Shape from shaded random surfaces.

The perception of surface relief from random shading patterns is measured by having observers adjust three-dimensional local probes, the projections of which are superimposed on the image. Three observers perform four settings of 91 probes on each of 14 images. These images are generated by calculating the Lambertian reflectance of a random superposition of elliptical Gaussian hills and valleys illuminated by a single distant light source as well as by ambient light. Neither the surface reflectance equation nor the light source direction is conveyed to our observers in any way. Mathematically, this "pure" shape-from-shading problem has highly non-unique solutions. Perception of a well-defined, stable shape therefore implies that the ambiguity is resolved, i.e. a gauge is fixed. We analyse the surface ambiguity or gauge freedom which is left unconstrained by pure shading information and we investigate possible ways of restricting it. Statistical analysis of the curl component of the field of probe settings reveals that the settings are significantly consistent with an underlying perceived surface. In spite of the large theoretical ambiguity in the stimuli, the settings are reproducible and show considerable inter-observer agreement. Even the correlation of the settings with the real surfaces is surprisingly large. If the settings are compared to the real surface normals, one finds a series of biases, the strongest of which is that the global surface slant is systematically underestimated, even in those cases where ending occluding contours or high-contrast luminance ridges, indicative of "almost" contours, are present in the image. Another bias then is that the corresponding rims on the surface are seen as roughly parallel to the picture plane.