Paired comparisons data from each participant were pre-processed by taking as a proportion the number of times a stimulus was selected as glossier over the total number of times it appeared in each 2AFC experimental session. This proportion directly reflects the probability that a given image will be chosen as glossier for any two images randomly selected from our image pool. Given that gloss was expected to be contingent on the relationship between the closeness in orientation of the specular highlights and surface geometry specified by the diffuse shading profile, we also simulated the observers' predicted responses by correlating the peak responses of locally oriented filters to the matte (diffuse) and specular image layers used to construct the test images. This analysis is motivated by the suggestion by a number of authors that the perception of shape from shading is based on the pattern of isophotes (Koenderink & van Doorn,
1980) or “shading flow” (Ben-Shahar & Zucker,
2001; Breton & Zucker,
1996; Fleming, Dror, & Adelson,
2003; Fleming, Torralba, & Adelson,
2004; Huggins, Chen, Belhumeur, & Zucker,
2001). More specifically, we constructed “orientation fields” of the matte image and gloss map by convolving each location in the image with a Gabor filter (four pixels wavelength, zero phase offset, 1:1 aspect ratio, and one octave bandwidth) for angles ranging between 0 and 170 degrees (at steps of 10 degrees). The orientation field value at a pixel was taken as the angular filter value that yielded the greatest response over this range. Point-wise correlation between the diffuse and gloss orientation fields was performed for all points within the gloss map that were greater than zero, yielding an index of consistency in the orientation field responses between the gloss and matte images. These correlations were multiplicatively scaled between 0 and 1, giving rise to ideal performance in our paired-comparisons experiment. Due to inevitable response noise, these ideal responses were re-scaled by estimating observers' false positives and false negatives from the data set we obtained, yielding the prediction curves in
Figures 4 and
5. Range scaling of the prediction curves was performed according to:
where
Pi is the probability of selecting image
i with an orientation field correlation of
Oi and error parameter
E0 (estimate of false positives) was taken as the inverse of the probability the image with the smallest (here, zero) angular/linear transformation of the gloss map was selected as glossier. Error parameter
E1 (estimate of false negatives) was taken as the average probability the image(s) with the largest angular/linear transformation of their respective gloss maps was selected as glossier.