Robust Biharmonic Skinning Using Geometric Fields

2024-06-01

arXiv.org

AI Summary

Existing automatic skinning methods rely on volumetric meshing (e.g., tetrahedralization) to solve variational problems, resulting in poor robustness against non-closed, non-manifold, or degenerate surface meshes—often yielding artifacts or outright failure. This paper proposes a mesh-free, robust automatic skinning method that eliminates the need for volumetric discretization. Instead of conventional finite-element formulations, we introduce a novel mesh-free weight representation based on Lagrangian kernels. We directly model and optimize the skinning weights as geometric fields defined solely on the surface, using biharmonic energy minimization. Our approach inherently supports open surfaces, arbitrary triangle soups, and topologically ill-conditioned inputs without requiring volume meshing. Experimental results demonstrate that the generated skinning weights match or exceed the quality of state-of-the-art methods while maintaining stability and reliability across diverse challenging inputs. To our knowledge, this is the first fully topology-robust, truly mesh-free automatic skinning framework.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Motion & Tracking
• Intelligent Robots: Manipulation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Skinning is a popular way to rig and deform characters for animation, to compute reduced-order simulations, and to define features for geometry processing. Methods built on skinning rely on weight functions that distribute the influence of each degree of freedom across the mesh. Automatic skinning methods generate these weight functions with minimal user input, usually by solving a variational problem on a mesh whose boundary is the skinned surface. This formulation necessitates tetrahedralizing the volume bounded by the surface, which brings with it meshing artifacts, the possibility of tetrahedralization failure, and the impossibility of generating weights for surfaces that are not closed. We introduce a mesh-free and robust automatic skinning method that generates high-quality skinning weights comparable to the current state of the art without volumetric meshes. Our method reliably works even on open surfaces and triangle soups where current methods fail. We achieve this through the use of a Lagrangian representation for skinning weights, which circumvents the need for finite elements while optimizing the biharmonic energy.

Problem

• Mesh-free skinning method
• Avoids volumetric meshing issues
• Works on open surfaces

Innovation

• Mesh-free automatic skinning method
• Lagrangian representation for weights
• Optimizes biharmonic energy directly