Testing the indeterminacy of linear color mechanisms from color discrimination data

It has previously been reported that, for some choices of the fixed spatial and temporal characteristics of test stimuli, it was possible to estimate the spectral sensitivities of chromatic mechanisms from chromatic discrimination data alone. If mechanism sensitivities could be reliably estimated for any choice of test stimuli characteristics, the influence of spatial and temporal factors on chromatic discrimination performance could be directly measured. Previous studies, using test stimuli with other spatio-temporal characteristics, have found equi-discrimination contours whose ellipsoidal shapes seem to preclude estimation of mechanisms. Since there is no commonly-accepted method for testing the adequacy of ellipsoidal fits of chromatic equi-discrimination contours, it is possible that alternative psychophysical procedures combined with more powerful statistical tests could detect the pattern of deviations from ellipticality reported previously. In this paper, we describe psychophysical tests and statistical analyses that, taken together, provide a more powerful test of the indeterminacy of mechanisms than previous methods. We develop a method based on analysis of residuals for detecting the pattern of deviations from ellipticality. We apply these tests under fixed experimental conditions similar to those in which other researchers have found ellipsoidal equi-discrimination contours.For these conditions, for any of the tests performed, we do not reject the hypothesis that equi-discrimination surfaces are ellipsoidal.