Visual Computer manuscript No will be inserted by the editor

Vincent Vidal

Description

Visual Computer manuscript No. (will be inserted by the editor) Combinatorial mesh optimization Vincent Vidal · Christian Wolf · Florent Dupont Received: date / Accepted: date Abstract A new mesh optimization framework for 3D triangular surface meshes is presented, which formu- lates the task as an energy minimization problem in the same spirit as in Hoppe et al. [1]. The desired mesh properties are controlled through a global energy func- tion including data attached terms measuring the fi- delity to the original mesh, shape potentials favoring high quality triangles and connectivity as well as budget terms controlling the sampling density. The optimiza- tion algorithm modifies mesh connectivity as well as the vertex positions. Solutions for the vertex repositioning step are obtained by a discrete graph cut algorithm ex- amining global combinations of local candidates. Results on various 3D meshes compare favorably to recent state-of-the-art algorithms. Applications con- sist in optimizing triangular meshes and in simplifying meshes, while maintaining high mesh quality. Targeted areas are the improvement of the accuracy of numeri- cal simulations, the convergence of numerical schemes, improvements of mesh rendering (normal field smooth- ness) or improvements of the geometric prediction in mesh compression techniques. Keywords Triangular meshes · mesh optimization · discrete optimization · graph cuts This work has been supported by the French National Research Agency (ANR) through the MDCO program (project MADRAS No.

• all optimization


• vertex position


• refined using local


• mesh


• output quality


• detec- tion process


• global energy

Sujets

• Université
• DuPont

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Visual Computer manuscript No. (will be inserted by the editor)

Combinatorial mesh optimization Vincent Vidal ∙ Christian Wolf ∙ Florent Dupont

Received: date / Accepted: date

Abstract A new mesh optimization framework for 3D 1 Introduction triangular surface meshes is presented, which formu- lates the task as an energy minimization problem in  Nowadays, 3D triangular meshes are commonly used in the same spirit as in Hoppe et al. [1]. The desired mesh  many fields, as the hundreds of thousands of existing properties are controlled through a global energy func-  3D triangular models can attest. They are of interest tion including data attached terms measuring the fi-  in visual effects, video games, scientific visualization, delity to the original mesh, shape potentials favoring  3D animation and medical surgery simulation based on high quality triangles and connectivity as well as budget  finite element methods, to name a few. Most of the terms controlling the sampling density. The optimiza- existing triangular meshes are of unsatisfying quality tion algorithm modifies mesh connectivity as well as the  because of their inappropriate vertex sampling, which vertex positions. Solutions for the vertex repositioning is responsible for inequilateral triangles and irregular step are obtained by a discrete graph cut algorithm ex-  connectivity. The origin of this irregular sampling may amining global combinations of local candidates. be due to the scanning device, to 3D interactive solid Results on various 3D meshes compare favorably  modeling software or to simplification algorithms. to recent state-of-the-art algorithms. Applications con-  This poor quality causes instability and divergence sist in optimizing triangular meshes and in simplifying  of various mesh processing applications [2]. In that meshes, while maintaining high mesh quality. Targeted  context, several remeshing techniques have been intro- areas are the improvement of the accuracy of numeri-  duced in the literature. They consist in improving some cal simulations, the convergence of numerical schemes,  quality requirements under soft and/or hard constraint improvements of mesh rendering (normal field smooth-  conditions. Targeted goals vary according to the ap- ness) or improvements of the geometric prediction in  plication [3]. Simplification techniques tend to preserve mesh compression techniques.  the overall shape of the mesh while removing as many Keywords Triangular meshes ∙ mesh optimization ∙ triangles as possible. Mesh smoothing methods consist discrete optimization ∙ graphcuts i F n in re al m ly o , vi M n e g sh hi o g p h ti fr m e i q z u a e ti n o c n y a n i o m is s e a s t o i a m s p t r o o f v a i i n r g t t h h e e m m e e s s h h . This work has been supported by the French National Research quality, i.e. the regularity of the sampling and of the Agency (ANR) through the MDCO program (project MADRAS connectivity. No. ANR-07-MDCO-015) In this paper, the mesh optimization problem is V. Vidal and C. Wolf stated as an energy minimization problem. The pro- Universite´deLyon,CNRS posed energy function (see equation 4) captures the fi- INSA-Lyon, LIRIS, UMR5205, Villeurbanne F-69621, France Tel.: [phone] E-mail: { vincent.vidal,christian.wolf } @liris.cnrs.fr delity to the initial mesh geometry, the mesh quality (expressed in terms of triangle shape and vertex va- F. Dupont lence) and the number of vertices (simplification versus Universite´deLyon,CNRS Universite´Lyon1,LIRIS,UMR5205,VilleurbanneF-69622, remeshing). Hence, according to the initial mesh and France desired goals of the method, it is possible to improve the E-mail: fl[e-mail] compactness of the representation, the triangle shape,