Perceptual spatial frequency--orientation surface: psychophysics and line element theory

We have investigated the discriminability of gratings which simultaneously vary in spatial frequency and orientation. Thirteen and nine reference gratings were used with two observers, and bivariate discrimination probability surfaces were determined around each grating. These data were then fitted to a general bivariate Gaussian function. The results clearly demonstrate local separability in this log frequency and orientation discrimination domain. Our results also show that the factor contributing most to the non-Euclidean nature of such frequency/orientation discrimination is orientation anisotropia, although we also find some evidence for smaller changes in the associated Riemannian line-element at different frequency ranges. These results cast doubt upon claims for a "pseudo line-element" for frequency discrimination based upon the nonlinear outputs of a fixed set of detectors.