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Optimization on shape curves with application to specular stereo

: Balzer, J.; Höfer, S.; Werling, S.; Beyerer, J.


Goesele, M.; Roth, S.; Kuijper, A.; Schiele, B.; Schindler, K. ; Deutsche Arbeitsgemeinschaft für Mustererkennung -DAGM-:
Pattern recognition. 32nd DAGM Symposium 2010 : Darmstadt, Germany, September 22-24, 2010; proceedings
Berlin: Springer, 2010 (Lecture Notes in Computer Science 6376)
ISBN: 3-642-15985-0
ISBN: 978-3-642-15985-5
ISSN: 0302-9743
Deutsche Arbeitsgemeinschaft für Mustererkennung (DAGM Symposium) <32, 2010, Darmstadt>
Fraunhofer IOSB ()

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.