Open Access
21 August 2002 Network flow optimization for restoration of images
Boris A. Zalesky
J. Appl. Math. 2(4): 199-218 (21 August 2002). DOI: 10.1155/S1110757X02110035


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)=λi|yixi|+i,jβi,j|xixj| and U2(x)=iλi(yixi)2+i,jβi,j(xixj)2, with parameters λ,λi,βi,j>0 and vectors x=(x1,,xn), y=(y1,,yn){0,,L1}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 U1(x),U2(x) by the network flow algorithms is described.


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Boris A. Zalesky. "Network flow optimization for restoration of images." J. Appl. Math. 2 (4) 199 - 218, 21 August 2002.


Published: 21 August 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1116.90321
MathSciNet: MR1948085
Digital Object Identifier: 10.1155/S1110757X02110035

Primary: 62M40 , 90C10
Secondary: 68U10 , 90C35

Rights: Copyright © 2002 Hindawi

Vol.2 • No. 4 • 21 August 2002
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