We present an approach to incorporate topological priors in the reconstruction of a surface from a point scan. We base the reconstruction on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain a likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated within the optimization algorithm to promote the correct topology. The result is a novel topology‐aware technique which can (i) weed out topological noise from point scans, and (ii) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We show results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.

中文翻译：

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点云的拓扑感知表面重建

我们提出了一种将拓扑先验纳入点扫描重建表面的方法。我们基于优化的基函数进行重建，以在满足预定义的拓扑约束的同时提供对点扫描的良好拟合。我们优化模型的参数以获得重建域上的似然函数。拓扑约束由持久性图捕获，持久性图并入优化算法以促进正确的拓扑。结果是一种新颖的拓扑感知技术，它可以 (i) 从点扫描中清除拓扑噪声，以及 (ii) 捕获底层形状的某些细微特性，否则在执行表面重建时可能会丢失这些特性。我们展示了重建具有多种潜在拓扑结构的形状的结果，