On the Evolution of Vector Distance Functions of Closed Curves

Authors:
Marc Niethammer;Patricio A. Vela;Allen Tannenbaum
Affiliations:
Georgia Institute of Technology, School of Electrical and Computer Engineering, Atlanta 30332-0250;Georgia Institute of Technology, School of Electrical and Computer Engineering, Atlanta 30332-0250;Georgia Institute of Technology, School of Electrical and Computer Engineering, Atlanta 30332-0250
Venue:
International Journal of Computer Vision
Year:
2005

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Abstract

Inspired by the work by Gomes et al., we describe and analyze a vector distance function approach for the implicit evolution of closed curves of codimension larger than one. The approach is set up in complete generality, and then applied to the evolution of dynamic geometric active contours in $$\mathbb{R}^4$$ (codimension three case). In order to carry this out one needs an explicit expression for the zero level set for which we propose a discrete connectivity method. This leads us to make connections with the new theory of cubical homology. We provide some explicit simulation results in order to illustrate the methodology.