Motion transparency provides a challenging test case for our understanding of how visual motion, and other attributes, are computed and represented in the brain. However, previous studies of visual transparency have used subjective criteria which do not confirm the existence of independent representations of the superimposed motions. We have developed measures of performance in motion transparency that require observers to extract information about two motions jointly, and therefore test the information that is simultaneously represented for each motion. Observers judged whether two motions were at 90 degrees to one another; the base direction was randomized so that neither motion taken alone was informative. The precision of performance was determined by the standard deviations (S.D.s) of probit functions fitted to the data. Observers also made judgments of orthogonal directions between a single motion stream and a line, for one of two transparent motions against a line and for two spatially segregated motions. The data show that direction judgments with transparency can be made with comparable accuracy to segregated (non-transparent) conditions, supporting the idea that transparency involves the equivalent representation of two global motions in the same region. The precision of this joint direction judgment is, however, 2-3 times poorer than that for a single motion stream. The precision in directional judgment for a single stream is reduced only by a factor of about 1.5 by superimposing a second stream. The major effect in performance, therefore, appears to be associated with the need to compute and compare two global representations of motion, rather than with interference between the dot streams per se. Experiment 2 tested the transparency of motions separated by a range of angles from 5 degrees to 180 degrees by requiring subjects to set a line matching the perceived direction of each motion. The S.D.s of these settings demonstrated that directions of transparent motions were represented independently for separations over 20 degrees. Increasing dot speeds from 1 to 10 deg/s improved directional performance but had no effect on transparency perception. Transparency was also unaffected by variations of density between 0.1 and 19 dots/deg(2)

Adelson has shown how two patches in a 5 by 5 array of grey patches can be perceived to consist of different shades, depending on whether they are represented at a 3-D horizontal or vertical ridge. Adelson interprets the illusion in terms of the orientation of the patches with respect to the inferred illuminant. We investigated: (1) the illusion in the vertical and horizontal stimuli and added a flat (ridgeless) control stimulus; (2) stimuli of varying ridge amplitudes to examine the effect more fully. 3-D renderings of real surfaces were modelled with computer graphics and displayed to observers who used a mouse to alter the brightness of a square to match patches indicated in the stimuli. Five observers were used for the vertical, flat and horizontal stimuli, while a larger group (n = 20) was used for an independent design when varying ridge amplitudes. A significant effect in the flat surface demonstrates that patches lying in the same plane can have their brightness altered without changes in their orientation. When the surface was seen as a 3-D ridge the size of the effect was a function of 3-D slope of the surface. By measuring each patch independently we have shown that the effect changes the brightness of the two patches to differing degrees. We offer an explanation of this based on a proposed qualitative shading rule for identifying reflectance and illumination edges.

A computational method for calibrating stereo using shape-from-texture is described together with five experiments that tested whether the human visual system implements the method. The experiments all tested the prediction that the perceived size of a step between two planar and slanted real surfaces should be affected by texture slant cues projected on to them that are inconsistent with the disparity cues. The predicted effect was observed but the results could be accounted for by a new phenomenon revealed in control conditions: the perceived size of a step between two slanted planes is in part determined by the size of the slants even when texture and stereo cues are held consistent. We conclude that the hypothesis that human stereo is calibrated by texture is not confirmed.

In order to perceive transparent motions the visual system must compute and represent two (or more) motion signals at some level of spatial representation. We have developed performance-based measures of transparency, based on the precision of a joint directional judgment of two superimposed global motions in a random-dot kinematogram (RDK). Qian, Andersen, and Adelson (1994 Journal of Neuroscience14 7357 – 7366) have reported that transparent motion is not perceived in RDK stimuli if each leftward moving dot is paired with a rightward moving dot that it meets at the midpoint of a short trajectory (locally balanced). Using performance-based measures of transparency we investigated the conditions for the occurrence of transparency in locally balanced stimuli. Using stimuli with the same parameters as Qian et al we found that the critical distance that the dots must travel to abolish transparency was 0.2 deg or less. Offsetting one set of dots, orthogonally to its motion direction, by 0.3 deg or more allowed for transparency-based judgments with the same degree of accuracy as for random distribution of the two motion directions. These values differ slightly from those reported by Qian et al (0.4 deg and 0.2 deg respectively), perhaps because Qian et al depended solely on subjective reports of transparency. The data suggest that different processes may be involved in detecting transparency when the trajectories are extended and when they are offset. When the trajectory length was varied, transparency-based judgments were possible when each dot pair had an average separation of approximately 0.1 deg over the course of their lifetimes. For the offset stimuli, transparency-based judgments required the dots to have an average separation of approximately 0.2,deg. However, our data are consistent with transparent motion signals not being represented at the most local levels of motion analysis, as proposed by Qian et al.