We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based 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 likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data.

翻译：我们提出一种方法,从点扫描到地貌学前科,为地表的重建提供信息; 重建的基础是基础功能,这些功能在满足预定的地形限制的同时,最优化地貌学前科以提供适合点扫描的优化功能; 我们优化模型的参数,以便在重建领域获得可能的功能; 将地形限制通过持久性图加以捕捉,该图被纳入优化算法,促进了正确的地形学; 其结果是一种新型的地貌学认知技术,它可以:(1) 从点扫描中除去地貌噪音;和(2) 捕捉在进行地表重建时本可以丢失的地貌特征的某些细微的特性。 我们用多种潜在地形来展示重建形状的结果,与其他古典地表构造技术进行比较,并显示实际扫描数据的完成情况。