The network flow optimization approach is offered for Bayesian segmentation of gray-scale and color images. It is supposed image pixels are characterized by a feature function taking finite number of arbitrary rational values (it can be either intensity values or other characteristics of images). The clusters of homogeneous pixels are described by labels with values in another set of rational numbers. They are assumed to be dependent and distributed according to either the exponential or the Gaussian Gibbs law. Instead traditionally used local neighborhoods of nearest pixels the completely connected graph of dependence of all pixels is employed for the Gibbs prior distributions. The methods developed reduce the problem of segmentation to the problem of determination of the minimum network cuts.