Surface characterizations of color thresholds.

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.