For geometric inference from images, what kind of statistical model is necessary?

In order to promote mutual understanding with researchers in other fields including statistics, this paper investigates the meaning of statistical methods for geometric inference based on image feature points. We trace back the origin of feature uncertainty to image processing operations and discuss the meaning of geometric fitting, geometric model selection, the geometric AIC, and the geometric MDL. Then, we discuss the implications of asymptotic analysis in reference to nuisance parameters, the Neyman-Scott problem, and semiparametric models and point out that application of statistical methods requires careful considerations about the peculiar nature of geometric inference. © 2004 Wiley Periodicals, Inc.