Jean-Marc Thiery

Sphere-Meshes: shape approximation using spherical quadric error metrics

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 R4, 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.

SimSelect: Similarity-based selection for 3D surfaces

Surface selection is one of the fundamental interactions in shape modeling. In the case of complex models, this task is often tedious for at least two reasons: firstly the local geometry of a given region may be hard to manually select and needs great accuracy; secondly the selection process may have to be repeated a large number of times for similar regions requiring similar subsequent editing. We propose SimSelect, a new system for interactive selection on 3D surfaces addressing these two issues. We cope with the accuracy issue by classifying selections in different types, namely components, parts and patches for which we independently optimize the selection process. Second, we address the repetitiveness issue by introducing an expansion process based on shape recognition which automatically retrieves potential selections similar to the user‐defined one. As a result, our system provides the user with a compact set of simple interaction primitives providing a smooth select‐and‐edit workflow.

Geometry and Attribute Compression for Voxel Scenes

Voxel‐based approaches are todays standard to encode volume data. Recently, directed acyclic graphs (DAGs) were successfully used for compressing sparse voxel scenes as well, but they are restricted to a single bit of (geometry) information per voxel. We present a method to compress arbitrary data, such as colors, normals, or reflectance information. By decoupling geometry and voxel data via a novel mapping scheme, we are able to apply the DAG principle to encode the topology, while using a palette‐based compression for the voxel attributes, leading to a drastic memory reduction. Our method outperforms existing state‐of‐the‐art techniques and is well‐suited for GPU architectures. We achieve real‐time performance on commodity hardware for colored scenes with up to 17 hierarchical levels (a 128K3voxel resolution), which are stored fully in core.

CageR: Cage-Based Reverse Engineering of Animated 3D Shapes

We present CageR: A novel framework for converting animated 3D shape sequences into compact and stable cage‐based representations. Given a raw animated sequence with one‐to‐one point correspondences together with an initial cage embedding, our algorithm automatically generates smoothly varying cage embeddings which faithfully reconstruct the enclosed object deformation. Our technique is fast, automatic, oblivious to the cage coordinate system, provides controllable error and exploits a GPU implementation. At the core of our method, we introduce a new algebraic algorithm based on maximum volume sub‐matrices (maxvol) to speed up and stabilize the deformation inversion. We also present a new spectral regularization algorithm that can apply arbitrary regularization terms on selected subparts of the inversion spectrum. This step allows to enforce a highly localized cage regularization, guaranteeing its smooth variation along the sequence. We demonstrate the speed, accuracy and robustness of our framework on various synthetic and acquired data sets. The benefits of our approach are illustrated in applications such as animation compression and post‐editing.

Progressive medial axis filtration

The Scale Axis Transform provides a parametric simplification of the Medial Axis of a 3D shape which can be seen as a hierarchical description. However, this powerful shape analysis method has a significant computational cost, requiring several minutes for a single scale on a mesh of few thousands vertices. Moreover, the scale axis can be artificially complexified at large scales, introducing new topological structures in the simplified model. In this paper, we propose a progressive medial axis simplification method inspired from surface optimization techniques which retains the geometric intuition of the scale axis transform. We compute a hierarchy of simplified medial axes by means of successive edge-collapses of the input medial axis. These operations prevent the creation of artificial tunnels that can occur in the original scale axis transform. As a result, our progressive simplification approach allows to compute the complete hierarchy of scales in a few seconds on typical input medial axes. We show how this variation of the scale axis transform impacts the resulting medial structure.

Jacobians and Hessians of mean value coordinates for closed triangular meshes

Mean value coordinates provide an efficient mechanism for the interpolation of scalar functions defined on orientable domains with a nonconvex boundary. They present several interesting features, including the simplicity and speed that yield from their closed-form expression. In several applications though, it is desirable to enforce additional constraints involving the partial derivatives of the interpolated function, as done in the case of the Green coordinates approximation scheme (Ben-Chen, Weber, Gotsman, ACM Trans. Graph.:1–11, 2009) for interactive 3D model deformation.In this paper, we introduce the analytic expressions of the Jacobian and the Hessian of functions interpolated through mean value coordinates. We provide these expressions both for the 2D and 3D case. We also provide a thorough analysis of their degenerate configurations along with accurate approximations of the partial derivatives in these configurations. Extensive numerical experiments show the accuracy of our derivation. In particular, we illustrate the improvements of our formulae over a variety of finite differences schemes in terms of precision and usability. We demonstrate the utility of this derivation in several applications, including cage-based implicit 3D model deformations (i.e., variational MVC deformations). This technique allows for easy and interactive model deformations with sparse positional, rotational, and smoothness constraints. Moreover, the cages produced by the algorithm can be directly reused for further manipulations, which makes our framework directly compatible with existing software supporting mean value coordinates based deformations.

Indoor Scene Reconstruction Using Near-Light Photometric Stereo

We propose a novel framework for photometric stereo (PS) under low-light conditions using uncalibrated near-light illumination. It operates on free-form video sequences captured with a minimalistic and affordable setup. We address issues such as albedo variations, shadowing, perspective projections, and camera noise. Our method uses specular spheres detected with a perspective-correcting Hough transform to robustly triangulate light positions in the presence of outliers via a least-squares approach. Furthermore, we propose an iterative reweighting scheme in combination with an

Multi-material adaptive volume remesher

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Animated Mesh Approximation With Sphere-Meshes

-norm minimizer to robustly solve the calibrated near-light PS problem. In contrast to other approaches, our framework reconstructs depth, albedo (relative to light source intensity), and normals simultaneously and is demonstrated on synthetic and real-world scenes.

SMI 2012: Short VoxMorph: 3-scale freeform deformation of large voxel grids

We propose a practical iterative remeshing algorithm for multi-material tetrahedral meshes which is solely based on simple local topological operations, such as edge collapse, flip, split and vertex smoothing. To do so, we exploit an intermediate implicit feature complex which reconstructs piecewise smooth multi-material boundaries made of surface patches, feature edges and corner vertices. Furthermore, we design specific feature-aware local remeshing rules which, combined with a moving least square projection, result in high quality isotropic meshes representing the input mesh at a user defined resolution while preserving important features. Our algorithm uses only topology-aware local operations, which allows us to process difficult input meshes such as self-intersecting ones. We evaluate our approach on a collection of examples and experimentally show that it is fast and scales well. Graphical abstractDisplay Omitted HighlightsRobust tetrahedral remeshing: can process self-intersecting and poor quality meshes.Multi-material tetrahedral meshes: high-quality segemented meshes at any resolution.Using local operators: edge collapse, flip, split and vertex smoothing.Feature preserving: feature-aware local rules with a moving least square projection.