Model Selection Criteria for Geometric Inference

Abstract

Model selection criteria are designed for selecting an appropriate hypothesis for the phenomenon in question. In traditional statistics, a hypothesis has a parametric expression that combines a deterministic input-output relationship and random fluctuations. However, most of the problems encountered in computer vision do not fit in this framework. In this chapter, we illustrate this difference by taking line fitting as a typical example. First, we discuss the classical regression problem and show how the Akaike Information Criterion (AIC) can be used for model selection. Then, we go on to the geometric fitting problem described in the form that typically appears in computer vision applications. Since the two problems are different, we must modify the AIC; we call the resulting criterion the “geometric AIC.“ We generalize this idea to an abstract framework and compare it with other criteria such as cross-validation, jackknife, bootstrap, C _P , Bayesian Information Criterion (BIC), and Minimum Description Length (MDL). We conclude by discussing some of the fundamental issues that lie behind all these criteria.