Dynamic Programming (DP)

Abstract

Some problems of computer vision can be formulated in a recursive manner. For this class of problems, the paradigm of dynamic programming (DP) represents an interesting tool in order to obtain a fast discrete solution. Here, the overall problem is broken down into a series of sub-problems, which are built upon each other and can therefore be solved iteratively. This way computation can be sped up considerably through the reusage of information gathered in already solved sub-problems. This chapter starts with presenting the well-known method of Dijkstra as an example of shortest path algorithms, which are closely related to DP. “Intelligent scissors” interactively segmenting an image are one example application. Furthermore, this chapter deals with two ways of applying the dynamic programming paradigm. First, dynamic programming is applicable if optimal positions or labels are to be found for a sequence of points, where the optimality criterion for each point depends on its predecessor(s). The task of calculating active contours can be reformulated in this manner. Second, some problems show a treelike structure, which makes a recursive formulation possible, too. The recognition of objects which are modeled as a configuration of parts is one example of this.