Camera model selection based on geometric AIC

Abstract

The problem of selecting a camera model is addressed here using the Geometric AIC (Akaike Information Criterion) proposed by Kanatani, which considers both the residual of the data fitting to the model as well as the complexity of the model. Camera models describe the geometrical relation between the 3D location of object points and the image location of their projections. The most commonly used camera models are the projective/perspective camera model and the affine camera model. Intuitively, the projective camera model, which is nonlinear and is characterized by more parameters, models the imaging geometry better, but also, is believed to lead to numerically less stable solutions. The affine camera model, which is an approximation to the projective camera model with less parameters, is recommended to be used when the object depth is much smaller than the object distance. However, there is no quantitative criterion for the decision: which camera model should be used, projective or affine? In this paper, the Geometric AIC criterion is used for deciding between the two camera models is the context of two tasks: estimating the projection matrix from 3D and corresponding 2D data, and estimating the fundamental matrix from two sets of 3D data. It is found that in most cases, it is the projective camera model which is more appropriate. Still, in the cases where the affine camera model is traditionally used, the measures of appropriateness of the two models are roughly the same (with a small advantage to the affine camera model).