Triplet Markov Chains and Image Segmentation

Pieczynski, Wojciech

doi:10.1002/9781118603864.ch4

Cited by 3 publications

(3 citation statements)

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“…Here we develop an algorithm for hierarchical Markovian models [108,118,119,120]. Our approach is similar in spirit to Iterative Conditional Estimation [149,175] as well as to the EM algorithm [48,181]: we recursively look at the Maximum a Posteriori (MAP) estimate of the label field given the estimated parameters then we look at the Maximum Likelihood (ML) estimate of the parameters given a tentative labeling obtained in the 111 previous step. The only parameter supposed to be known is the number of labels, all the other parameters are estimated.…”

Section: Parameter Estimationmentioning

confidence: 99%

Markov Random Fields in Image Segmentation

Kató¹

2011

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This monograph gives an introduction to the fundamentals of Markovian modeling in image segmentation as well as a brief overview of recent advances in the field. Segmentation is considered in a common framework, called image labeling, where the problem is reduced to assigning labels to pixels. In a probabilistic approach, label dependencies are modeled by Markov random fields (MRF) and an optimal labeling is determined by Bayesian estimation, in particular maximum a posteriori (MAP) estimation. The main advantage of MRF models is that prior information can be imposed locally through clique potentials. The primary goal is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multiscale and hierarchical implementations as well as their combination in a multilayer model. MRF models usually yield a non-convex energy function. The minimization of this function is crucial in order to find the most likely segmentation according to the MRF model. Besides classical optimization algorithms, like simulated annealing or deterministic relaxation, we also present recently introduced graph cutbased algorithms. We briefly discuss the possible parallelization techniques of simulated annealing, which allows efficient implementation on, e.g., GPU hardware without compromising convergence properties of the algorithms. While the main focus of this monograph is on generic model construction and related energy minimization methods, many sample applications are also presented to demonstrate the applicability of these models in real life problems such as remote sensing, biomedical imaging, change detection, and color-and motion-based segmentation. In real-life applications, parameter estimation is an important issue when implementing completely data-driven algorithms. Therefore some basic procedures, such as expectation-maximization, are also presented in the context of color image segmentation. Note: A sample implementation of the most important segmentation algorithms is available in grey scale at http://dx.doi.org/ 10.1561/2000000035 demogray and in color at http://dx.doi.org/ 10.1561/2000000035 democolor. ix 4 Graph Cut 4.1 Exact MAP of Binary MRFs via Standard Maxflow/Mincut 4.2 Solving Multilabel and Higher Order MRFs via GraphCut 4.3 An Example: Interactive Segmentation of Fluorescent Microscopic Images 5 Parameter Estimation and Sample Applications 5.1 Unsupervised Image Segmentation 5.2 Classification of Synthetic Aperture Radar Images 5.3 Multilayer MRF Models 6 Conclusion Acknowledgments References Dedication "To the memory of my mother" Zoltan Kato "To the memory of my beloved sister Elise who passed away in August 2012" Josiane Zerubia xi 1.1 Image Segmentation 3Ω is finite, although huge. A widely accepted standard, also motivated by the human visual system [121,162], is to construct this probability measure in a Bayesian framework [37,161,214]: We shall assume that we have a set of observed (Y ) and hidden (X) random variables. In our context, any observed value y ∈...

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Section: Parameter Estimationmentioning

confidence: 99%

Markov Random Fields in Image Segmentation

Kató¹

2011

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“…They have since been extensively applied to quadtrees [53,54] or similar structures [55]. In the same way, Hidden Markov Chains (HMC) allow an exact inference based on Maximum of Posterior Marginal (MPM) criterion and both approaches on chains [56,57] and quadtrees [58] have been refined through pairwise or triplet models in the past decade. Indeed, Markovian chains share similar properties with Markovian quadtrees than can be seen as hierarchical Markov chains [59].…”

Section: Contributionsmentioning

confidence: 99%

Connected image processing with multivariate attributes: An unsupervised Markovian classification approach

Collet¹

2015

Computer Vision and Image Understanding

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This article presents a new approach for constructing connected operators for image processing and analysis. It relies on a hierarchical Markovian unsupervised algorithm in order to classify the nodes of the traditional Max-Tree. This approach enables to naturally handle multivariate attributes in a robust non-local way. The technique is demonstrated on several image analysis tasks: filtering, segmentation, and source detection, on astronomical and biomedical images. The obtained results show that the method is competitive despite its general formulation. This article provides also a new insight in the field of hierarchical Markovian image processing showing that morphological trees can advantageously replace traditional quadtrees.

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“…The authors introduced a statistical model based on the hidden Markov random field which took into ac-count spatial dependencies between data. In statistical image processing, Pieczynski [10][11][12] introduced new systems dedicated to image segmentation by Markov models such as pairwise Markov chains and triplet Markov chains. These particular models can better take into account the boundaries between classes, which can be of great interest for the segmentation of satellite images.…”

Section: Introductionmentioning

confidence: 99%