Concepts and Applications of Markov Random Field (Markov Random Field) (I)

For the sake of work, you often need to read some documents. In image processing, there will be random relationships between probability, segmentation, clustering, optimization, and other issues, it is not a Conditional Random Field (CRF) or a Markov Random Field (MRF), which is a headache. So I plan to take the time to see what MRF is.
In general, MRF contains two meanings:
1) Markov Properties
It refers to the distribution of the nth + 1st moment when a random variable sequence is arranged in sequence by time, regardless of the value of the random variable before the nth moment. Take the weather for example. If we assume that the weather is Markov, we assume that today's weather only has a probability relationship with yesterday's weather, but it has nothing to do with the weather of the day before yesterday and before the day before yesterday. Other spreading patterns, such as infectious diseases and rumors, are Markov.
2) Random Field
It is called a random field when a phase space value is randomly assigned to each location according to a certain distribution. Let's take the land for example. There are two concepts: location and phase space ). "Location" is like a acre of farmland; "phase space" is like planting various crops. We can plant different crops for different places. This is like assigning different values in the phase space to each "location" of the random field. As a saying goes, a random field is a field where crops are planted.
The Markov random field, for example, can be expressed as: If the crop types in any field are only related to the crop types in the adjacent field, it has nothing to do with the types of crops in other places, so the collection of crops in these places is a Markov Random Field.

 

References:

1. http://baike.baidu.com/view/1017664.htm