SGER: Computational Topology for Surface Reconstruction

University Of Connecticut, Storrs CT

Investigators

Abstract

ABSTRACT 0226504 Thomas Peters U of Connecticut Research on surface reconstruction has prospered by productive interactions between computational geometers and classical topologists. The initial reconstruction techniques on unorganized point data relied upon visual inspection to verify topological correctness. Recent advances have led to rigorous sufficient conditions that guarantee correct topological form first, by equivalence under homeomorphisms and subsequently by the stronger ambient isotopy. These theoretical advances have led to improved surface reconstructions for reverse engineering and medical modeling for a significant subset of the surfaces considered in those applications. This prompts a speculative unifying intellectual question: Can contemporary modifications of classical difierential geometry, topology and knot theory lead to a broader scope for computational topology that will result in further algorithmic improvements? More specifically, can these classical mathematical tools be applied to extend the domain of surface reconstruction algorithms? This research will explore how this already successful synergy between classical mathematics and computer science can be accelerated. Graduate student support is requested and this successful project outcome will then serve as an exemplar for further student involvement in interdisciplinary work between computer scientists and mathematicians.