We investigate topological descriptors for 3D surface analysis, i.e. the
classification of surfaces according to their geometric fine structure. On a
dataset of high-resolution 3D surface reconstructions we compute persistence
diagrams for a 2D cubical filtration. In the next step we investigate different
topological descriptors and measure their ability to discriminate structurally
different 3D surface patches. We evaluate their sensitivity to different
parameters and compare the performance of the resulting topological descriptors
to alternative (non-topological) descriptors. We present a comprehensive
evaluation that shows that topological descriptors are (i) robust, (ii) yield
state-of-the-art performance for the task of 3D surface analysis and (iii)
improve classification performance when combined with non-topological
descriptors.

本研究探讨了用于 3D 表面分析的拓扑描述符，通过计算高分辨率 3D 表面重构数据集的 2D 立方体过滤的持久性图，研究了不同的拓扑描述符对结构不同的 3D 面片的区分能力，并评估了它们对不同参数的灵敏度和与非拓扑描述符相结合后改进的分类性能。结果表明，拓扑描述符具有鲁棒性，且与非拓扑描述符相结合可以实现 3D 表面分析的最佳表现。