Geometric Information Criterion for Model Selection

In building a 3-D model of the environment from image and sensor data, one must fit to the data an appropriate class of models, which can be regarded as a parametrized manifold, or geometric model, defined in the data space. In this paper, we present a statistical framework for detecting degeneracies of a geometric model by evaluating its predictive capability in terms of the expected residual and derive the geometric AIC. We show that it allows us to detect singularities in a structure-from-motion analysis without introducing any empirically adjustable thresholds. We illustrate our approach by simulation examples. We also discuss the application potential of this theory for a wide range of computer vision and robotics problems.