This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a ... more This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampling as an initial configuration for building a weighted centroidal Voronoi diagram in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay triangulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother gradation. We demonstrate the versatility of our approach through various remeshing examples.
Remeshing is a key component of many geometric algorithms, including modeling, editing, animation... more Remeshing is a key component of many geometric algorithms, including modeling, editing, animation and simulation. As such, the rapidly developing field of geometry processing has produced a profusion of new remeshing techniques over the past few years. In this paper we survey recent developments in remeshing of surfaces, focusing mainly on graphics applications. We classify the techniques into five categories based on their end goal: structured, compatible, high quality, feature and error-driven remeshing. We limit our description to the main ideas and intuition behind each technique, and a brief comparison between some of the techniques. We also list some open questions and directions for future research.
We propose a modular framework for robust 3D reconstruction from unorganized, unoriented, noisy, ... more We propose a modular framework for robust 3D reconstruction from unorganized, unoriented, noisy, and outlierridden geometric data. We gain robustness and scalability over previous methods through an unsigned distance approximation to the input data followed by a global stochastic signing of the function. An isosurface reconstruction is finally deduced via a sparse linear solve. We show with experiments on large, raw, geometric datasets that this approach is scalable while robust to noise, outliers, and holes. The modularity of our approach facilitates customization of the pipeline components to exploit specific idiosyncracies of datasets, while the simplicity of each component leads to a straightforward implementation.
Figure 1: (left) State-of-the-art parametrization based quad mesh generators, working with greedy... more Figure 1: (left) State-of-the-art parametrization based quad mesh generators, working with greedy rounding and stiffening, perform well if the target element sizing is chosen conservatively w.r.t. the distance of singularities but fail otherwise. Degeneracies in the map that prevent the iso-lines from stitching to a valid quad mesh-which mostly cannot be repaired locally-are highlighted in red. (right) Our novel reliable algorithm produces a valid output for any target sizing and thus in addition to ordinary quad-remeshing can be applied to coarse quad layout generation as well. The target edge length, indicated by bars, is identical for the left and the right triple.
We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewi... more We present a practical approach to isotropic tetrahedral meshing of 3D domains bounded by piecewise smooth surfaces. Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria. This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone. A careful treatment of boundaries and their features is presented, offering a versatile framework for designing smoothly graded tetrahedral meshes.
We present a method for automatic reconstruction of permanent structures of indoor scenes, such a... more We present a method for automatic reconstruction of permanent structures of indoor scenes, such as walls, floors and ceilings, from raw point clouds acquired by laser scanners. Our approach employs graph-cut to solve an inside/outside labeling of a space decomposition. To allow for an accurate reconstruction the space decomposition is aligned with permanent structures. A Hough Transform is applied for extracting the wall directions while allowing a flexible reconstruction of scenes. The graph-cut formulation takes into account data consistency through an inside/outside prediction for the cells of the space decomposition by stochastic ray casting, while favoring low geometric complexity of the model. Our experiments produces watertight reconstructed models of multi-level buildings and complex scenes.
In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of sur... more In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or man-made geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input geometry patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply point-sampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
Notre approche consiste a considerer le nuage de points en entree comme une mesure discrete (une ... more Notre approche consiste a considerer le nuage de points en entree comme une mesure discrete (une distribution de masses), et a construire une approximation par une mesure continue (et constante par morceaux)sur les faces d’un complexe simplicial. La distance entre les deux mesures est calculee par une approximation du transport optimal obtenue par programmation lineaire, et le complexe simplicial est obtenu par decimation et optimisation d’une triangulation de Delaunay initialisee avec un sous-ensemble des points en entree. La distance utilisee est robuste a la fois au bruit et aux donnees aberrantes, et preserve les aretes vives et les bords des formes a reconstruire. Cette distance peut egalement servir comme outil de post-traitement sur des surfaces lisses reconstruites avec des methodes par fonction implicite.
The Cgal library provides a rich variety of Voronoi diagrams and Delaunay triangulations. This va... more The Cgal library provides a rich variety of Voronoi diagrams and Delaunay triangulations. This variety covers several aspects: generators, dimensions and metrics, which we describe in Section 2. One aim of this paper is to present the main paradigms used in CGAL: Generic programming, separation between predicates/constructions and combinatorics, and exact geometric computation (not to be confused with exact arithmetic!). The first two paradigms translate into software design choices, described in Section 4, while the last covers both robustness and efficiency issues, respectively described in Sec- tion 6 and 7. Other important aspects of the Cgal library are the interface issues, be they for traversing a tessellation, or for interoperability with other libraries or languages, see Section 5. We present in Section 8 some tessellations at work in the context of surface reconstruction and mesh generation. Section 9 is devoted to some on-going and future work on periodic triangulations (...
