Concurrent propagation for solving ill-posed problems of global discrete optimisation

Classical frameworks for global 1D discrete optimisation: dynamic programming (DP) and belief propagation (BP) - presume well-posed problems with unique solutions. Ill-posed problems, being the most common in applied pattern recognition and computer vision, are regularised to restore well-posedness. However, typical heuristic regularisation does not guarantee that a set of multiple equivalent solutions is reduced to a single solution. An alternative concurrent propagation (CP) proposed in this paper extends the DP to allow for determining whether the problem is well- or ill-posed and storing implicitly in the latter case the entire set of solutions (e.g. for its structural analysis to improve regularisation). The CP, DP, and BP have similar computational complexity.

[1]  Richard Szeliski,et al.  A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms , 2001, International Journal of Computer Vision.

[2]  Pedro F. Felzenszwalb,et al.  Efficient belief propagation for early vision , 2004, CVPR 2004.

[3]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[4]  Massimiliano Pontil,et al.  Regularization and statistical learning theory for data analysis , 2002 .

[5]  Michael S. Waterman,et al.  A dynamic programming algorithm to find all solutions in a neighborhood of the optimum , 1985 .

[6]  Richard Szeliski,et al.  High-accuracy stereo depth maps using structured light , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[7]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[8]  Brendan J. Frey,et al.  Graphical Models for Machine Learning and Digital Communication , 1998 .

[9]  Radu Nicolescu,et al.  P Systems in Stereo Matching , 2011, CAIP.

[10]  Ramin Zabih,et al.  Dynamic Programming and Graph Algorithms in Computer Vision , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[12]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[13]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[14]  Georgy L. Gimel'farb,et al.  Probabilistic regularisation and symmetry in binocular dynamic programming stereo , 2002, Pattern Recognit. Lett..

[15]  Van Nostrand,et al.  Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm , 1967 .

[16]  R Bellman,et al.  On the Theory of Dynamic Programming. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Averill M. Law,et al.  The art and theory of dynamic programming , 1977 .