Canonical Views, or the Stability and Likelihood of Images of 3d Objects

We develop the concepts of view stability and likelihood for general objects. These quantities permit a quantitative characterization of the ability of a two dimensional view, or image , to represent a three dimensional object. Given objects with salient points, we provide explicit expressions from which the stability and likelihood of any image of a general object can be computed using its three second moments. To identify canonical (or representative) views, we show that the \\attest" view of the object is both the most stable and the most likely view. Given smooth objects, we rst discuss image comparison, arguing for comparison via interest points (deened as points of high curvature on the occluding contour). Prior to measuring image stability and likelihood , we characterize points on surfaces of smooth objects by measuring the \number" of viewpoints from which they approximately appear as points of interest (if any).