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,U1(x)=λ∑i|yi−xi|+∑i,j βi,j|xi−xj|andU2(x)=∑i λi (yi−xi)2+∑i,j βi,j (xi−xj)2, with parametersλ,λi,βi,j>0and vectorsx=(x1,…,xn),y=(y1,…,yn)∈{0,…,L−1}n. Those functions constitute the energy ones for the Ising model of color and gray-scale images. In the caseL=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 ofU1(x),U2(x)by the network flow algorithms is described.
A Linear Time Algorithm for a Variant of the MAX CUT Problem in Series Parallel Graphs
