A gradient descent procedure for variational dynamic surface problems with constraints

Authors:
Jan Erik Solem;Niels Chr. Overgaard
Affiliations:
Applied Mathematics Group, School of Technology and Society, Malmö University, Sweden;Applied Mathematics Group, School of Technology and Society, Malmö University, Sweden
Venue:
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Year:
2005

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Abstract

Many problems in image analysis and computer vision involving boundaries and regions can be cast in a variational formulation. This means that m-surfaces, e.g. curves and surfaces, are determined as minimizers of functionals using e.g. the variational level set method. In this paper we consider such variational problems with constraints given by functionals. We use the geometric interpretation of gradients for functionals to construct gradient descent evolutions for these constrained problems. The result is a generalization of the standard gradient projection method to an infinite-dimensional level set framework. The method is illustrated with examples and the results are valid for surfaces of any dimension.