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Keywords
(12)
Calculus of Variation
Computer Vision
Correspondence Problem
Curves and Surfaces
Maximum Flow
Mean Curvature Flow
Mean Curvature Motion
Partial Differential Equation
submodular functions
Total Variation
Total Variation Minimization
Variational Approach
Related Publications
(1)
An Integral Solution to Surface Evolution PDEs Via Geocuts
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On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows,10.1007/s1126300902389,International Journal of Computer Visio
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On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows
(
Citations: 15
)
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Antonin Chambolle
,
Jérôme Darbon
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 geocuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003). We recall in this paper how this is related to wellknown 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 subpixel accuracy using Parametric
Maximum Flow
techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term.
Journal:
International Journal of Computer Vision  IJCV
, vol. 84, no. 3, pp. 288307, 2009
DOI:
10.1007/s1126300902389
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Citation Context
(8)
...This is related to the work of [3] and [
6
], where gradient flows of interphases were studied in an integral framework,incasetheoriginalenergyfunctionalisgraphrepresentableinthediscretesetting.Thispaperdiffersintwomaindirections: we study images instead of interphases, and we do not require the original energy functional to be graph representable, i.e., we allow more complicated energy functionals involving ...
Egil Bae
,
et al.
Graph Cuts for Curvature Based Image Denoising
...We are of course aware of maxflow/mincut type algorithms, for instance the one in [
16
]...
Sylvain Durand
,
et al.
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
...For these cases we refer to [
36
] for the associated graph constructions...
...At this point we have to mention another paper on the subject which we came across during the resubmission phase of this paper. In [
36
], the priors of the form...
...The authors of [
36
] also claim, without proof, that the approach described in [18] could be applied for minimization of energies with such priors...
Mehmet Haydar Karcí
,
et al.
Minimization of Monotonically Levelable Higher Order MRF Energies via ...
... approximation via locally quadratic functionals as in the work of Vese et al. [2,37]; (4) iterative thresholding algorithms based on projections onto convex sets as in the work of Chambolle [10] as well as in the work of Combettes and Wajs [15] and Daubechies et al. [19]; (5) iterative minimization of the Bregman distance as in the work of Osher et al. [32] (also notice the very recent Bregman split approach [27]); (6) graph cuts [
11
,16] ...
...We expect that the use of other algorithms [
11
,16,27,32,39] may change quantitatively the results but not qualitatively...
Massimo Fornasier
,
et al.
A convergent overlapping domain decomposition method for total variati...
...Finally, such motions can be compared with others where the interplay between time and space discretization is crucial (as in [8, 10,
17
])...
Andrea Braides
,
et al.
Motion and Pinning of Discrete Interfaces
References
(55)
Total Variation Regularization for Image Denoising, I. Geometric Theory
(
Citations: 13
)
William K. Allard
Journal:
Siam Journal on Mathematical Analysis  SIAM J MATH ANAL
, vol. 39, no. 4, pp. 11501190, 2007
Variational algorithms and pattern formation in dendritic solidification
(
Citations: 32
)
Robert Almgren
Journal:
Journal of Computational Physics  J COMPUT PHYS
, vol. 106, no. 2, pp. 337354, 1993
Curvature  driven flows: a variational approach
(
Citations: 99
)
F. Almgren
,
J. E. Taylor
,
L. Wang
Journal:
Siam Journal on Control and Optimization  SIAM
, 1993
A characterization of convex calibrable sets in
(
Citations: 26
)
F. Alter
,
V. Caselles
,
A. Chambolle
Journal:
Mathematische Annalen  MATH ANN
, vol. 332, no. 2, pp. 329366, 2005
Experimental Evaluation of Parametric MaxFlow Algorithms
(
Citations: 8
)
Maxim A. Babenko
,
Jonathan Derryberry
,
Andrew V. Goldberg
,
Robert Endre Tarjan
,
Yunhong Zhou
Conference:
Workshop on Experimental and Efficient Algorithms  WEA
, pp. 256269, 2007
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Citations
(15)
Graph Cuts for Curvature Based Image Denoising
Egil Bae
,
Juan Shi
,
XueCheng Tai
Journal:
IEEE Transactions on Image Processing
, vol. 20, no. 5, pp. 11991210, 2011
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
(
Citations: 8
)
Sylvain Durand
,
Jalal Fadili
,
Mila Nikolova
Journal:
Journal of Mathematical Imaging and Vision  JMIV
, vol. 36, no. 3, pp. 201226, 2010
Structured sparsityinducing norms through submodular functions
(
Citations: 4
)
Francis Bach
Journal:
Computing Research Repository  CORR
, vol. abs/1008.4, 2010
Convex Analysis and Optimization with Submodular Functions: a Tutorial
(
Citations: 1
)
Francis Bach
Published in 2010.
Minimization of Monotonically Levelable Higher Order MRF Energies via Graph Cuts
Mehmet Haydar Karcí
,
Mübeccel Demirekler
Journal:
IEEE Transactions on Image Processing
, vol. 19, no. 11, pp. 28492860, 2010