We evaluate how well three different parametric shapes, ellipsoids, rectangles, and parallelograms, serve as models of three-dimensional detection contours. We describe how the procedures for deriving the best-fitting shapes constrain inferences about the theoretical visual detection mechanisms. The ellipsoidal shape, commonly assumed by vector-length theories, is related to a class of visual mechanisms that are unique only up to orthogonal transformations. The rectangle shape is related to a unique set of visual mechanisms, but since the rectangle is not invariant with respect to linear transformations the estimated visual mechanisms are dependent on the stimulus coordinate frame. The parallelogram is related to a unique set of visual mechanisms and can be derived by methods that are independent of the stimulus coordinate frame. We evaluate how well these shapes approximate detection contours, using 2-deg test fields with a long (1-sec) Gaussian time course. Two statistical tests suggest that the parallelogram model is too strong. First, we find that the ellipsoid and rectangle shapes fit the data with the same precision as the variance in repeated threshold measurements. The parallelogram model, which has more free parameters, fits the data with more precision than the variance in repeated threshold measurements. Second, although the parallelogram model provides a slightly better fit of our data than the other two shapes, it does not serve as a better guide than the ellipsoidal model for interpolating from the measurements to thresholds in novel color directions.
Sensitivities of color-normal observers to temporal variations in stimulus luminance and chromaticity were measured for sine-wave stimuli between 1.5 and 20 Hz. Clear differences were found in observers' sensitivities to isochromatic luminance variations and to isoluminous chromaticity variations for wavelength pairs selected to test temporal discriminability along the red-green and yellow-blue dimensions, respectively. Despite interobserver differences in individual red-green functions, a given observer's sensitivity could be described by a single curve shape specific to that observer. Overall sensitivity for yellow-blue was less than that for red-green for all observers. Differences in curve shape between red-green and yellow-blue functions are found for individual observers, but group averages reveal that the differences are not systematic. Red-green temporal sensitivity is largely unaffected by adapting backgrounds in red-green equilibrium but is attenuated at low frequencies by nonequilibrium backgrounds of the same luminance. Isochromatic luminance sensitivity is largely independent of our adapting backgrounds, but heterochromatic luminance modulation functions undergo expected changes in form.
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