cs.GRFeb 26, 2026

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

Authors: Gorkem Yildiz

Organizations: Independent Researcher

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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.

Figures & tables

Figure 1: The Helmlab MetricSpace forward transform pipeline. Blue: linear operations; yellow: nonlinear corrections; green: structural guarantees (NC, rotation). The 72 jointly-optimized parameters are distributed across the eleven stages as shown.
Figure 2: stress on COMBVD (3,813 pairs). Lower is better. MetricSpace v21 is bottom-row.
MethodcombvdMacAdamHumFBAvg
MetricSpace v2122.4819.5123.2621.75
CIE9433.3719.7859.7537.63
CIEDE200029.2022.1362.5437.96
DIN9935.5723.3156.4438.44
JzazbzJ_{z}a_{z}b_{z}41.9224.1461.7442.60
CIE Lab ( ΔE76∗\Delta E^{*}_{76} )42.8624.5362.3243.24
Table 1: stress across three datasets. Lower is better. HumFB = 3,552 self-collected screen-condition judgements from 71+ observers, see caveat in Section 6.1 . Avg is the unweighted three-dataset mean. He et al. 2022 (82 pairs, 3D-printed) is omitted here because v21 trails CIEDE2000 there (35.9 vs 32.6); see Section 6.1 . All baselines use Euclidean distance in their native Cartesian coordinates with per-pair Bradford CAT to D65 where appropriate.
Figure 3: Predicted vs observed color differences on COMBVD for MetricSpace v21.
Figure 4: Cross-dataset validation on held-out data.
Figure 5: Left: neutral ramp step uniformity. Right: achromatic chroma leakage. Helmlab ’s NC drives C<10−5C<10^{-5} for grays on the 21-step ramp.
PropertyValue
Achromatic max CC (NC on)<10−5<10^{-5}
Hue RMS (6 sRGB primaries)26.4°
Hue max error53.4°
Round-trip (sRGB)∼\sim 7 ×\times 10 -15
Round-trip (random XYZ)∼\sim 1 ×\times 10 -13
Munsell CV (3,590 iso-hue pairs)32.0%
Table 2: Generation quality metrics for MetricSpace v21.
ConfigurationCOMBVD stressΔ\Delta
Full MetricSpace v2122.48—
Euclidean distance only∼\sim 27.6+5.1+5.1
No H-K embedding∼\sim 26.5+4.0+4.0
No hue correction (Stage 4)∼\sim 37.9+15.4+15.4
No dark-L compression∼\sim 22.7+0.2+0.2
Rotation φ=−28.2\varphi=-28.2 °22.480.00
Table 3: Frozen ablation on v21: effect of disabling components without re-optimisation.
Sub-datasetNNv21CIEDE2000
BFD-P(C)20029.0829.08
BFD-P(D65)2,02821.5424.09
BFD-P(M)54821.7535.23
LEEDS30721.8419.25
RIT-DuPont31221.9019.47
WITT41830.9330.22
Table 4: stress on individual combvd sub-datasets (v21 production checkpoint).
Figure 6: GenSpace v0.11.1 vs OKLab — per-category breakdown across all 90 ColorBench metrics. Headline tally is 65W / 9L / 16T ( Table 5 ). Categories ordered by total metric count.
CategoryGenSpaceOKLabTies
Gamut geometry2403
Application903
Gradient quality731
Independent †610
Perceptual500
Structural422
Table 5: GenSpace v0.11.1 vs OKLab — head-to-head on ColorBench. † Independent = Hung-Berns, Ebner-Fairchild, Pointer-gamut metrics (held out from optimizer). Visual breakdown in Figure 6 .
Figure 7: sRGB gamut in Helmlab aa – bb plane at three L levels. Points colored by their sRGB values.
Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

StageParameterValueDescription
M1\mathbf{M}_{1} (9)Row 0[ −- 0.7213, −- 0.4534, −- 0.1929]XYZ →\to cone-like
Row 1[ −- 0.7882, −- 1.7952, −- 0.0876] 
Row 2[ −- 0.0918, −- 0.4577, −- 1.2922] 
γ\gamma (3)γ0,γ1,γ2\gamma_{0},\gamma_{1},\gamma_{2}0.4723, 0.5149, 0.5113Signed power compression
M2\mathbf{M}_{2} (9)Row 0[ −- 0.2636, −- 0.4168, −- 0.4927]Compressed →\to Lab
Row 1[ −- 1.8898, −- 3.1212, −- 1.0422] 
Appendix
Table 6: MetricSpace v21 parameters ( φ=−28.2\varphi=-28.2 °). Trained on combvd + He 2022 + MacAdam 1974 with sub-dataset-balanced loss ( Equation 16 ).
StageValue
M1\mathbf{M}_{1}3 ×\times 3, see JSON (Bradford CAT pre-baked)
Transferdepcubic, α=0.021\alpha=0.021
M2\mathbf{M}_{2}3 ×\times 3, see JSON
Chroma power0.978
PW LL correction19-point dense, see JSON
EnrichmentL-gated hue rotation
Appendix
Table 7: GenSpace v0.11.1 parameters.

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