How Are Statistical Methods for Geometric Inference Justified?

This paper investigates the meaning of “statistical methods” for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations for computer vision in general, we discuss implications of asymptotic analysis in reference to “geometric fitting” and “geometric model selection”. For the latter, we point out the prominent characteristics of the “geometric AIC” and the “geometric MDL” as compared with Akaike’s AIC and Rissanen’s MDL and present a dual interpretation between the standard and geometric inferences. We also evaluate their degeneracy detection performance by simulation, showing that their asymptotic characteristics are very contrasting. Finally, we discuss some issues concerning “nuisance parameters” and “semiparametric models”. We conclude that application of statistical methods requires careful considerations about the peculiar nature of the geometric inference problem.