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Abstract
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| and , with parameters λ, λi, βi,j > 0 and vectors x = (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 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.
Highlights
We present a new multiresolution algorithm for finding the minimum network flow cut and methods of efficient integer minimization of the function U1(x) = λ i |yi − xi|+ i,j βi,j |xi − xj | and U2(x) = i λi(yi − xi)2 +
The problem is posed in terms of Bayesian approach to image restoration to have unified canvas of presentation of the results, and since the results developed were tested and turned out efficient for the processing of corrupted images
For some types of networks, this highly parallel method turns out more speedy and more efficient in comparison with known maximum network flow algorithms. It was successfully used for identification of minimum cuts of large networks, while classical methods were not able to solve the problem
Summary
We present a new multiresolution algorithm for finding the minimum network flow cut and methods of efficient integer minimization of the function U1(x) = λ i |yi − xi|+ i,j βi,j |xi − xj | and U2(x) = i λi(yi − xi)2 +. Known maximum network flow algorithms still did not allow computation of the real binary images having size n = 256 × 256 or more. Some additional theoretical reasons allowed describing a new algorithm, which identifies the exact minimum cut using special modifications of subnetworks of the partitioned original network. This algorithm can be exploited for an arbitrary network.
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