Optimization on shape curves with application to specular stereo

Authors:
Jonathan Balzer;Sebastian Höfer;Stefan Werling;Jürgen Beyerer
Affiliations:
King Abdullah University of Science and Technology, Geometric Modeling and Scientific Visualization Center, Thuwal, Kingdom of Saudi Arabia;Lehrstuhl für Interaktive Echtzeitsysteme, Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany;Lehrstuhl für Interaktive Echtzeitsysteme, Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany;Lehrstuhl für Interaktive Echtzeitsysteme, Institute for Anthropomatics, Karlsruhe Institute of Technology, Germany
Venue:
Proceedings of the 32nd DAGM conference on Pattern recognition
Year:
2010

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Abstract

We state that a one-dimensional manifold of shapes in 3- space can be modeled by a level set function. Finding a minimizer of an independent functional among all points on such a shape curve has interesting applications in computer vision. It is shown how to replace the commonly encountered practice of gradient projection by a projection onto the curve itself. The outcome is an algorithm for constrained optimization, which, as we demonstrate theoretically and numerically, provides some important benefits in stereo reconstruction of specular surfaces.