In this work, we study the perception problem for garments using tools from computational topology: the identification of their geometry and position in space from point-cloud samples, as obtained e.g. with 3D scanners. We present a reconstruction algorithm based on a direct topological study of the sampled textile surface that allows us to obtain a cellular decomposition of it via a Morse function. No intermediate triangulation or local implicit equations are used, avoiding reconstruction-induced artifices. No a priori knowledge of the surface topology, density or regularity of the point-sample is required to run the algorithm. The results are a piecewise decomposition of the surface as a union of Morse cells (i.e. topological disks), suitable for tasks such as noise-filtering or mesh-independent reparametrization, and a cell complex of small rank determining the surface topology. This algorithm can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.

翻译：本文利用计算拓扑学工具研究服装的感知问题：即从点云样本（如通过三维扫描仪获得）中识别其几何形状与空间位置。我们提出一种基于采样纺织品表面直接拓扑分析的重建算法，该算法通过莫尔斯函数获得表面的胞腔分解。该方法不使用中间三角化或局部隐式方程，从而避免重建引入的伪影。算法运行无需预先获知表面拓扑结构、点样本密度或规则性。其结果为：将表面分解为莫尔斯胞腔（即拓扑圆盘）的片状并集，适用于噪声过滤或网格独立重参数化等任务；以及确定表面拓扑结构的小秩胞腔复形。本算法可应用于任意维度环境空间中带边界或无边界的光滑表面。