Statistical approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. CNN is a fast parallel processor array for image processing. However, CNN is basically a deterministic analog circuit. Herein we use the CNN-UM architecture for statistical image segmentation. The Modified Metropolis Dynamics (MMD) method can be implemented into the raw analog architecture of the CNN. With a single random input signal, we were able to implement a (pseudo) random field generator using one layer (one memory/cell) of the CNN. The whole algorithm needs 8 memories/cell. We can introduce this pseudo-stochastic segmentation process in the CNN structure. Considering the simple structure of the analog VLSI design, we use simple arithmetic functions (addition, multiplication) and very simple nonlinear output functions (step, jigsaw). With this architecture, a real VLSI CNN chip can execute a pseudo-stochastic relaxation algorithm of about 100 iterations in about 1msec.

In the Makov Random Field (MRF) theory, one important problem is parameter estimation. The random segmentation process must be preceded by the estimation of the gray-level distribution of the different classes on small image segments. This process is basically supervised. Usually the histograms of noisy images can be modelled as simple gaussian distributions. This approach cannot be held in a CNN structure, since there should be as many additional layers as the number of classes. We should follow another way.

We have developed a pixel-level distribution model. The CNN turns the original image into a smooth one using the heat-diffusion equation (Laplace operator) for a given time. Then we have two gray-level values for every pixel: the original and the smoothed one. If the pixel is inside a region, the smoothed value is a good estimation of the unnoisy gray-level of the image. If the pixel is on the border of a region, then the best estimation is between the original and the smoothed values. The probable mean is half the way between the two values, while the variance is the halfwidth of their distance. Furthermore, the probable gray-levels of the different classes can be estimated using the histogram of the smoothed image. The histogram peaks of this cleaned but unsharp image correspond to the gray-level means of the classes. Using this automatic estimation, we can avoid the supervised method.

In case of low SNR, we use a larger neighborhood (3-rd order MRF) to avoid the misclassification errors at the region boundaries coming from the estimation difficulties.

Our model has been checked on a few synthetic and real data (satellite and texture images). These experiments show that our approach of raw computing and pixel-level distribution estimation is usable for difficult segmentation problems.