Algorithms of Approximate Pairwise Separable Optimization for Image Processing

摘要

The variational approach to designing algorithms for processing 2D data arrays, in particular, images, is considered. The possibility of optimizing a pairwise separable objective function with a lattice-like variable adjacency graph representing the neighborhood of pixel grid elements is investigated. It is based on combining all variables in each row into groups with respect to the number of rows and on applying the dynamic programming to searching for optimal values of such group variables whose adjacency graph becomes a chain. A heuristic approach is proposed based on the replacement of Bellman functions by some appropriate pairwise separable functions to overcome difficulties arising in the processing.