four types of user interactive operation are introduced to manipulate cloth patterns for pre-positioning, virtual sewing and later obtaining cloth simulation. In the cloth simulation, we propose a simplified cloth dynamic model and an integration scheme to realize a high quality real-time cloth simulation. We demonstrate the robustness of our proposed systems by complex garment style virtual try-on and cloth simulation.

Aiming at robust surface structure recovery, we extend the powerful optimization technique of variational shape approximation by allowing for several different primitives to represent the geometric proxy of a surface region. While the original paper only considered planes, we also include spheres, cylinders, and more complex rollingball blend patches. The motivation for this choice is the fact that most technical CAD objects consist of patches from these four categories. The robust segmentation and global optimization properties which have been observed for the variational shape approximation carry over to our hybrid extension. Hence, we can use our algorithm to segment a given mesh model into characteristic patches and provide a corresponding geometric proxy for each patch. The expected result that we recover surface structures more robustly and thus obtain better approximations with a smaller number of primitives, is validated and demonstrated on a number of examples.

This thesis presents a set of novel optimization approaches for dealing with three different architecturally motivated rationalization tasks: First, a planarization technique for enabling efficient (e.g., glass) panelings of tessellated freeform geometries is presented. The formulation is based on plane intersections and yields planar panels by construction. Furthermore, the used constraints are straightforward algebraic expressions of lower polynomial degree than used in various comparable methods. The generality of the method is demonstrated by application to a variety of architecturally inspired optimization problems. Then, for a new type of support structures called point-folded structures an anti-diversification technique is developed for reducing the number of geometrically different panels. By a problem-adapted parametrization and carefully designed search strategy, the shape redundancy can be reduced by over 90% for various freeform designs, enabling significant reductions of fabrication costs in practice. Finally, for the still largely unexplored high potential area of constrained tessellation techniques, i.e., tessellation algorithms restricted to using only structural elements from a predefined set, two novel approaches based on a commercially available construction system (Zometool) are presented. The first method concerns approximation of closed surfaces of arbitrary genus, and implements an effective model-exploration strategy to efficiently find a solution. Furthermore, for guaranteeing planarity of panels when tessellating the architecturally important class of freeform surface patches, a second method based on an advancing front method guided by a novel growing strategy is developed.

Shape approximation algorithms aim at computing simple geometric descriptions of dense surface meshes. Many such algorithms are based on mesh decimation techniques, generating coarse triangulations while optimizing for a particular metric which models the distance to the original shape. This approximation scheme is very efficient when enough polygons are allowed for the simplified model. However, as coarser approximations are reached, the intrinsic piecewise linear point interpolation which defines the decimated geometry fails at capturing even simple structures. We claim that when reaching such extreme simplification levels, highly instrumental in shape analysis, the approximating representation should explicitly and progressively model the volumetric extent of the original shape. In this paper, we propose Sphere-Meshes , a new shape representation designed for extreme approximations and substituting a sphere interpolation for the classic point interpolation of surface meshes. From a technical point-of-view, we propose a new shape approximation algorithm, generating a sphere-mesh at a prescribed level of detail from a classical polygon mesh. We also introduce a new metric to guide this approximation, the Spherical Quadric Error Metric in R 4 , whose minimizer finds the sphere that best approximates a set of tangent planes in the input and which is sensitive to surface orientation, thus distinguishing naturally between the inside and the outside of an object. We evaluate the performance of our algorithm on a collection of models covering a wide range of topological and geometric structures and compare it against alternate methods. Lastly, we propose an application to deformation control where a sphere-mesh hierarchy is used as a convenient rig for altering the input shape interactively.

In this paper, we introduce the concept of an exoskeleton as a new abstraction of arbitrary shapes that succinctly conveys both the perceptual and the geometric structure of a 3D model. We extract exoskeletons via a principled framework that combines segmentation and shape approximation. Our method starts from a segmentation of the shape into perceptually relevant parts and then constructs the exoskeleton using a novel extension of the Variational Shape Approximation method. Benefits of the exoskeleton abstraction to graphics applications such as simplification and chartification are presented.

Shading can be used as an independent cue for exact shape recovery, or it can be used as a supplementary cue for shape interpolation between features whose depths are known from other cues. Exact shape cannot be inferred from a local analysis of shading. However, for shape interpolation a crude local approximation may be sufficient. This paper explores the limits of such local approximations that are easy to compute. In particular, the shape of shading is used to approximate the surface in areas of monotonic change of intensity. This analysis is accompanied by a method for computing the direction of a single-point light source from the shading on occluding contours. A qualitative classification of shape near shading singularities is also discussed.