STITCH augments Neural-Pull with a topological loss derived from persistent homology to encourage a single connected component in reconstructed surfaces.
Cardinality of definable families of sets in o-minimal structures
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abstract
We prove that any definable family of subsets of a definable infinite set $A$ in an o-minimal structure has cardinality at most $|A|$. We derive some consequences in terms of counting definable types and existence of definable topological spaces.
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STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homology
STITCH augments Neural-Pull with a topological loss derived from persistent homology to encourage a single connected component in reconstructed surfaces.