Theoretically, metric solid shape is not determined uniquely by shading. Consequently, human vision has difficulty in categorizing shape when shading is the only cue. In the present research, subjects were required to categorize shaded quadric surfaces. We found that they were rather poor at this task; they confused hyperbolic and elliptic (both convex and concave) shapes easily. When a cast shadow visually indicated the direction of the illuminant, they were able to notice the concavity or convexity of elliptic shapes. However, they still confused elliptic and hyperbolic ones. Finally, when an animated sequence of eight intensity patterns belonging to one quadric shape had been displayed, the subjects were able to categorize the quadrics. However, the results are still quite moderate. Our experiments indicate that local shading structure is only a weak shape cue when presented in the absence of other visual cues. 145With the present generation of rendering algorithms, it is apparently relatively easy to generate very "natural" images on a computer screen. The three-dimensional impression created by these images is very compelling. However, such an informal observation has to be quantified. Very little research has been done on the perception of solid shape on the basis of shading.Computer images provide several visual cues that potentially contribute to the perception of solid shape (Gibson, 1950). The role of shading in these images is complicated because extracting shape from shading is not a trivial task. The shading is determined by the surface orientation, the illuminant direction, and the surface properties. This means that the same luminance distribution can be generated by several different surfaces. For instance, the luminance distribution of concave and convex spheres is exactly the same. Thus, in order to find the local surface structure on the basis of shading, one has to make assumptions about the illuminant direction and the surface properties (Horn, 1975(Horn, , 1977Pentland, 1984Pentland, , 1989. Another method to estimate the local surface structure from shading is to combine the information given by several intensity patterns of one shape (Woodham, 1980). Most computational theories on shape from shading calculate the surface shape locally (Horn, 1975(Horn, , 1977Pentland, 1984Pentland, , 1989Woodham, 1980). It is not clear whether human observers are able to judge the local shape of an object on the basis of shading.Several psychophysical experiments report observers' ability to estimate local surface structure from shading (Biilthoff & Mallot, 1988;Mingolla & Todd, 1986;Todd & Mingolla, 1983;Todd & Reichel, 1991). These experiments indicated that human observers are very poor at this. Other experiments have shown that observers cannot distinguish local shapes such as concave and convex spheres when they do not know the illuminant direction (Berbaum, Bever, & Sup Chung, 1984;Ramachandran, 1988). In most of these studies, a very restricted set of shapes such as spheres (Berbaum et al., 1984), ...

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In theory, global shading may help with the estimation of local surface structure from shading (e.g., in specifying the illuminant direction). Empirically, we do not know whether human observers combine the information given by the local and global shading to estimate local shape.Observers had to indicate the orientation of a local elongated perturbation with or without global shading information provided by a background surface. Our psychophysical results show the following:1. Observers do not estimate the orientation of the local perturbation more accurately with global shading information than they do in the absence of such information.2. Responses depend dramatically on the inclination between the illuminant direction and the viewing direction. For an inclination of 20 0 , observers indicate more or less the orientation of the local ridge; however, for an inclination of 40 0 , they indicate either the direction of the illuminant or an orientation close to the shadow edge ofthe perturbation. Most subjects show some combination of these behaviors. This behavior is not altered by global shading information.We conclude that in our paradigm, global shading information does not aid the estimation of local shape.In most theoretical work on "shape from shading, " the three-dimensional (3-D) structure of a surface is calculated from the local luminance distribution. (Horn, 1975(Horn, , 1977 Ikeuchi & Horn, 1981;Oliensis, 1991;Pentland, 1982Pentland, , 1984Pentland, , 1989. However, the shading of an object is not determined just by the surface orientation but also by the illuminant direction and the nature of the surface material. It is therefore impossible to estimate the local shape uniquely from a local shading pattern. Constraints necessary to find local surface structure from patterns of shading can be given by the global shading of the surrounding background surface. For example, the global shading can be used to estimate the illuminant direction (Oliensis, 1991;Pentland, 1982).Some of these shape-from-shadingtheories are proposed for human vision (Pentland, 1982(Pentland, , 1984(Pentland, , 1989. However, we do not know empirically whether human observers combine both local and global shading to estimate local shape. In our experiments, we report on the extent to which observers can indicate the orientation of a local ridge on a background surface (examples of the set of stimuli are given in the first column of Figure I). The global shading information is controlled by the background surface; a spherical background surface reveals global shading information, whereas a planar one does not (equal gray value). In this paper, we investigate whether the responses of observers are altered by the nature of the background surface.Furthermore, we investigate how the responses of the observers depend on the illurninant direction. What is the influence of the inclination between the illuminant direction and the viewing direction on the ability of observers to indicate the orientation of the local ridge? Do observers resp...

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.

We report on the extent to which human observers are able to indicate the gradient direction of a luminance ramp. In our experiment modulation depth ranged from 1 to 64% and field sizes subtended 0.5 to 47.5' of visual angle. Observers are not able to indicate the gradient direction for modulation depths below 6%. For values above this threshold, the angular standard deviation in the responses decreases proportionally with the logarithm of the modulation depth and is about 11' for a modulation depth of 64%. The angular standard deviations for supra-threshold contrast are slightly increased for the field sizes of 0.5 and 47.5' but are constant over a range of field sizes of 1 to 25'. Thus, size invariance holds well for this range of field sizes.