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.
翻译:作为3D 形状的最常见表示方式, 网状通常被分解存储为 3D 形状。 然而, 现实世界中的 3D 形状会持续呈现。 在本文中, 我们建议学习一个连续的表示方式, 用于固定的表层, 在许多面、 手和身体相关应用中, 一个常见和实用的环境。 首先, 我们将模板分割为多个封闭的多倍元- 0 毫谢, 这样每个genus- 0 毫谢可以被参数化为单位范围 。 然后我们学习球形隐含表面( SIS), 它包含一个球形的坐标, 一个全球特征或一组地方特征, 作为输入。 预测与坐标相对应的顶点, 作为输出。 由于球形的坐标是连续的, SIS 可以在任意的分辨率中描述一个符号。 ISIS 代表方式在3D 形状的离散和连续代表之间搭建一座桥梁。 具体地, 我们以自我监督的方式培训SIS 网络, 执行两个任务: 重建任务和超分辨率任务。 实验显示, 我们的任意分辨率代表方式固定了我所设计的方法。