Classification of binary random patterns

Abend, Kenneth; Harley, Thomas J.; Kanal, Laveen N.

doi:10.1109/tit.1965.1053827

Cited by 228 publications

(108 citation statements)

References 5 publications

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“…To mitigate this artifact, let us consider another important class of random fields. MMRFs, also known as causal MRF or Unilateral MRFs (UMRFs) were first introduced in [8], [12], [13]. Let us consider a finite rectangular lattice S with each site s ∈ S being associated with one or more random variables collected in a vector x.…”

Section: Hierarchical Hidden Markov Mesh Models a Mrf And Mmrf Tmentioning

confidence: 99%

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Multi-resolution classification of urban areas using hierarchical symmetric Markov mesh models

Hedhli

Moser

Zerubia

2017

2017 Joint Urban Remote Sensing Event (JURSE)

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Abstract-In this paper we investigate a new hierarchical method for high resolution remotely sensed image classification. The proposed approach integrates an explicit hierarchical graphbased classifier, which uses a quad-tree structure to model multiscale interactions, and a symmetric Markov mesh random field to deal with pixelwise contextual information at the same scale. The choice of a quad-tree and the symmetric Markov mesh allow taking benefit from their good analytical properties (especially causality) and consequently applying time-efficient non-iterative inference algorithms.

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Section: Hierarchical Hidden Markov Mesh Models a Mrf And Mmrf Tmentioning

confidence: 99%

“…1], however this is proven to be false [12]. Indeed, the MMRF with neighboring size of two results in an abnormal unbalanced MRF behaves in "cornerdependent" way.…”

Section: B Smmrf Techniquesmentioning

confidence: 99%

Multi-resolution classification of urban areas using hierarchical symmetric Markov mesh models

Hedhli

Moser

Zerubia

2017

2017 Joint Urban Remote Sensing Event (JURSE)

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“…Several previous researches have addressed the problem of binary vectors classification and clustering. For example, a likelihood ratio classification method based on Markov chain and Markov mesh assumption has been proposed in [3]. A kernel-based method for multivariate binary vectors discrimination has been proposed in [4].…”

Section: Introductionmentioning

confidence: 99%

A Robust Approach for Multivariate Binary Vectors Clustering and Feature Selection

Mashrgy

Bouguila

Daoudi

2011

Neural Information Processing

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“…We refer to [24] for an excellent introduction. Going back at least as far as Abend's work [1], Markov random fields have endured a sustained interest in the vision community. Besag [3] applied them in the context of binary image restoration and Derin [8] and Gimelfarb and coworkers [12] analyzed texture in the context of a Markov random field using learned priors based on gray level co-occurrences.…”

Section: Introductionmentioning

confidence: 99%

Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts

Cremers

Grady

2006

Computer Vision – ECCV 2006

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Abstract. Bayesian inference provides a powerful framework to optimally integrate statistically learned prior knowledge into numerous computer vision algorithms. While the Bayesian approach has been successfully applied in the Markov random field literature, the resulting combinatorial optimization problems have been commonly treated with rather inefficient and inexact general purpose optimization methods such as Simulated Annealing. An efficient method to compute the global optima of certain classes of cost functions defined on binary-valued variables is given by graph min-cuts. In this paper, we propose to reconsider the problem of statistical learning for Bayesian inference in the context of efficient optimization schemes. Specifically, we address the question: Which prior information may be learned while retaining the ability to apply Graph Cut optimization? We provide a framework to learn and impose prior knowledge on the distribution of pairs and triplets of labels. As an illustration, we demonstrate that one can optimally restore binary textures from very noisy images with runtimes on the order of a second while imposing hundreds of statistically learned constraints per pixel.

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Classification of binary random patterns

Cited by 228 publications

References 5 publications

Multi-resolution classification of urban areas using hierarchical symmetric Markov mesh models

Multi-resolution classification of urban areas using hierarchical symmetric Markov mesh models

A Robust Approach for Multivariate Binary Vectors Clustering and Feature Selection

Statistical Priors for Efficient Combinatorial Optimization Via Graph Cuts

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