Shape from Shading. II. Geodesic Bisection and Alignment

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Abstract
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.