Researchers Propose Simplified Conformally-Euclidean Model for Measuring Color Differences
A new preprint on arXiv introduces a conformally-Euclidean line element that simplifies the mathematical description of how humans perceive differences between colors. The work builds on a previously proposed line element, extending it to additional 'surface color' datasets and reducing it to a form where color difference equals a standard Euclidean distance multiplied by a luminance-dependent factor. This matters because it offers a conceptually simpler alternative to existing color difference metrics like CIELab while reportedly matching experimental data equally well.
Physicist Patrick De Visschere has submitted a preprint to arXiv proposing a conformally-Euclidean line element as a new way to quantify perceptual color differences. The approach simplifies a previously proposed line element by incorporating additional surface color datasets, arriving at a formulation where color difference is expressed as a standard Euclidean distance scaled by a factor that depends solely on luminance. A key consequence of this structure is that in subspaces of constant luminance — the setting studied by MacAdam in his classic ellipse experiments — the scaling factor becomes constant and the color space is geometrically flat. The same flat behavior emerges at sufficiently high luminances. From this line element, the authors derive a set of perceptual coordinates (A, l_c, s_c) that are closely analogous to the widely used CIELab coordinates (L*, a*, b*), potentially easing practical adoption. The work is currently a preprint and has not yet undergone formal peer review.
What's missing
As a preprint, this work has not yet been peer reviewed. The abstract does not specify which surface color datasets were used for validation, how many datasets were tested, or provide quantitative goodness-of-fit comparisons against existing metrics such as CIEDE2000. It is also unclear whether the proposed perceptual coordinates have been validated against observer data beyond the datasets used to derive the line element.
What different sources said
- arXiv physicsCenter
A conformally-Euclidean Line Element for evaluating color differences
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