An adaptive deterministic annealing approach for medical image segmentation

Mitra, Sunanda; Castellanos, Ramiro; Joshi, S.

doi:10.1109/nafips.2000.877392

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…ζ i j log ζ i j ; (11) here observe that Γ(P, P) = L(P). Therefore ∆(P, P + ) = Γ(P, P) − Γ(P + , P + ),…”

Section: Convergence Analysismentioning

confidence: 77%

“…We show that ∆ 1 ≥ 0 by showing that Γ(P + , σ ) (a quadratic function of σ with fixed P + ) achieves its minimum when σ = P + . The stationary point is obtained by setting ∂ Γ ∂ σ i j (P + ,σ ) = 0 in (11), which yields…”

Section: Convergence Analysismentioning

confidence: 99%

“…In the context of data clustering this MEP based heuristic has resulted in the deterministic annealing (DA) algorithm [9]. DA has been successfully applied to a large class of optimization problems such as, pattern classification [10], image segmentation [11], graph aggregation [12], robust speech recognition [13], multiple travelling salesman [14] and coverage control [15]. However, DA is primarily a resource allocation algorithm and requires the precise knowledge of coordinates of data points that need to be clustered.…”

Section: Introductionmentioning

confidence: 99%

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Multiway k-Cut in Static and Dynamic Graphs: A Maximum Entropy Principle Approach

Baranwal

Srivastava

Salapaka

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This work presents a maximum entropy principle based algorithm for solving minimum multiway k-cut problem defined over static and dynamic digraphs. A multiway k-cut problem requires partitioning the set of nodes in a graph into k subsets, such that each subset contains one prespecified node, and the corresponding total cut weight is minimized. These problems arise in many applications and are computationally complex (NP-hard). In the static setting this article presents an approach that uses a relaxed multiway k-cut cost function; we show that the resulting algorithm converges to a local minimum. This iterative algorithm is designed to avoid poor local minima with its run-time complexity as ∼ O(kIN 3 ), where N is the number of vertices and I is the number of iterations. In the dynamic setting, the edge-weight matrix has an associated dynamics with some of the edges in the graph capable of being influenced by an external input. The objective is to design the dynamics of the controllable edges so that multiway kcut value remains small (or decreases) as the graph evolves under the dynamics. Also it is required to determine the timevarying partition that defines the minimum multiway k-cut value. Our approach is to choose a relaxation of multiway k-cut value, derived using maximum entropy principle, and treat it as a control Lyapunov function to design control laws that affect the weight dynamics. Simulations on practical examples of interactive foreground-background segmentation, minimum multiway k-cut optimization for non-planar graphs and dynamically evolving graphs that demonstrate the efficacy of the algorithm, are presented. arXiv:1907.08720v1 [math.OC]

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“…ζ i j log ζ i j ; (11) here observe that Γ(P, P) = L(P). Therefore ∆(P, P + ) = Γ(P, P) − Γ(P + , P + ),…”

Section: Convergence Analysismentioning

confidence: 77%

Section: Convergence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiway k-Cut in Static and Dynamic Graphs: A Maximum Entropy Principle Approach

Baranwal

Srivastava

Salapaka

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…Additional classification methods include clustering [ 16 , 17 ], fuzzy classification [ 18 ], neural networks [ 19 ], deterministic annealing [ 7 ]. Hybrid “neuro-fuzzy” methods, see [ 2 , 20 , 21 ], combining fuzzy logic and neural networks perform an unsupervised learning process. Another class of statistical methods is based on Markov Random Field (MRF) [ 22 – 25 ].…”

Section: Introductionmentioning

confidence: 99%

Brain MRI Segmentation with Multiphase Minimal Partitioning: A Comparative Study

Angelini

Song

Mensh

et al. 2007

International Journal of Biomedical Imaging

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This paper presents the implementation and quantitative evaluation of a multiphase three-dimensional deformable model in a level set framework for automated segmentation of brain MRIs. The segmentation algorithm performs an optimal partitioning of three-dimensional data based on homogeneity measures that naturally evolves to the extraction of different tissue types in the brain. Random seed initialization was used to minimize the sensitivity of the method to initial conditions while avoiding the need for a priori information. This random initialization ensures robustness of the method with respect to the initialization and the minimization set up. Postprocessing corrections with morphological operators were applied to refine the details of the global segmentation method. A clinical study was performed on a database of 10 adult brain MRI volumes to compare the level set segmentation to three other methods: “idealized” intensity thresholding, fuzzy connectedness, and an expectation maximization classification using hidden Markov random fields. Quantitative evaluation of segmentation accuracy was performed with comparison to manual segmentation computing true positive and false positive volume fractions. A statistical comparison of the segmentation methods was performed through a Wilcoxon analysis of these error rates and results showed very high quality and stability of the multiphase three-dimensional level set method.

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