Stochastic Relaxation for Continuous Values--Standard Regularization Based on Gaussian MRF--

Sadayuki HONGO  Isamu YOROIZAWA  

IEICE TRANSACTIONS on Information and Systems   Vol.E77-D   No.4   pp.425-432
Publication Date: 1994/04/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Neurocomputing)
Category: Regularization
neuro computing,  algorithm and computational complexity,  image processing,  

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We propose a fast computation method of stochastic relaxation for the continuous-valued Markov random field (MRF) whose energy function is represented in the quadratic form. In the case of regularization in visual information processing, the probability density function of a state transition can be transformed to a Gaussian function, therefore, the probablistic state transition is realized with Gaussian random numbers whose mean value and variance are calculated based on the condition of the input data and the neighborhood. Early visual information processing can be represented with a coupled MRF model which consists of continuity and discontinuity processes. Each of the continuity or discontinuity processes represents a visual property, which is like an intensity 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 probability density of local computation variables in the continuity process is equivalent to the Gaussian function. If we use this characteristic, it is not necessary for the discrimination function computation to calculate the summation of the probabilities corresponding to all possible states, therefore, the computation load for the state transition is drastically decreased. Furthermore, if the continuous-valued discontinuity process is introduced, the MRF model can directly represent the strength of discontinuity. Moreover, the discrimination function of this energy function in the discontinuity process, which is linear, can also be calculated without probability summation. In this paper, a fast method for calculating the state transition probability for the continuous-valued MRF on the visual informtion processing is theoretically explained. Next, initial condition dependency, computation time and dependency on the statistical estimation of the condition are investigated in comparison with conventional methods using the examples of the data restoration for a corrupted square wave and a corrupted one-dimensional slice of a natural image.