Topology-Aware Surface Reconstruction for Point Clouds
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We provide an approach to utilize topological priors to reconstruct the surface of a point scan. In particular, we learn parameters for the basis functions that are used for surface reconstruction, satisfying predefined topological constraints. These requirements are captured by persistence diagrams, and these are used to inform the optimization process that learns the parameters. We obtain parameters to build a likelihood function over the reconstruction domain. This novel topology-aware technique is useful to weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape, that could otherwise be lost while performing direct surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques and show completion of medical and real scan data.
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