Model Selection and Surface Merging in Reconstruction Algorithms

The problem of model selection — automatically choosing the correct function to describe a data set — is relevant to many areas of computer vision. Many model selection criteria have been used in the vision literature and many more have been proposed in statistics, but the relative strengths of these criteria have not been analyzed in vision. Using the problem of surface reconstruction as our context, we analyze existing criteria using simulations and real data, introduce new criteria from statistics, develop novel criteria capable of handling unknown error distributions and outliers, and extend model selection criteria to apply to the surface merging problem. The new surface merging rules improve upon previous results, and work well even at small step heights (h = 3 ) and crease discontinuities. Our results show that when the error distribution is known (at least approximately), Bayesian criteria for model selection and surface merging introduced here works best, although for time-sensitive applications a variant of the Akaike criterion may be a better choice. For unknown distributions, the Bayesian criteria combined with a bootstrapped estimate of the error distribution gives the best performance. Unfortunately, none of the criteria work reliably for small datasets, implying that model selection and surface merging should be avoided unless there is sufficient data.