Discrete orthogonal decomposition and variational fluid flow estimation

Authors:
Jing Yuan;Paul Ruhnau;Etinne Mémin;Christoph Schnörr
Affiliations:
Department of Mathematics and Computer Science, Computer Vision, Graphics, and Pattern Recognition Group, University of Mannheim, Mannheim, Germany;Department of Mathematics and Computer Science, Computer Vision, Graphics, and Pattern Recognition Group, University of Mannheim, Mannheim, Germany;IRISA Rennes, Rennes Cedex, France;Department of Mathematics and Computer Science, Computer Vision, Graphics, and Pattern Recognition Group, University of Mannheim, Mannheim, Germany
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

The decomposition of motion vector fields into components of orthogonal subspaces is an important representation for both the analysis and the variational estimation of complex motions. Common finite differencing or finite element methods, however, do not preserve the basic identities of vector analysis. Therefore, we introduce in this paper the mimetic finite difference method for the estimation of fluid flows from image sequences. Using this discrete setting, we represent the motion components directly in terms of potential functions which are useful for motion pattern analysis. Additionally, we analyze well-posedness which has been lacking in previous work. Experimental results, including hard physical constraints like vanishing divergence of the flow, validate the theory.