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14 Uncertainty Modeling and Geometric Inference

Statistical inference from images is one of the key components of computer vision research today. Traditionally, statistical methods have been used for recognition and classification purposes. Recently, however, there are many studies of statistical analysis for geometric inference based on geometric primitives such as points and lines extracted by image processing operations. However, the term “statistical” has somewhat a different meaning for such geometric inference problems than for the traditional recognition and classification purposes. This difference has often been overlooked, causing controversies over the validity of the statistical approach to geometric problems in general. In Sect. , we take a close look at this problem, tracing back the origin of feature uncertainty to image processing operations. In Sect. , we discuss the implications of asymptotic analysis in reference to geometric fitting and geometric model selection. In Sect. , we point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the geometric AIC and the geometric MDL in detecting degeneracy. In Sect. , we review recent progress in geometric fitting techniques for linear constraints, describing the FNS method, the HEIV method, the renormalization method, and other related techniques. In Sect. , we discuss the Neyman–Scott problem and semiparametric models in relation to geometric inference. Sect. presents our concluding remarks.