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A foundational question in perceptual science is the extent to which we can describe the relations between stimuli within the framework of a metric geometry. In the case of color, careful experiments have rejected the possibility that a Euclidean geometry can accurately describe suprathreshold judgments. Open, however, is whether a more general Riemannian geometry can play this role. A key factor that has limited firm conclusions is that to fully test Riemannian ideas, one requires a full characterization of color discrimination thresholds around every point in color space and for perturbations in every color direction. Recent advances in machine learning make measurement of this discrimination field tractable, and we have now made comprehensive measurements of color discrimination thresholds. The measurements enable computation of Riemannian geodesic distance between any two points in color space. I will describe our procedures, threshold and suprathreshold color difference measurements, and evaluation of geometric models of color comparison.
