Thoughts on MRF of Markov Random Field

Thoughts on MRF of Markov Random Field

Markov Random Fields (MRF) is the probability representation of undirected graph. The following describes its application in computer vision.

The MRF application is equivalent to a labeling problem in vision. More specifically, the label of each node in the graph is determined by map inference. The advantages of MRF over other methods are: 1) a prinled led method is provided to model prior knowledge, and 2) MRF can easily describe contextual information using quantitative methods. Therefore, compared with other pixel-based or local-based methods, it can take into account the impact of environmental knowledge. If the graph model is created properly, it may obtain the global optimal interpretation.
Vision is a step closer.

 

When it comes to the MRF inference, graph construction and parameter learning must be included first, and finally the inference must be established. The graph is generally created to model the problem itself, for example, in Image Restoration and image segmentation, we usually use the 4-neighborhood or 8-neighborhood pairwise model. In this way, the 4-or 8-adjacent pixels are connected by edges. This model is the paradigmatic pairwise Markov model, if you want to add a High-Order (> = 3) potential, it is equivalent to introducing more constraints, such as: connectivity
Constraints on the results of non-Christian classification ..., when talking about the constraints of unsupervised classification results, note that it must be other classification methods, rather than the classification results of MRF itself constitute a new constraint.

 

The Parameter Learning Method in MRF is omitted here and will be supplemented later.

The following describes the MRF inference problem, that is, the problem of minimum energy of the energy function. For classic MRF models with only unary and binary potential, graph cut can be solved in linear time. If a higher potential is added, although the problem may become NP-hard, there are still many approximate algorithms, such as loopy belief propagation (HSV), tree-reweighted message passing (TRW), Metropolis-Hastings, and MCMC. The essence of these methods is:
Energy Minimization, it is worth mentioning that cvpr now has a workshop dedicated to this issue, called energy minimization Methods incomputer vision and pattern recognition (emmcvpr ). organizers: Yuri boykov (uwo), Fredrik Kahl, Victor lempitsky, Vladimir Kolmogorov (UCL), Olga Veksler (uwo ), all of them are active in the cutting-edge fields of algorithms, discrete mathematics, variational methods, and graph theory. Therefore, if you are interested in optimization methods with minimal energy, you can pay attention to the home pages of these professors, they also focus on Computer Vision Applications, so most of their publication will be published on iccv, cvpr, eccv, and nips.

 

The above rough section outlines the three steps of MRF. Next I will talk about my views on MRF: 1) Although it obtains the overall maximal likely solution through map, if only local constraints are taken into account when modeling the problem itself, the result obtained by MRF is still local. For example, the most classic image segmentation is considered. If only pairwise model is used, it is very likely that a complete object is divided into two or more parts. 2) When more constaints are introduced, different constraints are not independent. In general, we use the glasdistribution to describe the Markov network. Different potential values are the addition relationship and are converted to the probability, it is a multiplication, that is, the two clique that are not independent are directly multiplied, so there is a parameter redundancy (redundency), so Parameter
This problem needs to be solved during learning (this problem is called parameter significance detection in measurement data processing ).

 

Below are some good materials:

A tutorial of MRF on CV:Markov Random Field ModelsInComputer Vision(ECCV
94, S. Z. li)

MRF inference, prof. Yuri: http://www.csd.uwo.ca /~ Yuri/

Prof.Richard szeliski:ComparativeStudyOfEnergy Minimization MethodsForMarkovrandom Fields.
Richard's computer vision teaching material Computer Vision: algorithms and applications is being used by many universities around the world. There are trends in replacing computer vision: a modern approach, multiview geometry in computer vision and other authoritative teaching materials.

Code: http://vision.middlebury.edu/MRF/