Coarse-to-Fine Dynamic Programming

  • Authors:
  • Christopher Raphael

  • Affiliations:
  • Univ. of Massachusetts, Amherst

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 2001

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Abstract

We introduce an extension of dynamic programming (DP) we call 驴Coarse-to-Fine Dynamic Programming驴 (CFDP), ideally suited to DP problems with large state space. CFDP uses dynamic programming to solve a sequence of coarse approximations which are lower bounds to the original DP problem. These approximations are developed by merging states in the original graph into 驴superstates驴 in a coarser graph which uses an optimistic arc cost between superstates. The approximations are designed so that when CFDP terminates the optimal path through the original state graph has been found. CFDP leads to significant decreases in the amount of computation necessary to solve many DP problems and can, in some instances, make otherwise infeasible computations possible. CFDP generalizes to DP problems with continuous state space and we offer a convergence result for this extension. The computation of the approximations requires that we bound the arc cost over all possible arcs associated with an adjacent pair of superstates; thus the feasibility of our proposed method requires the identification of such a lower bound. We demonstrate applications of this technique to optimization of functions and boundary estimation in mine recognition.