Discrete Markov image modeling and inference on the quadtree

@article{Lafert2000DiscreteMI,
  title={Discrete Markov image modeling and inference on the quadtree},
  author={Jean-Marc Lafert{\'e} and Patrick P{\'e}rez and Fabrice Heitz},
  journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society},
  year={2000},
  volume={9 3},
  pages={
          390-404
        }
}
Noncasual Markov (or energy-based) models are widely used in early vision applications for the representation of images in high-dimensional inverse problems. Due to their noncausal nature, these models generally lead to iterative inference algorithms that are computationally demanding. In this paper, we consider a special class of nonlinear Markov models which allow one to circumvent this drawback. These models are defined as discrete Markov random fields (MRF) attached to the nodes of a… 

Unsupervised image classification with a hierarchical EM algorithm

  • A. ChardinP. Pérez
  • Computer Science
    Proceedings of the Seventh IEEE International Conference on Computer Vision
  • 1999
TLDR
A new hierarchical stochastic model which benefits from both the spatial and hierarchical prior modeling is investigated, based on a tree which has been pollarded with nodes at the coarsest resolution exhibiting a grid-based interaction structure.

Semi-iterative Inferences with Hierarchical Energy-Based Models for Image Analysis

TLDR
This paper proposes to introduce newhi erarchical models based on a hybrid structure which combines a spatial grid of a reduced size at the coarsest level with sub-trees appended below it, down to the finest level.

A Hierarchical Markov Image Model and Its Inference Algorithm

TLDR
A new model based on the hierarchical MRFhalf tree model is proposed for only one image can be obtained in image segmentation, whose MPM (maximizer of the posterior marginals) algorithm is inferred too.

Markov Random Fields in Image Segmentation

TLDR
The primary goal of this monograph is to demonstrate the basic steps to construct an easily applicable MRF segmentation model and further develop its multi-scale and hierarchical implementations as well as their combination in a multilayer model.

Modèles de Markov en traitement d’images Markov models in image processing

TLDR
More recent models and processing techniques, such as Pairwise and Triplet Markov models, Dempster-Shafer fusion in a Markov context, and generalized mixture estimation, are discussed.

Statistical image segmentation using triplet Markov fields

TLDR
The PMF is generalized to Triplet Markov Fields (TMF) by adding a third random field U=(Us) and considering the Markovianity of (X, U, Y) and it is shown that in TMF X is still estimable from Y by Bayesian methods.

Hierarchical Markovian segmentation of multispectral images for the reconstruction of water depth maps

A tree-structured Markov random field model for Bayesian image segmentation

TLDR
Numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on "flat" MRF models, and its performance, in terms of segmentation accuracy and map smoothness, is comparable or even superior.

Varying complexity in tree-structured image distribution models

TLDR
It is argued that it is beneficial to allow more complex tree-structured models, the use of information theoretic penalties to choose the model complexity, and experimental results to support these proposals are presented.

Markov model for multispectral image analysis: application to small magellanic cloud segmentation

TLDR
This paper presents some results obtained on multiwavelength images of the small magellanic cloud, by using the marginal posterior mode (MPM) estimator on a quadtree structure under Markovian assumption.
...

References

SHOWING 1-10 OF 46 REFERENCES

Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation

TLDR
Two solutions are proposed to solve the problem of model parameter estimation from incomplete data: a Monte Carlo scheme and a scheme related to Besag's (1986) iterated conditional mode (ICM) method, both of which make use of Markov random-field modeling assumptions.

A multiscale random field model for Bayesian image segmentation

TLDR
Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing, and is found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.

Hierarchical statistical models for the fusion of multiresolution image data

This paper presents a class of nonlinear hierarchical algorithms for the fusion of multiresolution image data in low-level vision. The approach combines nonlinear causal Markov models defined on

Segmentation of textured images using a multiresolution Gaussian autoregressive model

TLDR
A new algorithm for segmentation of textured images using a multiresolution Bayesian approach which is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate.

An overlapping tree approach to multiscale stochastic modeling and estimation

TLDR
An efficient multiscale algorithm for generating sample paths of a random field whose second-order statistics match a prespecified covariance structure, to any desired degree of fidelity is developed.

Multiresolution Gauss-Markov random field models for texture segmentation

TLDR
The experiments with synthetic, Brodatz texture, and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm.

A multiscale stochastic image model for automated inspection

TLDR
A novel multiscale stochastic image model is developed to describe the appearance of a complex threedimensional object in a two-dimensional monochrome image that is used in conjunction with Bayesian estimation techniques to perform automated inspection.

A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification

TLDR
This paper presents a classical multiscale model which consists of a label pyramid and a whole observation field, and proposes a hierarchical Markov random field model based on this classical model, which results in a relaxation algorithm with a new annealing scheme: the multitemperatureAnnealing (MTA) scheme, which consist of associating higher temperatures to higher levels in order to be less sensitive to local minima at coarser grids.

Modeling and estimation of multiresolution stochastic processes

TLDR
It is shown how the wavelet transform directly suggests a modeling paradigm for multiresolution stochastic modeling and related notions of multiscale stationarity in which scale plays the role of a time-like variable.

Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination

TLDR
The authors illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using the algorithm achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally.