A Probabilistic Method for Point Matching in the Presence of Noise and Degeneracy

The Bayesian method is widely used in image processing and computer vision to solve ill-posed problems. This is commonly achieved by introducing a prior which, together with the data constraints, determines a unique and hopefully stable solution. Choosing a "correct" prior is however a well-known obstacle. This paper demonstrates that in a certain class of motion estimation problems, the Bayesian technique of integrating out the "nuisance parameters" yields stable solutions even if a flat prior on the motion parameters is used. The advantage of the suggested method is more noticeable when the domain points approach a degenerate configuration, and/or when the noise is relatively large with respect to the size of the point configuration.