Topology-Adaptive Mesh Deformation for Surface Evolution, Morphing, and Multi-View Reconstruction

TL;DR

This paper introduces TransforMesh, a novel mesh evolution framework that maintains surface manifold properties during deformation, effectively handling topological changes and self-intersections in explicit mesh representations for applications like morphing and reconstruction.

Contribution

The paper presents a new self-intersection removal algorithm and a mesh evolution framework that robustly manages topological changes in explicit surface meshes.

Findings

TransforMesh effectively removes self-intersections during surface deformation.

The method successfully handles topological changes such as merges and splits.

Applications demonstrate improved surface morphing and 3D reconstruction results.

Abstract

Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological changes. We introduce a new self-intersection removal algorithm, TransforMesh, and we propose a mesh evolution framework based on this algorithm. Numerous shape modelling applications use surface evolution in order to improve shape properties, such as appearance or accuracy. Both explicit and implicit representations can be considered for that purpose. However, explicit mesh representations, while allowing for accurate surface modelling, suffer from the inherent difficulty of reliably dealing with self-intersections and topological changes such as merges and splits. As a consequence, a majority of methods rely on implicit representations of surfaces, e.g. level-sets, that naturally overcome these issues. Nevertheless, these methods are based on volumetric discretizations, which introduce an unwanted precision-complexity trade-off. The method that we propose handles topological changes in a robust manner and removes self intersections, thus overcoming the traditional limitations of mesh-based approaches. To illustrate the effectiveness of TransforMesh, we describe two challenging applications, namely surface morphing and 3-D reconstruction.