Tree-serial dynamic programming for image processing

A lot of image analysis problems lend themselves to a unified mathematical formulation as optimization problems. Tree-serial dynamic programming is a particular case of the so-called nonserial dynamic programming designed for optimization of objective functions which are sums of partial functions each of a smaller number of variables. It is known that these problems are NP-hard in the general formulation, but, when the adjacency graph is a tree, they can be effectively solved by the tree-serial dynamic programming procedure. In this paper, we consider three ways of extending the tree-serial dynamic programming principle onto the optimization of pair-wise separable functions supported by a lattice-like graph, which is more natural for images than a tree.