Towards Implicit Correspondence in Signed Distance Field Evolution

Abstract

The level set framework is widely used in geometry processing due to its ability to handle topological changes and the readily accessible shape properties it provides, such as normals and curvature. However, its major drawback is the lack of correspondence preservation throughout the level set evolution. Therefore, data associated with the surface, such as colour, is lost. The objective of this paper is a variational approach for signed distance field evolution which implicitly preserves correspondences. We propose an energy functional based on a novel data term, which aligns the lowest-frequency Laplacian eigenfunction representations of the input and target shapes. As these encode information about natural deformations that the shape can undergo, our strategy manages to prevent data diffusion into the volume. We demonstrate that our system is able to preserve texture throughout articulated motion sequences, and evaluate its geometric accuracy on public data.