Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields

Derin, Haluk; Elliott, H.; Cristi, R.; Geman, Donald

doi:10.1109/tpami.1984.4767595

Cited by 183 publications

(65 citation statements)

References 23 publications

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“…MAP estimation is computationally direct and has experimentally been shown to work well in a variety of problems [17,18,19,20,21]. We will treat only the MAP estimation problem, since the ML estimate is the special case of a constant prior distribution.…”

Section: Discussionmentioning

confidence: 99%

“…We choose a discrete MRF model for F which is often used in segmentation problems [17,20,31]. This model encourages neighboring pixel to have the same densities.…”

Section: Non-gaussian Priorsmentioning

confidence: 99%

“…We can now add the log likelihood for the prior distribution to the expression of (17). If we use a Gaussian prior distribution, the optimum value for ∆f i is given by…”

Section: Gauss-seidelmentioning

confidence: 99%

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A local update strategy for iterative reconstruction from projections

Sauer

Bouman

1993

IEEE Trans. Signal Process.

433

422

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1Iterative methods for statistically-based reconstruction from projections are computationally costly relative to convolution backprojection, but allow useful image reconstruction from sparse and noisy data. We present a method for Bayesian reconstruction which relies on updates of single pixel values, rather than the entire image, at each iteration. The technique is similar to GaussSeidel (GS) iteration for the solution of differential equations on finite grids. The computational cost per iteration of the GS approach is found to be approximately equal to that of gradient methods. For continuously valued images, GS is found to have significantly better convergence at modes representing high spatial frequencies. In addition, GS is well suited to segmentation when the image is constrained to be discretely valued. We demonstrate that Bayesian segmentation using GS iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction. This paper includes analysis of the convergence properties of gradient ascent and GS for reconstruction from integral projections, and simulations of both maximum-likelihood and maximum a posteriori cases. EDICS #6.2.2 Image Processing and Analysis; Reconstruction Restoration and Recovery. † This work was supported by an NEC Faculty Fellowship.

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Section: Discussionmentioning

confidence: 99%

“…We choose a discrete MRF model for F which is often used in segmentation problems [17,20,31]. This model encourages neighboring pixel to have the same densities.…”

Section: Non-gaussian Priorsmentioning

confidence: 99%

See 1 more Smart Citation

A local update strategy for iterative reconstruction from projections

Sauer

Bouman

1993

IEEE Trans. Signal Process.

433

422

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“…If sij exists on the position (i, j), Kij is the constant number K. Otherwise K,, is zero. In a case in which a final solution cannot be known like this problem, the Bayesian Learning Algorithm is a powerful method to solve such problems [5]. In this method, unknown parameters are treated as distributions of probability.…”

Section: Estimation Of Altitude Inside Of Shadow (Eais)mentioning

confidence: 99%

Analysis of Detailed Geographical Features using Shadow of Satellite Images in the Case of Illegal dumping site on the Border between Aomori and Iwate Prefectures

Sasaki

Zhao

Fujita

2006

Int. J. Soc. Mater. Eng. Resour

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Recently, the analysis of geographical features by digital elevation models (DEM) which are made from satellite images, has become a widely researched topic. However, espacially in the case of old satellite image, DEM or the stereo pair to make it might be hard-to-find. Then we developed the estimation method for three-dimensional detailed geographical features shape using shadow of satellite images. In this study, we investigated the influence on the result of estimation by choosing the boundary of a shadow. Also, we examined the threshold of the brightness to discern the shadows of geographical features from old satellite images.

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“…See Refs. [10] and [11] for example, as for the Potts model in image processing. Here is the inverse temperature of the prior Gibbs distribution, and a;b is the Kronecker delta.…”

Section: Bethe/mpm Algorithm For Stochastic Image Segmentationmentioning

confidence: 99%

Unsupervised Image Segmentation Based on Bethe Approximation

Fan

Aoki

Horiguchi

2005

IIS

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We propose an approach for unsupervised image segmentation based on the Markov random field by using the Bethe approximation. We first derive the Bayesian information criterion under the Bethe approximation and then propose an iterative algorithm to search a model which fits the image data best. For this aim, we derive a criterion for merging two components among several components in terms of a perturbation expansion. Namely, annihilation of components is implemented by merging two components into one component after each convergence of the supervised segmentation with a fixed number of components. We find by numerical experiments that the optimal number of components is selected from the series of local optima with different numbers of components and the best result for segmentation is obtained with good performance.

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Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields

Cited by 183 publications

References 23 publications

A local update strategy for iterative reconstruction from projections

A local update strategy for iterative reconstruction from projections

Analysis of Detailed Geographical Features using Shadow of Satellite Images in the Case of Illegal dumping site on the Border between Aomori and Iwate Prefectures

Unsupervised Image Segmentation Based on Bethe Approximation

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