Application of Markov random field modeling in image analysis (reading notes) _ reading notes

The 1.mrf-gibbs equivalence theorem states that the MRF Joint distribution (joint distribution) is a Gibbs distribution (Gibbs distribution), and the latter can take a simple form. For statistical image analysis, this not only brings us to the mathematical discovery, but also provides us with the Mathematical Easy processing tool (Grenander 1983;geman and Geman 1984).

The 2.MRF theory tells us how to model a priori probability of a context-dependent pattern, such as texture and object characteristics. A specific MRF model supports its own schema class, rather than other schema classes, by having the pattern associated with a greater probability. MRF theory usually combines statistical decision and estimation theory so that the objective function (objective functions) can be described according to the established optimization principles.

3. On the basis of regularity and continuity, we classify visual marking issues as one of the following four categories:
Class I (LP1): rule position with continuous marking
Class II (LP2): rule location with discrete tags
Category III (LP3): Irregular locations using discrete markers
Class Fourth (LP4): Irregular position with continuous markers

function of 4.1.2.2 energy function (role functions)
In the minimized vision, the function of the energy function is twofold. (1) The Global Optimal Solution (2) of the quantitative measurement solution is used to guide the search of the minimal solution. As a quantitative measure, the energy function defines the minimum solution as the global minimum. Based on this, it is important to formulate energy functions. The "right solution" is the minimization of energy functions, which we call formulaic correctness.
To understand the optimal path, we should not mix the problem in the formula with the problem in the search. Distinguishing between these two problems can help us correct the errors in the model. For example, if the output of an optimized process (assuming the process is correct) is not what we expect, there are two possible causes: (1) The formulated objective function does not correctly model the real object (2) The output is a low mass local minimum value. Before we extend the model, we have to determine which reason the problem originated.
The guiding function of energy function to search can be either complete or incomplete. For example, when minimizing an entity, when the energy function is a convex function that is smooth, its global minimum is equal to the local minimum, and the gradient of the energy function provides sufficient information to search the global solution. In this case, the guidance of the search is complete. However, when the problem is not convex, there will be no general method to effectively use the energy function to guide the retrieval, in which case the guidance of the energy function will be limited.
In specific cases, it is advantageous to formulate energy functions and search at the same time. That is, the appropriate promotion search at the same time as the formulation energy function. This is what Blake and Zisserman wrote in 1987 based on cumulative non-convex (gnc:graduated non-convexity). In that article, the energy function is gradually transformed from a convex form to a target form, along with a process based on the gradient approximate global optimal solution.
In real space, local minimization is the most mature field in optimization, there are many formal methods to solve the problem of local minimization, but not for combination and global minimization. For the latter case, heuristic has become an important essential element in practical applications. When we use heuristic method to find the global optimal solution, we need to attach a hypothetical condition. For example a bounded model (Baird 1985; Breuel 1992). The model assumes that under a given threshold (threshold), the measurement error has an upper bound (under the given threshold, the assumed error is uniformly distributed). The assumption is valid depending on the threshold value. When the threshold value is infinite, this assumption is clearly correct. In practice, however, thresholds are always set to a value that is less than the value required to fully validate the bounded error assumptions. The smaller the value, the higher the efficiency, but the generalization of the algorithm will also be reduced.
In the hypothesis-validation method, an effective algorithm is used to form a hypothetical algorithm, such as Hough Transform (Hough 1962; Duda and Hart 1972), Interpretation Tree Search (interpretation) (Grimson and Lozano-prez 1987), geometric hashing (Lamdan and Wolfson 1988), algorithm The validity of the solution is derived from the fast hashing (fast elimination) method, which is not feasible, or by using heuristics to trim the solution space. In this way, a small number of candidate solutions can be selected quickly and can be fully validated and evaluated, for example by using energy functions. At this point the energy function is used only for estimation purposes, not as a search guide.
We note that the use of a formal approach in the estimation has great advantages, and the use of heuristics in search has great advantages. A good strategy for a given system is to use heuristics to quickly find a small number of alternate solutions.
The optimal solution is found by using the energy function to evaluate the alternate solution.