An algorithm for minimizing the Mumford-Shah functional

By Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle. IEEE International Conference on Computer Vision, 2009

416 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/6d2867d1f424425b3bee7df4a2094da75fd0b4c7

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In Biomedical Engineering

In Computer Vision and Pattern Recognition

Citations in the corpus

Convergence Rate Analysis of Several Splitting Schemes (2014, methodology): “We also determine exactly how fast the relaxed PRS algorithm can be; these results uncover fundamental limits on the speed of the large class operator-splitting schemes that extend relaxed PRS [21, 23, 53, 14, 7, 8, 19, 6, 20, 48, 16].”
An introduction to Total Variation for Image Analysis (2009, positive): “We have provided recently in [63] the following variant, inspired by a paper of L.”
Optimal Primal-Dual Methods for a Class of Saddle Point Problems (2013, background): “The study on ﬁrst-order primal-dual method for nonsmooth convex optimization has been mainly motivated by solving total variation based image processing problems (e.g. [45, 9, 37, 6, 4, 13]).”
An Inertial Forward-Backward Algorithm for Monotone Inclusions (2014, methodology): “– Primal-dual algorithms: Setting in (19) P∗ = Q = 0 and let in (21) αk = 0, we clearly obtain the firstorder primal-dual algorithm investigated in [10,22,27, 43].”
Second order total generalized variation (TGV) for MRI (2011, methodology): “Here, we employ the first-order primal dual algorithm of (15,16).”
A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model (2013, methodology): “As before we employ the primal– dual algorithm published in Pock et al. (2009) based on the following update scheme: ξ t+1 = ξ t + 12+n ⎛ ⎝∇ūt + ( ∑ j>i μ̄ti j − ∑ i> j μ̄tj i ) 1≤i≤n ⎞ ⎠ qt+1 = ΠQ ( qt + (−μ̄) ) ut+1 = ΠB ( ut − 14 ( f − div ξ t+1) ) μt+1 = μt − 13 ( ξi − ξ j − qi j ) ūt+1 =…”
Modern regularization methods for inverse problems (2018, methodology): “The inner variational regularization method is solved via the primal-dual hybrid gradient method (PDHGM), see [373, 307, 171, 113, 115].”
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging (2011, positive): “2 we re-visit a primal-dual algorithm proposed by Pock, Bischof, Cremers and Chambolle in [29] for minimizing a convex relaxation of the Mumford-Shah functional.”
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science (2010, methodology): “Other examples of first order methods popular for TV minimization include gradient descent, Chambolle's method, FTVd and split Bregman.”
A Three-Operator Splitting Scheme and its Optimization Applications (2015, background): “A large variety of recent algorithms [12,26,37] and their generalizations and enhancements [4,7,6,8,16,17, 18,20,28,39] are (skillful) applications of one of the following three operator-splitting schemes: (i) forwardbackward-forward splitting (FBFS) [38], (ii) forward-backward splitting (FBS) [36],”
An introduction to continuous optimization for imaging (2016, methodology): “Different numerical approaches have been proposed to find approximate solutions to the Mumford–Shah problem (Ambrosio and Tortorelli 1992, Chambolle 1999, Chan and Vese 2002, Pock et al. 2009).”
On the ergodic convergence rates of a first-order primal–dual algorithm (2016, methodology): “In this work we revisit a first-order primal-dual algorithm which was introduced in [26, 15] and its accelerated variants which were studied in [5].”
On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, neutral): “The derivation of an O (1 /N 2 ) algorithm, if at all possible for this problem, would be more interesting. analysis Our and proof is inspired by [17, 18] (who discuss a primal-dual algorithm for another problem) and by [16].”