Estimating the Illuminant Color from the Shading of a Smooth Surface

\0\05{\0\0\0\0\0\0\0\0 a uniform wall illuminated by a spot light often gives a strong impression of the illuminant color. How can it be possible to know if it is a white wall illuminated by yellow light or a yellow wall illuminated by white light? If the wall is a Lambertian reflector, it would not be possible to tell the difference. However, in the real world, some amount of specular reflection is almost always present. In this memo, it is shown that the computation is possible in most practical cases.

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.

Shape from Shading: A Method for Obtaining the Shape of a Smooth Opaque Object from One View

A method will be described for finding the shape of a smooth apaque object form a monocular image, given a knowledge of the surface photometry, the position of the lightsource and certain auxiliary information to resolve ambiguities. This method is complementary to the use of stereoscopy which relies on matching up sharp detail and will fail on smooth objects. Until now the image processing of single views has been restricted to objects which can meaningfully be considered two-dimensional or bounded by plane surfaces. It is possible to derive a first-order non-linear partial differential equation in two unknowns relating the intensity at the image points to the shape of the objects. This equation can be solved by means of an equivalent set of five ordinary differential equations. A curve traced out by solving this set of equations for one set of starting values is called a characteristic strip. Starting one of these strips from each point on some initial curve will produce the whole solution surface. The initial curves can usually be constructed around so-called singular points. A number of applications of this metod will be discussed including one to lunar topography and one to the scanning electron microscope. In both of these cases great simplifications occur in the equations. A note on polyhedra follows and a quantitative theory of facial make-up is touched upon. An implementation of some of these ideas on the PDP-6 computer with its attached image-dissector camera at the Artificial intelligence Laboratory will be described, and also a nose-recognition program.

Slow and Smooth: A Bayesian Theory for the Combination of Local Motion Signals in Human Vision

In order to estimate the motion of an object, the visual system needs to combine multiple local measurements, each of which carries some degree of ambiguity. We present a model of motion perception whereby measurements from different image regions are combined according to a Bayesian estimator --- the estimated motion maximizes the posterior probability assuming a prior favoring slow and smooth velocities. In reviewing a large number of previously published phenomena we find that the Bayesian estimator predicts a wide range of psychophysical results. This suggests that the seemingly complex set of illusions arise from a single computational strategy that is optimal under reasonable assumptions.