Coordinate-based representations of time-varying meshes

Current 3D capture technology acquires moving objects with high quality. However, the resulting data is temporally incoherent, since each frame is treated separately during reconstruction, giving sequences of triangle meshes with changing connectivity, known as time-varying meshes (TVMs). While TVMs can model topology changes, it is very hard to establish correspondences between the individual frames, which is important for downstream tasks like compression and editing. This project aims to overcome this limitation by investigating two novel coordinate-based representations of TVMs. First, we will explore the use of barycentric coordinates to describe the TVMs relative to a dynamic cage, which is itself a polyhedral mesh of constant connectivity chosen such that it approximates the shape of the TVM in each frame. Second, we will study the use of geodesic distance coordinates with respect to a certain set of points with time-invariant position relative to the observed shape. These coordinates are particularly useful for objects that undergo near-isometric deformations.