The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

Object Recognition By Alignment Using Invariant Projections of Planar Surfaces

In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.

The Perception of Subjective Surfaces

It is proposed that subjective contours are an artifact of the perception of natural three-dimensional surfaces. A recent theory of surface interpolation implies that "subjective surfaces" are constructed in the visual system by interpolation between three-dimensional values arising from interpretation of a variety of surface cues. We show that subjective surfaces can take any form, including singly and doubly curved surfaces, as well as the commonly discussed fronto-parallel planes. In addition, it is necessary in the context of computational vision to make explicit the discontinuities, both in depth and in surface orientation, in the surfaces constructed by interpolation. It is proposed that subjective surfaces and subjective contours are demonstrated. The role played by figure completion and enhanced brightness contrast in the determination of subjective surfaces is discussed. All considerations of surface perception apply equally to subjective surfaces.