  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.
