The network flow optimization approach is offered for restoration
of gray-scale and color images corrupted by noise. The Ising
models are used as a statistical background of the proposed
method. We present the new multiresolution network flow minimum
cut algorithm, which is especially efficient in identification of
the maximum a posteriori (MAP) estimates of corrupted images. The
algorithm is able to compute the MAP estimates of large-size
images and can be used in a concurrent mode. We also consider the
problem of integer minimization of two functions,
$U_1(\mathbf{x}) = \lambda\sum_i|y_i-x_i| +\sum_{i,j}\beta_{i,j}|x_i-x_j|$
and
$U_2(\mathbf{x}) =\sum_i\lambda_i(y_i-x_i)^2 +\sum_{i,j}\beta_{i,j}(x_i-x_j)^2$ , with parameters
$\lambda,\lambda_i,\beta_{i,j} > 0$
and vectors
$\mathbf{x}=(x_1,\dotsc,x_n)$ ,
$\mathbf{y} = (y_1,\dotsc,y_n)\in\{0,\dotsc,L-1\}^n$ .
Those functions constitute the energy ones for the Ising model of
color and gray-scale images. In the case $L = 2$ , they coincide,
determining the energy function of the Ising model of binary
images, and their minimization becomes equivalent to the network
flow minimum cut problem. The efficient integer minimization of
$U_1(\mathbf{x}),U_2(\mathbf{x})$
by the network flow
algorithms is described.