Stability and Likelihood of Views of Three Dimensional Objects

Abstract

Stability and Likelihood of Views of Three Dimensional Objects. Evaluating the representative power of two dimensional images of three dimensional objects has come up in a number of applications, mostly concerning 3D object recognition. We address the question of image characterization independently of these applications. We first introduce the basic concepts of view stability and likelihood for general objects. The stability and likelihood functions are then used to quantitatively characterize the repre-sentability of images. For objects composed of localized features, we develop explicit expressions through which the stability and likelihood functions of any view of a general object can be evaluated from its three principal second moments. This permits a quantitative characterization of the viewing sphere of objects. By way of qualitative analysis we compute the most stable and most likely views, which can identify the characteristic views of objects. We show that the most stable and most likely views of an object are the same and are often unique. This view is the “flattest” view of the object, obtained when the three dimensional object has its minimal spread along the viewing direction. We demonstrate these results using images of familiar objects.