Topology-Adaptive Mesh Deformation for Surface Evolution, Morphing, and Multi-View Reconstruction
This work addresses the problem of robustly handling topological changes and self-intersections in explicit mesh representations, which is a long-standing challenge for shape modeling applications.
The authors introduce TransforMesh, a self-intersection removal algorithm that enables a mesh evolution framework to maintain manifold properties during strong deformations and topological changes. This method overcomes the traditional limitations of explicit mesh representations by robustly handling topological changes and removing self-intersections.
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.