Comment comprime-t-on les formes sur un ordinateur ? En se limitant au cas des maillages de surfa... more Comment comprime-t-on les formes sur un ordinateur ? En se limitant au cas des maillages de surfaces, ce document decrit une technique de compression.
Le developpement fulgurant des reseaux et de l’Internet permet l’echange d’objets geometriques co... more Le developpement fulgurant des reseaux et de l’Internet permet l’echange d’objets geometriques complexes. Dans ce contexte les maillages jouent un role preponderant, qu’ils soient surfaciques ou volumiques, a condition d’en construire une representation adaptee a la transmission. Dans cet article nous passons en revue les principaux travaux effectues en compression mono-resolution, progres- sive et resiliente de maillages triangulaires, quadrangu- laires, polygonaux, tetraedriques et hexaedriques.
2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
Domain adaptation for semantic segmentation has recently been actively studied to increase the ge... more Domain adaptation for semantic segmentation has recently been actively studied to increase the generalization capabilities of deep learning models. The vast majority of the domain adaptation methods tackle single-source case, where the model trained on a single source domain is adapted to a target domain. However, these methods have limited practical real world applications, since usually one has multiple source domains with different data distributions. In this work, we deal with the multi-source domain adaptation problem. Our method, namely StandardGAN, standardizes each source and target domains so that all the data have similar data distributions. We then use the standardized source domains to train a classifier and segment the standardized target domain. We conduct extensive experiments on two remote sensing data sets, in which the first one consists of multiple cities from a single country, and the other one contains multiple cities from different countries. Our experimental results show that the standardized data generated by StandardGAN allow the classifiers to generate significantly better segmentation.
We contribute a reliable line/surface intersection method for trimmed NURBS surfaces, based on a ... more We contribute a reliable line/surface intersection method for trimmed NURBS surfaces, based on a novel matrixbased implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to intersection points with multiple pre-images. We then apply our intersection algorithm to mesh NURBS surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other intersection approaches as well as a variety of meshing experiments.
We present a novel approach for the decimation of triangle surface meshes. Our algorithm takes as... more We present a novel approach for the decimation of triangle surface meshes. Our algorithm takes as input a triangle surface mesh and a set of planar proxies detected in a preprocessing analysis step, and structured via an adjacency graph. It then performs greedy mesh decimation through a series of edge collapse, designed to approximate the local mesh geometry as well as the geometry and structure of proxies. Such structure-preserving approach is well suited to planar abstraction, i.e., extreme decimation approximating well the planar parts while filtering out the others. Our experiments on a variety of inputs illustrate the potential of our approach in terms of improved accuracy and preservation of structure.
IEEE Transactions on Visualization and Computer Graphics, 2016
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithf... more The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error δ, minimal interior angle θ and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound δ as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. Our optimization framework greedily searches for the coarsest mesh with minimal interior angle above θ and approximation error bounded by δ. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
Principal component analysis is a basic component of many geometric computing and processing algo... more Principal component analysis is a basic component of many geometric computing and processing algorithms. It is most commonly used on point sets, although applicable as well to sets of arbitrary primitives through the computation of covariance matrices. In this paper we provide closed form formulas of covariance matrices for sets of 2D and 3D geometric primitives such as segments, circles, triangles, iso rectangles, spheres, tetrahedra and iso cuboids. We also describe the method of deriving covariance matrices for their dimensional variants such as disks, balls etc. We nally discuss the exibility and added value of the present approach by discussing its potential use in applications. Our implementation will be available through the next release of the CGAL library.
This habilitation thesis presents a series of contributions in the field of digital geometry proc... more This habilitation thesis presents a series of contributions in the field of digital geometry processing. These contributions offer concepts and algorithms for surface reconstruction, surface approximation, quadrangle surface tiling and isotropic tetrahedron mesh generation. The narrative aims at highlighting the common feature shared among our contributions: we adopt a variational methodology throughout this document, in the sense that we tackle each digital geometric problem by casting it as an energy minimization so that low levels of these energies correspond to good solutions of the problem. The main motivation behind such formulations is a significantly increased quality and robustness, sometimes at the price of heavier computations than greedy algorithms. The data structures and concepts involved in our work lie between computational geometry, geometric computing, and numerical computing. A general summary also provides a vision of the many remaining challenges in the field.
A Tutorial on CGAL Polyhedron for Subdivision Algorithms
This document is a tutorial on how to get started with the polyhedron structure provided by CGAL,... more This document is a tutorial on how to get started with the polyhedron structure provided by CGAL, the Computational Geometry Algorithm Library. Assuming the reader to be familiar with the C++ template mechanisms and the key concepts of the STL (Standard Template ...
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