Learning Continuous Mesh Representation with Spherical Implicit Surface
This work addresses the gap between discrete and continuous 3D shape representation, particularly for fixed-topology meshes used in applications like faces, hands, and bodies, though it is incremental as it builds on existing implicit surface techniques.
The paper tackles the problem of representing 3D meshes continuously rather than discretely, proposing a spherical implicit surface (SIS) method that achieves comparable performance to state-of-the-art fixed-resolution methods and significantly outperforms arbitrary-resolution methods.
As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.