SHAPE FROM SHADED RANDOM SURFACES

The perception of surface relief from random shading patterns is measu red by having observers adjust three-dimensional local probes, the pro jections of which are superimposed on the image. Three observers perfo rm four settings of 91 probes on each of 14 images. These images are g enerated by calculating the Lambertian reflectance of a random superpo sition of elliptical Gaussian hills and valleys illuminated by a singl e distant light source as well as by ambient light. Neither the surfac e reflectance equation nor the light source direction is conveyed to o ur observers in any way. Mathematically, this ''pure'' shape-from-shad ing problem has highly non-unique solutions, Perception of a well-defi ned, 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 invest igate possible ways of restricting it. Statistical analysis of the cur l component of the field of probe settings reveals that the settings a re significantly consistent with an underlying perceived surface. In s pite of the large theoretical ambiguity in the stimuli, the settings a re reproducible and show considerable inter-observer agreement, Even t he correlation of the settings with the real surfaces is surprisingly large, If the settings are compared to the real surface normals, one f inds a series of biases, the strongest of which is that the global sur face slant is systematically underestimated, even in those cases where ending occluding contours or high-contrast luminance ridges, indicati ve of ''almost'' contours, are present in the image. Another bias then is that the corresponding rims on the surface are seen as roughly par allel to the picture plane.