# Markov Random Field Image Models and Their Applications to Computer Vision

@inproceedings{Geman2010MarkovRF, title={Markov Random Field Image Models and Their Applications to Computer Vision}, author={Stuart Geman}, year={2010} }

1. Introduction. Computer vision refers to a variety of applications involving a sensing device, a computer, and software for restoring and possibly interpreting the sensed data. Most commonly, visible light is sensed by a video camera and converted to an array of measured light intensities, each element corresponding to a small patch in the scene (a picture element, or "pixel"). The image is thereby "digitized," and this format is suitable for computer analysis. In some applications, the…

## 182 Citations

Markov Random Fields in Image Segmentation

- Computer ScienceFound. Trends Signal Process.
- 2012

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.

Image Restoration Using Particle Filters By Improving The Scale Of Texture WithMRF

- Computer Science
- 2012

A denoising technique based on particle filtering using MRF (Markov Random Field) to capture the scale of the texture and associates weights for each hypothesis according to its relevance and its contribution in the Denoising process.

Image classification and reconstruction using Markov Random Field modeling and sparsity

- Mathematics
- 2012

An evaluation of the quality of the reconstruction that uses only reconstruction's wavelet coefficients makes possible to stop the acquisition process at constant quality, and to capture only the needed measurements, and culminates in an efficient volume reconstruction with a dynamic restricted number of measurements.

Sparse Long-Range Random Field and Its Application to Image Denoising

- Computer ScienceECCV
- 2008

A graph structure with longer range connections that is designed to both capture important image statistics and be computationally efficient is considered, which incorporates long-range connections in a manner that limits the cliques to size 3, thereby capturing important second-order image statistics while still allowing efficient optimization due to the small clique size.

Seeing Things in Random-Dot Videos

- Computer ScienceACPR
- 2019

This work proposes a new detection and spatio-temporal grouping algorithm for signals when, per frame, the information on objects is both random and sparse and embedded in random noise, and sees in it a simple computational Gestalt model of human perception with only two parameters.

Learning coupled conditional random field for image decomposition: theory and application in object categorization

- Computer Science
- 2008

Experimental results demonstrate that the proposed computational model of “recognition-through-decomposition-andfusion” achieves better performance than most of the state-of-the-art methods in recognizing the objects in Caltech-101, especially when only a limited number of training samples are available.

Crowd Scene Analysis in Video Surveillance

- Computer Science
- 2016

A novel feature descriptor is proposed to encode regional optical flow features of video frames, where adaptive quantization and binarization of the feature code are employed to improve the discriminant ability of crowd motion patterns.

Learning for stereo vision using the structured support vector machine

- Computer Science2008 IEEE Conference on Computer Vision and Pattern Recognition
- 2008

This study shows that random field models with longer-range edges generally outperform the 4-connected grid and that this advantage is especially pronounced for noisy images.

A spatio-spectral hybridization for edge preservation and noisy image restoration via local parametric mixtures and Lagrangian relaxation

- MathematicsArXiv
- 2012

This paper investigates a fully unsupervised statistical method for edge preserving image restoration and compression using a spatial decomposition scheme and uses a widely used topological concept, partition of unity.

## References

SHOWING 1-10 OF 32 REFERENCES

Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1987

Two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of C MRF's, designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology.

Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

- PhysicsIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1984

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.

Markov Random Field Texture Models

- MathematicsIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1983

The power of the binomial model to produce blurry, sharp, line-like, and blob-like textures is demonstrated and the synthetic microtextures closely resembled their real counterparts, while the regular and inhomogeneous textures did not.

A Renormalization Group Approach to Image Processing Problems

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1989

The restoration algorithm is a global-optimization algorithm applicable to other optimization problems, and generates iteratively a multilevel cascode of restored images corresponding to different levels of resolution, or scale.

Statistics, images, and pattern recognition

- Mathematics
- 1986

Data are increasingly being collected in the form of images, especially in fields using remote sensing and microscopy. Statisticians are becoming interested in developing techniques to handle the…

Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1987

This paper presents random field models for noisy and textured image data based upon a hierarchy of Gibbs distributions, and presents dynamic programming based segmentation algorithms for chaotic images, considering a statistical maximum a posteriori (MAP) criterion.

Estimation of binary Markov random fields

- Computer Science
- 1986

A new estimation procedure is suggested that is analogous to minimum logit chi-squareestimation in logistic regression, does not involve non-linearoptimization, and decisively beats Maximum Pseudo-Likelihood in mean squarederror.

Probabilistic Solution of Ill-Posed Problems in Computational Vision

- Computer Science, Mathematics
- 1987

This work derives efficient algorithms and describes parallel implementations on digital parallel SIMD architectures, as well as a new class of parallel hybrid computers that mix digital with analog components.

Statistical Analysis of Non-Lattice Data

- Mathematics
- 1975

In rather formal terms, the situation with which this paper is concerned may be described as follows. We are given a fixed system of n sites, labelled by the first n positive integers, and an…