Graininess of RGB-Display Space

Abstract

RGB–display space, that is, the ‘RGB–cube’, was sampled at 3,000 locations, uniformly and randomly distributed. Fifty observers contributed 60 samples each. At each location, participants synthesised a copy of the target, using a generic colour picker. The statistical distributions of errors as a function of location are used to define an overall measure of graininess. A smooth field of interpolated three-dimensional covariance ellipsoids represents an explicit, empirical Riemannian metric. The unit step size is about 20 times larger than the size of the classical MacAdam ellipses. We speculate that this metric might be found useful in various settings involving applications, because it reflects typical fuzziness encountered in generic tasks involving colour patterns such as images. Some of the more obvious applications are discussed.

Categorical colour geometry

“…5. The figure is directly comparable to Fig 17 and 23 in [29] for the colour matching geometry; that the two geometries are substantially different is immediately clear.…”

“…Colour geometries, at the full level of detail of metric tensors throughout the colour solid, have previously been determined based on discrimination [84, 85] and matching [29]. We have presented the first colour geometry based on colour categorization, using Information Geometry to compute metric tensors in a principled way from population-level colour naming data.…”

“…The more convenient strategy we pursue is to compute and store the tensor at a sampled grid of colours, and estimate the tensor at intermediate colours using interpolation as needed. We base the sampling of our scheme around the RGB length Δ≔0.1 (approximately 10.0 in CIELAB units) – this is roughly the confusion scale for colours [29] and so it is unlikely that categorical structure has non-artefactual articulations on shorter length scales than this.…”

“…Recently a very different metric for surface colour has been proposed that is grounded, not on JNDs, but on colours being ‘vaguely’ the same [29]. This definition is operationalized by having subjects adjust a surface colour so that it matches a simultaneously present, but not contiguous, target colour.…”

Colors and Things

“…The mean ellipsoid volume of 4:17 10 À4 suggests a Weber fraction per RGB coordinate of about 7% to 8%. This far exceeds the psychophysical discrimination thresholds but is comparable to estimates of color reproduction from experimental phenomenology (Koenderink et al, 2016(Koenderink et al, , 2018. These estimates are roughly comparable with estimates based on hyperspectral images of natural scenes (Linhares et al, 2008;Marin-Franch & Foster, 2010).…”