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Proceedings ArticleDOI

Hierarchical Gibbs models for image processing

26 Jun 2004-Vol. 1, pp 174-176
TL;DR: In the paper an approach to image processing and image analysis based on hierarchical beamlet structure associated with Gibbs distribution is offered.
Abstract: Hierarchical models of images have been used in image processing rather widely because of evidently hierarchical nature of human vision Gibbs distribution due to its universality looks like the most convenient formalism for making use of those models In the paper an approach to image processing and image analysis based on hierarchical beamlet structure associated with Gibbs distribution is offered
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Journal ArticleDOI
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Abstract: We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.

18,761 citations


"Hierarchical Gibbs models for image..." refers background in this paper

  • ...[1] Sun, S and Zhang, Y, "Ihe Application of Intelligent Control System in a Power Plant', The First IEEE Regional Conference on , May 25-27, Pp:278 282, 1993 [2] Naser, J....

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Book ChapterDOI
01 Jan 2002
TL;DR: A framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis is described.
Abstract: We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis.

272 citations

Proceedings Article
06 Jul 2003
TL;DR: For the purpose of increasing the quality of grayscale and color picture reconstruction a new hierarchical two-level Gibbs model using as a lower layer a line process describing edges of regions is suggested, and this algorithm as a by-product extracts edges of picture regions.
Abstract: Gibbs models are being applied in image processing due to easiness of taking into account of pixel interactions. An iteration class of algorithms known as stochastic relaxation is the most powerful tool for solving a great many tasks in image processing. In spite of the fact that many researchers concern themselves with Gibbs model application to image processing, there are problems in this field that are not solved up to date. In this work, authors present some new results obtained recently. In particular new methods of finite-state Gibbs model parameter estimation based on sufficient statistics and on conditional moments, algorithms of texture segmentation, algorithms of grayscale and color picture reconstruction are presented. These algorithms are suitable for reconstructing not only artificially distorted model images, as in most cases of published works, but for reconstructing the images obtained by plain cameras as well. For the purpose of increasing the quality of grayscale and color picture reconstruction a new hierarchical two-level Gibbs model using as a lower layer a line process describing edges of regions is suggested. Experiments give a demonstration of increasing the visually perceptible quality of recovered images. Moreover, this algorithm as a by-product extracts edges of picture regions.

3 citations

Proceedings Article
01 Jan 2003

2 citations