Markov random field

About: Markov random field is a research topic. Over the lifetime, 5669 publications have been published within this topic receiving 179568 citations. The topic is also known as: MRF.

Statistical analysis of dirty pictures

Abstract: A continuous two-dimensional region is partitioned into a fine rectangular array of sites, or ‘pixels', each pixel having a particular '‘colour’ belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a non-degenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable large-scale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does ...

Occlusion-aware 3D Morphable Models and an Illumination Prior for Face Image Analysis

Abstract: Faces in natural images are often occluded by a variety of objects We propose a fully automated, probabilistic and occlusion-aware 3D morphable face model adaptation framework following an analysis-by-synthesis setup The key idea is to segment the image into regions explained by separate models Our framework includes a 3D morphable face model, a prototype-based beard model and a simple model for occlusions and background regions The segmentation and all the model parameters have to be inferred from the single target image Face model adaptation and segmentation are solved jointly using an expectation–maximization-like procedure During the E-step, we update the segmentation and in the M-step the face model parameters are updated For face model adaptation we apply a stochastic sampling strategy based on the Metropolis–Hastings algorithm For segmentation, we apply loopy belief propagation for inference in a Markov random field Illumination estimation is critical for occlusion handling Our combined segmentation and model adaptation needs a proper initialization of the illumination parameters We propose a RANSAC-based robust illumination estimation technique By applying this method to a large face image database we obtain a first empirical distribution of real-world illumination conditions The obtained empirical distribution is made publicly available and can be used as prior in probabilistic frameworks, for regularization or to synthesize data for deep learning methods

Bayesian learning in undirected graphical models: approximate MCMC algorithms

Abstract: Bayesian learning in undirected graphical models---computing posterior distributions over parameters and predictive quantities---is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over parameters. While this intractability, due to the partition function, is familiar to those performing parameter optimisation, Bayesian learning of posterior distributions over undirected model parameters has been unexplored and poses novel challenges. We propose several approximate MCMC schemes and test on fully observed binary models (Boltzmann machines) for a small coronary heart disease data set and larger artificial systems. While approximations must perform well on the model, their interaction with the sampling scheme is also important. Samplers based on variational mean-field approximations generally performed poorly, more advanced methods using loopy propagation, brief sampling and stochastic dynamics lead to acceptable parameter posteriors. Finally, we demonstrate these techniques on a Markov random field with hidden variables.

Belief Propagation in a 3D Spatio-temporal MRF for Moving Object Detection

Abstract: Previous pixel-level change detection methods either contain a background updating step that is costly for moving cameras (background subtraction) or can not locate object position and shape accurately (frame differencing). In this paper we present a belief propagation approach for moving object detection using a 3D Markov random field (MRF) model. Each hidden state in the 3D MRF model represents a pixel's motion likelihood and is estimated using message passing in a 6-connected spatio-temporal neighborhood. This approach deals effectively with difficult moving object detection problems like objects camouflaged by similar appearance to the background, or objects with uniform color that frame difference methods can only partially detect. Three examples are presented where moving objects are detected and tracked successfully while handling appearance change, shape change, varied moving speed/direction, scale change and occlusion/clutter.