Energy functions for regularization algorithms

Herve Delingette; Martial Hebert; Katsushi Ikeuchi

doi:10.1117/12.49979

1 September 1991 Energy functions for regularization algorithms

Herve Delingette, Martial Hebert, Katsushi Ikeuchi

Proceedings Volume 1570, Geometric Methods in Computer Vision; (1991) https://doi.org/10.1117/12.49979
Event: San Diego, '91, 1991, San Diego, CA, United States

Abstract

Energy functions used for regularization algorithms measure the smoothness of a curve or surface. In order, to render acceptable solutions, these energies have to verify certain properties such as invariance with Euclidean transformations or invariance with parametrization. This paper extends the notion of smoothness energy to the notion of differential stabilizer. If an analogy is made with mechanics, smoothness energy corresponds to potential energy while differential stabilizers correspond to forces. To avoid the systematic underestimation of curvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. Finally a set of stabilizers is proposed that meets this condition as well as invariance with rotation and parametrization.

Citation Download Citation

Herve Delingette, Martial Hebert, and Katsushi Ikeuchi "Energy functions for regularization algorithms", Proc. SPIE 1570, Geometric Methods in Computer Vision, (1 September 1991); https://doi.org/10.1117/12.49979

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