On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006 ) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003 ). We recall in this paper h...

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Bibliographic Details
Published in:International journal of computer vision 2009-09, Vol.84 (3), p.288-307
Main Authors: Chambolle, Antonin, Darbon, Jérôme
Format: Article
Language:English
Subjects:
Applied sciences
Artificial Intelligence
C (programming language)
Computation
Computer Imaging
Computer Science
Computer science
control theory
systems
Computer vision
Conferences
Curvature
Evolution
Exact sciences and technology
Image Processing and Computer Vision
Information retrieval. Graph
Mathematical analysis
Optimization
Partial differential equations
Pattern Recognition
Pattern Recognition and Graphics
Pattern recognition. Digital image processing. Computational geometry
Theoretical computing
Vision
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Summary:In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006 ) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003 ). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. (SIAM Journal on Control and Optimization 31(2):387–438, 1993 ) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253–271, 1995 ), and show how the corresponding problems can be solved with  sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term.
ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-009-0238-9