Total Variation Minimization and a Class of Binary MRF Models

By Antonin Chambolle. Energy Minimization Methods in Computer Vision and Pattern Recognition, 2005

384 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/8407e86736ff14e6a7ac611b3ad77339046c8523

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, positive): “blems easily solvable (i.e. not limited to deconvolution problems on regular grids, to orthogonal matrices, etc.). Iterative algorithms for the denoising case (K = 1) can, amongst others, be found in [5, 6]. For general K, an algorithm that uses a smoothing parameter is found in [7], an algorithm wh”
Phase Unwrapping via Graph Cuts (2005, methodology): “Other related works are the steepest descent algorithm of Murota for minimizing L functions [50], the very fast algorithms of Jérôme Darbon and Marc Sigelle [51], Antonin Chambolle [52], and Hochbaum [53], if pairwise terms are absolute differences.”
The Split Bregman Method for L1-Regularized Problems (2009, methodology): “To compare our method to another unregularized iterative method, we have also plotted the convergence curve for the gradient descent algorithm [8], which is based on the dual formulation of the ROF functional.”
Adaptive total variation image deblurring: A majorization-minimization approach (2009, background): “Given that the TV regularizer is not differentiable (due to the presence of the absolute value function), solving (3) is a challenging task, which has been the focus of a considerable amount of work over the last decade [16, 17, 19, 20, 21, 22, 23].”
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging (2011, neutral): “• PGD: O(1/N) projected (sub)gradient descent on the dual ROF problem (66) [2, 7].”
Sparse Modeling for Image and Vision Processing (2014, positive): “The penalty can easily be extended to two-dimensional signals, and has been widely used for regularizing inverse problems in image processing [Chambolle, 2005].”
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods (2010, methodology): “This can be realized in different ways, e.g., by the simple gradient descent reprojection algo-rithm in [15] or by faster multistep algorithms [6, 50, 63].”
An introduction to continuous optimization for imaging (2016, methodology): “In fact a minimizer of (7.23) is obtained by minimizing (7.1), with u = w being the input image, and then thresholding the solution u at the 0 level (Chambolle 2004a, 2005).”
Optimization with Sparsity-Inducing Penalties (2011, methodology): “This is typically the case, when working with ordinal variables5.”
A New Total Variation Method for Multiplicative Noise Removal (2009, positive): “The minimizer of the optimization problem, can be solved by many TV denoising methods such as the Chambolle projection algorithm [4], semismooth Newton’s method [13], multilevel optimization method [6], and graph-based optimization method [5].”
Deblurring Poissonian images by split Bregman techniques (2010, methodology): “Similarly, for solving the TV subproblem (19) we compared the gradient descent reprojection algorithm [10] to the alternating split Bregman algorithm in [14].”
Structured sparsity through convex optimization (2011, background): “Submodular functions (Fujishige, 2005; Bach, 2010) • F : 2 → R is submodular if and only if ∀A,B ⊂ V, F (A) + F (B) > F (A ∩B) + F (A ∪B) ⇔ ∀k ∈ V, A 7→ F (A ∪ {k})− F (A) is non-increasing • Intuition 1: defined like concave functions (“diminishing returns”) – Example: F : A 7→ g(Card(A)) is submod”
Continuous Global Optimization in Multiview 3D Reconstruction (2007, background): “In a series of works (Chan et al. 2006; Chambolle 2005; Bresson et al. 2005) image segmentation functionals, namely the two-phase piecewise constant Mumford-Shah model (Mumford and Shah 1989) and the snakes (Kass et al.”