Abstract
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Highlights
It was early discovered that it is not possible to construct a colour space that scales the Munsell hue and chroma scales such that the resulting chromatic diagram appears uniform [1]
It is demonstrated that state-of-the-art Euclidean colour metrics can be statistically significantly improved by moving from Euclidean to hyperbolic geometry for the representation of the chromatic plane
It is shown that one of the hyperbolic metrics derived from the existing Euclidean one can outperform even the state-of-the-art non-Euclidean metric CIEDE2000
Summary
It was early discovered that it is not possible to construct a colour space that scales the Munsell hue and chroma scales such that the resulting chromatic diagram appears uniform [1]. Due to the hue super-importance – which in the first place was observed from a colour order point of view – a perceptually isotropic colour solid cannot be represented in Euclidean space. For supra-threshold experiments, metrics that implicitly define negatively curved chromatic planes, such as CMC( : c) [7], CIE94 [8], and CIEDE2000 [9], give good fit to the experimentally observed colour differences. Judd [2] suggested that the chromatic plane can be modelled as a folded fan in order to achieve hue cirles of a total angle greater than 2π. Such a model would have zero curvature everywhere, except at the centre, where the curvature would be undefined. An experiment with well established Euclidean colour metrics and colour difference data sets is conducted and the results are compared to the stateof-the-art colour metric CIEDE2000
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