Independent encoding of surface orientation and surface curvature.

Marr [(1982) Vision, San Francisco, Calif.: Freeman] proposed that we represent surface geometry in terms of a viewer-centred description of surface orientation and distance. This description is computed by a range of independent processing systems which take as input particular kinds of information present in images, like surface texture, shading, retinal disparity and motion parallax. The outputs of these modules are integrated in order to provide a unitary representation of the layout of visible surfaces. Higher order properties of surface geometry, like surface curvature, might be computed from this symbolic representation or might be encoded independently from the visual information available at the retinae. We measured surface slant and surface curvature discrimination thresholds for surface patches defined by shading, texture and retinal disparity as a function of the elevation of the illumination. We found that observers judgements about the curvature of local surface patches were too precise to be based on a symbolic representation of surface orientation and we conclude that surface curvature is computed directly from depth cues present in the retinal images.

Human discrimination of surface slant in fractal and related textured images.

Slant-discrimination thresholds were measured for textures with the property that their power spectra, when log transformed, are inversely proportional to log spatial frequency: P(f) alpha f-beta. As the exponent beta changes from high values to low values, the slope of the power spectrum of the image decreases. As the parameter passes through values in the fractal range the resulting texture changes from having the appearance of a cloud-like surface through to a granite-like surface. Exponents below the fractal range produce textures that converge towards the appearance of a random grey-level noise pattern. Since fractal patterns are self-similar at a range of scales, one might think it would be difficult to recover changes in depth in fractal images; however, slant-discrimination thresholds did not differ substantially as a function of the slope of the power spectrum. Reducing the size of the viewing aperture increased thresholds significantly, suggesting that slant discrimination benefits from a global analysis. The effect of texture regularity on perceived slant was investigated using bandpassed fractal textures. As the bandwidth of a bandpass filter is reduced, the bandpassed texture was perceived to be increasingly more slanted than its fractal counterpart.

Shape from shading. I: Surface curvature and orientation.

The human visual system makes effective use of shading alone in recovering the shape of objects. Pictures of sculptures are readily interpreted--a situation where shading provides virtually the sole cue to shape. However, shading has been considered a poor cue to depth in comparison with retinal disparity and kinetic cues. Curvature discrimination thresholds were measured with the use of a surface-alignment task for a range of surface curvatures from 0.16 cm-1 to 1.06 cm-1. Weber fractions were around 0.1, demonstrating considerable precision in this task. Weber fractions did not vary substantially as a function of surface curvature. Rotation of the light source around the line of sight had no effect on curvature discrimination but rotation towards the viewer increased discrimination thresholds. In contrast, slant discrimination declined with rotation of the light-source vector towards the viewpoint. When a band-limited random grey-level texture was mapped onto the sphere, curvature discrimination thresholds increased gradually as a function of texture contrast, even though texture and shading provided consistent cues to depth. Adding texture also increased slant discrimination thresholds, demonstrating that texture can act as a source of noise in shape-from-shading tasks. The psychophysical findings have been used to evaluate whether current algorithms for shape from shading in computer vision could serve as models of human three-dimensional shape analysis and to highlight low-level intramodular interactions between depth cues. It is demonstrated that, in the case of surfaces defined by shading, curvature descriptions are primary and do not depend upon the prior encoding of surface orientation, and Koenderink's local-shape index is suggested as an alternative intermediate representation of surface shape in the human visual system.

Shape from shading. II. Geodesic bisection and alignment.

Pattern-acuity tasks have provided valuable information about the precision with which the visual system can make judgments about relative spatial position in two-dimensional images. However, outside the laboratory the visual system is habitually faced with the more difficult task of making positional judgments within a three-dimensional spatial environment. Thus our perceptual systems for representing surface shape also need to support the recovery of the location and disposition of features in a three-dimensional space. An investigation of the precision of three-dimensional position judgments in two spatial-judgment tasks, arc length bisection along geodesics and geodesic alignment, is reported. The spatial-judgment tasks were defined with reference to a sphere rendered by means of ray-casting techniques. The presence of shading and texture cues had no effect on discrimination thresholds in either task. Observers' constant errors were generally less than the just noticeable distance, demonstrating that the observers can perform these positional judgment tasks without substantial bias. It is argued that there is no explicit computation of arc length on the basis of shading and texture information and that surface-orientation information cannot be used as a reference in geodesic-alignment tasks. The results raise questions about the utility of a representation of surface orientation in the human visual system.