PreprintCC BY-NC-ND 4.0arXiv
A conformally-Euclidean Line Element for evaluating color differences
Abstract
Starting from our previously proposed line element and considering more ``surface color'' datasets, we derive a simplified version which matches experimental datasets equally well and resulted into a conformally-Euclidean line element, which is conceptually much simpler than any existing color difference metrics. The color difference is written as an Euclidean difference multiplied with a simple factor which depends on the luminance only. In a subspace with constant luminance, as considered by MacAdam, this factor becomes constant and the subspace is flat. The same holds for sufficiently large luminances. Based on this LE we derive perceptual coordinates (A,lc,sc) very similar to the CIELab (L*,a*,b*).
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BibTeX
@misc{visschere2026conformallyeuclidean,
title = {{A conformally-Euclidean Line Element for evaluating color differences}},
author = {Patrick De Visschere and Patrick Candry and Kristiaan Neyts},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.12588},
eprint = {2606.12588},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12588},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A conformally-Euclidean Line Element for evaluating color differences
AU - Patrick De Visschere
AU - Patrick Candry
AU - Kristiaan Neyts
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2606.12588
UR - https://arxiv.org/abs/2606.12588
AB - Starting from our previously proposed line element and considering more ``surface color'' datasets, we derive a simplified version which matches experimental datasets equally well and resulted into a conformally-Euclidean line element, which is conceptually much simpler than any existing color difference metrics. The color difference is written as an Euclidean difference multiplied with a simple factor which depends on the luminance only. In a subspace with constant luminance, as considered by MacAdam, this factor becomes constant and the subspace is flat. The same holds for sufficiently large luminances. Based on this LE we derive perceptual coordinates (A,l_c,s_c) very similar to the CIELab (L^*,a^*,b^*).
ER -