Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models

By Tony F. Chan, Selim Esedoglu, Mila Nikolova. SIAM Journal on Applied Mathematics, 2006

1,171 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/8d0165b52b1b4f5598776e8b4ff01ee98fb439bd

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Citations in the corpus

A convex relaxation approach for computing minimal partitions (2009, background): “In [11], Chan, Esedoglu and Nikolova gave a convex formulation of (1) for k = 1, by rewriting it in terms of the variational model”
Total Variation Minimization and a Class of Binary MRF Models (2005, background): “In image processing, the observation that (1) can be solved by nding the appropriate superlevel of the solution of (4) was also mentioned recently in [12, 13].”
A Survey and Comparison of Discrete and Continuous Multi-label Optimization Approaches for the Potts Model (2013, background): “Such total-variation based approaches to partitioning problems were proposed in Chan et al. (2006), Cremers et al. (2004) and Cremers et al. (2006).”
An Octree-Based Approach towards Efficient Variational Range Data Fusion (2016, background): “of the level sets in u and in combination, TV-L1 induces a pure geometric regularization, as found in [6].”
Continuous Global Optimization in Multiview 3D Reconstruction (2007, methodology): “It is stated by the following theorem, based on the work of (Chan et al., 2006): Theorem: If u * : V → R is any minimizer of the functional (22), then for any threshold µ ∈ (0, 1) the binary function 1 Σµ(u * ) (x) : V → {0, 1} with Σ µ (u) := {x : u(x) > µ} is also a minimizer of (22).”
Variable Selection (2019, methodology): “Using convex relaxation techniques, this allows to solve certain classes of weighted minimal surface problems, which, for instance, arise in segmentation [12] and 3D reconstruction [10], in a globally optimal manner.”
Fast Global Minimization of the Active Contour/Snake Model (2007, methodology): “Like the energy of ACWE [13], Energy E2 is homogeneous of degree 1 in u.”
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction (2010, methodology): “As described in algorithm 2, the convexiﬁed segmentation can be reduced to a sequence of problems of the form where We wish to solve this problem eﬃciently without the use of regularization [17, 10].”
GrabCut in One Cut (2013, methodology): “One important practical advantage of this basic energy is that there are efficient methods for their global minimization using graph cuts [4] or continuous relaxations [5, 18].”
An algorithm for minimizing the Mumford-Shah functional (2009, background): “Alternatively the level set framework can be replaced by graph cut algorithms [14] or convex relaxation approaches [9, 7].”
Deep Level Sets for Salient Object Detection (2017, background): “Although pointed out by Chan et al [7] that variational level set segmentation problem is non-convex, a well-initialized level sets and momentum-based learning strategies used in training neural network can help to achieve an optimal result [3].”
Segmentation and Shape Tracking of Whole Fluorescent Cells Based on the Chan–Vese Model (2013, methodology): “For the sake of completeness, we refer the interested reader to the convex optimization framework [50], [51], in which the nonconvex Chan–Vese model is reformulated as a convex minimization problem and solved directly using fast iterative methods.”
Image segmentation with a bounding box prior (2009, background): “Furthermore, tackling the optimization problem (1) with the convex continuous optimization allows to replace the pairwise terms with the total variation terms [11].”
Machine Learning and Radiology (2012, background): “Chan et al. (2006) showed how to convert some non-convex minimization problems from image processing and computer vision into convex ones.”
An introduction to Total Variation for Image Analysis (2009, background): “This has been observed several times in the past [26], and probably the first time for numerical purposes in [14].”