Helmlab: A Two-Space Family of Analytical, Data-Driven Color Spaces for UI Design Systems

arXiv:2602.23010v3 Announce Type: replace-cross Abstract: We present Helmlab, a family of two purpose-built color spaces for UI design systems sharing a common 11-stage analytical structure: MetricSpace, a 72-parameter space optimized for color-difference prediction, and GenSpace, a 44-parameter space optimized for gradient and palette generation. The forward transform maps CIE XYZ to a perceptually-organized Lab representation through learned matrices, per-channel power compression, Fourier hue correction, and embedded Helmholtz-Kohlrausch lightness adjustment. A post-pipeline neutral correction holds gray-axis chroma below 1e-5 on a 21-step ramp, and a rigid rotation of the chromatic plane improves hue-angle alignment without affecting the distance metric (which is invariant under isometries). On COMBVD (3,813 color pairs), MetricSpace v21 achieves STRESS 22.48, a 23 percent reduction from CIEDE2000 (29.20). On the held-out MacAdam 1974 dataset it scores 19.51 (CIEDE2000: 22.13; CAM16-UCS leads at 18.71). On a self-collected 3,552-judgement screen-condition set it scores 23.26 vs 62.54 for CIEDE2000. On academic He et al. 2022 (82 3D-printed pairs) MetricSpace scores 35.9 vs CIEDE2000 32.6, a regression we own. Averaging the three primary datasets, MetricSpace scores 21.75 vs the next-best baseline CIECAM02-UCS at 35.98. GenSpace v0.11.1 trades distance accuracy for generation quality: on a 90-metric, 3,038-pair gradient/palette benchmark across sRGB, P3, and Rec.2020, it wins 65 of 90 vs OKLab. The transform is invertible with round-trip errors below 1e-13. Production implementations ship on PyPI, npm, Color.js (PR 722, merged), and as a PostCSS plugin.