STOCHASTIC RELAXATION FOR CONTINUOUS VALUES - STANDARD REGULARIZATIONBASED ON GAUSSIAN MRF

We propose a fast computation method of stochastic relaxation for the continuous-valued Markov random field (MRF) whose energy function is r epresented in the quadratic form. In the case of regularization in vis ual information processing, the probability density function of a stat e transition can be transformed to a Gaussian function, therefore, the probablistic state transition is realized with Gaussian random number s whose mean value and variance are calculated based on the condition of the input data and the neighborhood. Early visual information proce ssing can be represented with a coupled MRF model which consists of co ntinuity and discontinuity processes. Each of the continuity or discon tinuity processes represents a visual property, which is like an inten sity pattern, or a discontinuity of the continuity process. Since most of the energy function for early visual information processing can be represented by the quadratic form in the continuity process, the prob ability density of local computation variables in the continuity proce ss is equivalent to the Gaussian function. If we use this characterist ic, it is not necessary for the discrimination function computation to calculate the summation of the probabilities corresponding to all pos sible states, therefore, the computation load for the state transition is drastically decreased. Furthermore, if the continuous-valued disco ntinuity process is introduced, the MRF model can directly represent t he strength of discontinuity. Moreover, the discrimination function of this energy function in the discontinuity process, which is linear, c an also be calculated without probability summation. In this paper, a fast method for calculating the state transition probability for the c ontinuous-valued MRF on the visual information processing is theoretic ally explained. Next, initial condition dependency, computation time a nd dependency on the statistical estimation of the condition are inves tigated in comparison with conventional methods using the examples of the data restoration for a corrupted square wave and a corrupted one-d imensional slice of a natural image.