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 addressed. In particular, the curvature method is applied to ellipsoidal objects and the error for different rotations of the objects is computed analytically. It is seen that the error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases as the ellipsoid becomes elongated in the Z-direction. It is shown 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