Computational topology for reconstruction of surfaces with boundary: integrating experiments and theory

We report new techniques and theory in computational topology for reconstructing surfaces with boundary. This complements and extends known techniques for surfaces without boundary. Our approach is motivated by differential geometry and differential topology. We have also conducted significant exper...

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Bibliographic Details
Main Authors: Abe, K., Bisceglio, J., Peters, T.J., Russell, A.C., Ferguson, D.R., Sakkalis, T.
Format: Conference Proceeding
Language:English
Subjects:
Algorithm design and analysis
differential geometry
differential topology
Geometry
Image reconstruction
manifold
medial axis
Sampling methods
Shape
Surface reconstruction
Testing
Topology
twice-differentiable
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Description
Summary:We report new techniques and theory in computational topology for reconstructing surfaces with boundary. This complements and extends known techniques for surfaces without boundary. Our approach is motivated by differential geometry and differential topology. We have also conducted significant experimental work to test our resultant implementations. We discuss some problematic issues that can arise regarding the roles of the medial axis and sampling density. The crucial topics for C2 manifolds are (1) important defining properties of C2 manifolds with boundary, (2) creation of auxiliary surfaces, with emphasis near the boundary,(3) sampling density, and (4) successful practical algorithms and examples.
DOI:10.1109/SMI.2005.8