Network flow optimization for restoration of images

[摘要] The network flow optimization approach is offered for restorationof gray-scale and color images corrupted by noise. The Isingmodels are used as a statistical background of the proposedmethod. We present the new multiresolution network flow minimumcut algorithm, which is especially efficient in identification ofthe maximum a posteriori (MAP) estimates of corrupted images. Thealgorithm is able to compute the MAP estimates of large-sizeimages and can be used in a concurrent mode. We also consider theproblem 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 ofcolor and gray-scale images. In the caseL=2, they coincide,determining the energy function of the Ising model of binaryimages, and their minimization becomes equivalent to the networkflow minimum cut problem. The efficient integer minimization ofU1(x),U2(x)by the network flowalgorithms is described.

[学科分类] 应用数学