Coarse-to-Fine Dynamic Programming

We introduce an extension of dynamic programming, we call "coarse-to-fine dynamic programming" (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 "superstates" in a coarser graph which uses an optimistic arc cost between superstates. The approximations are designed so that CFDP terminates when 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. We demonstrate applications of this technique to optimization of functions and boundary estimation in mine recognition.

[1]  Yong K. Hwang,et al.  SANDROS: a dynamic graph search algorithm for motion planning , 1998, IEEE Trans. Robotics Autom..

[2]  Seth Hutchinson,et al.  Efficient search and hierarchical motion planning by dynamically maintaining single-source shortest paths trees , 1995, IEEE Trans. Robotics Autom..

[3]  Judea Pearl,et al.  Heuristics : intelligent search strategies for computer problem solving , 1984 .

[4]  Jean-Claude Latombe,et al.  New heuristic algorithms for efficient hierarchical path planning , 1991, IEEE Trans. Robotics Autom..

[5]  Douglas J. Muder.  Minimal trellises for block codes , 1988, IEEE Trans. Inf. Theory.

[6]  Kai-Fu Lee,et al.  On large-vocabulary speaker-independent continuous speech recognition , 1988, Speech Commun..

[7]  Tadao Kasami,et al.  A Trellis-Based Recursive Maximum-Likelihood Decoding Algorithm for Binary Linear Block Codes , 1998, IEEE Trans. Inf. Theory.

[8]  Christopher Raphael,et al.  Grammatical approach to mine detection , 1997, Defense, Security, and Sensing.

[9]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[10]  Shu Lin,et al.  On complexity of trellis structure of linear block codes , 1993, IEEE Trans. Inf. Theory.

[11]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[12]  Alok Gupta,et al.  Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[14]  Hanan Samet,et al.  A hierarchical strategy for path planning among moving obstacles [mobile robot] , 1989, IEEE Trans. Robotics Autom..

[15]  Gary E. Kopec,et al.  Heuristic image decoding using separable source models , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[16]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[17]  Paul D. Gader,et al.  Handwritten Word Recognition Using Segmentation-Free Hidden Markov Modeling and Segmentation-Based Dynamic Programming Techniques , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Kevin Georey.  Dynamic Programming Algorithms for Maximum Likelihood Decoding , 1998 .

[19]  Raj Reddy,et al.  Large-vocabulary speaker-independent continuous speech recognition: the sphinx system , 1988 .

[20]  Lalit R. Bahl,et al.  A Maximum Likelihood Approach to Continuous Speech Recognition , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Stuart Geman,et al.  Dynamic programming algorithms for maximum likelihood decoding , 1998 .

[22]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Josiane Zerubia,et al.  New Prospects in Line Detection by Dynamic Programming , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Richard M. Schwartz,et al.  An Omnifont Open-Vocabulary OCR System for English and Arabic , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Jack K. Wolf,et al.  Efficient maximum likelihood decoding of linear block codes using a trellis , 1978, IEEE Trans. Inf. Theory.

[26]  Philip A. Chou,et al.  Document Image Decoding Using Markov Source Models , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[27]  Michael I. Miller,et al.  Dynamic Programming Generation of Curves on Brain Surfaces , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Larry S. Davis,et al.  Multiresolution path planning for mobile robots , 1986, IEEE J. Robotics Autom..

[29]  Abinash C. Dubey,et al.  Detection and Remediation Technologies for Mines and Minelike Targets II , 1997 .