Surface reconstruction of sampled textiles via Morse theory
在这项工作中，我们使用计算拓扑学工具研究服装的感知问题：从点云样本中识别它们的几何形状和位置，例如使用3D扫描仪。我们提出了一个基于直接拓扑研究采样纺织表面重建算法，可以通过莫尔斯函数获得其细胞分解。没有使用中间三角化或局部隐式方程，避免了重建引起的伪影。不需要对点样本的表面拓扑、密度或规则性进行先验知识。结果是将表面分割为莫尔斯细胞（即拓扑盘）的并集，适用于诸如滤波或独立网格重新映射等任务，以及具有小秩的细胞群决定表面拓扑。该算法可以应用于任意维度的环境中平滑的表面。
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.
https://arxiv.org/abs/2405.17257
https://arxiv.org/pdf/2405.17257.pdf