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.
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.
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