Helmlab

A family of purpose-built color spaces for UI design systems.

Helmlab provides two complementary color spaces: MetricSpace for perceptual distance measurement (STRESS 23.30 on COMBVD — 20% better than CIEDE2000), and GenSpace for gradient/palette generation (60-8 vs OKLab on ColorBench's 83 metrics, 360/360/360 gamut cusps, zero monotonicity violations).

Website | Documentation | Demo | Paper

Key Features

• State-of-the-art color difference — MetricSpace: STRESS 23.30 vs CIEDE2000's 29.18 on COMBVD (3,813 pairs)
• Superior gradient generation — GenSpace: 60 wins vs OKLab's 8 across 83 ColorBench metrics (3,038 gradient pairs, 3 gamuts), 360/360/360 valid cusps, zero monotonicity violations
• Depressed cubic transfer — y³ + αy = x (α=0.021): eliminates cusp singularities while preserving gradient quality. Exact analytical inverse via hyperbolic functions
• Chroma power — Mild compression (C^0.978) improves gradient step uniformity across 3,038 pairs
• L-gated hue enrichment — Targeted hue rotation in the blue region, gated by lightness. Fixes blue→white purple shift without affecting other colors
• True blue gradients — Blue→White midpoint is sky blue (G/R = 1.51), not lavender
• Perfect achromatic axis — Grays map to C* < 10⁻¹⁵ (structural guarantee from uniform transfer function)
• Perfectly uniform gradients — Built-in CIEDE2000 arc-length reparameterization, CV ≈ 0% on any pair
• Embedded Helmholtz-Kohlrausch — MetricSpace: lightness is chroma-dependent, learned from data
• UI tooling — Gamut mapping, WCAG contrast enforcement, palette generation, dark/light mode adaptation
• Token export — CSS (oklch()), Android XML, iOS Swift (Display P3), Tailwind, JSON

Installation

npm (TypeScript / JavaScript)

npm install helmlab

import { Helmlab } from 'helmlab';

const hl = new Helmlab();

const lab = hl.fromHex('#3B82F6');                    // Hex → Helmlab Lab
const hex = hl.toHex([0.5, -0.1, 0.2]);              // Lab → hex (gamut mapped)
hl.contrastRatio('#ffffff', '#3B82F6');                // → 3.68
hl.ensureContrast('#3B82F6', '#ffffff', 4.5);         // Adjust to meet 4.5:1
hl.deltaE('#ff0000', '#00ff00');                      // Perceptual distance
hl.gradient('#ff0000', '#0000ff', 8);                 // Perfectly uniform gradient
hl.semanticScale('#3B82F6');                          // Tailwind-style 50–950 scale

~12KB gzipped, zero dependencies, ESM + CJS with full TypeScript types. See the npm package README for the full API.

PostCSS

Use Helmlab color spaces directly in CSS — transformed to rgb() at build time:

npm install postcss-helmlab

/* Input */
.card { color: helmlab(0.78 0.52 -0.20); }
.bg   { background: linear-gradient(in helmgen, #e63946, #457b9d); }

/* Output */
.card { color: rgb(255, 76, 119); }
.bg   { background: linear-gradient(#e63946 0.0%, ..., #457b9d 100.0%); }

Python (pip)

pip install helmlab

Quick Start (Python)

from helmlab import Helmlab

hl = Helmlab()

# sRGB to Helmlab Lab
lab = hl.from_srgb([0.2, 0.5, 0.8])
print(f"L={lab[0]:.3f}, a={lab[1]:.3f}, b={lab[2]:.3f}")

# Color difference between two sRGB colors
dist = hl.delta_e("#ff0000", "#00ff00")

# Perfectly uniform gradient (arc-length reparameterized)
gradient = hl.gradient("#ff0000", "#0000ff", 8)

# Ensure WCAG AA contrast (4.5:1)
adjusted = hl.ensure_contrast("#ffffff", "#3B82F6", min_ratio=4.5)

# Generate a palette (Tailwind-style 50-950 scale)
scale = hl.semantic_scale("#3B82F6")

Architecture

Helmlab is a family of purpose-built color spaces:

Helmlab (UI layer)
├── MetricSpace — 72-param enriched pipeline (distance, deltaE)
│   XYZ → M₁ → γ → M₂ → Hue → H-K → L → C → HL → NC → φ → Lab
│
└── GenSpace — generation-optimized pipeline (gradient, palette)
    XYZ → M₁ → depcubic(α) → M₂ → C^cp → PW_L_corr → L-gated enrichment → Lab
    + CIEDE2000 arc-length reparameterization for gradient()

MetricSpace (72 parameters)

Jointly optimized against COMBVD using L-BFGS-B with 8 random restarts. 13-stage enriched pipeline with hue correction, Helmholtz-Kohlrausch, chroma scaling, neutral correction, and rigid rotation. STRESS 23.30 — the lowest published figure on COMBVD.

GenSpace (v0.11.1 — Depressed Cubic + Chroma Power + L-Gated Enrichment)

Pipeline: XYZ → M₁ → depcubic(α=0.021) → M₂ → chroma_power(0.978) → PW L_corr → L-gated hue enrichment → Lab

Transfer function: y³ + αy = x (depressed cubic, α=0.021)

Solved analytically via y = 2s·sinh(arcsinh(x/2s³)/3) where s = √(α/3), refined with a single Halley iteration for full precision. The inverse is trivial: x = y³ + αy. This depressed cubic has a finite derivative at zero (unlike standard x^(1/3)), which eliminates gamut boundary singularities.

Chroma power: C' = C^0.978 — mild chroma compression applied post-M2 that improves gradient step uniformity. Analytically invertible (C = C'^(1/0.978)).

L-gated hue enrichment: A targeted hue rotation h' = h + A·gate(L)·gauss(h−center) applied post-M2, where the gate function sin²(π·(L−L_lo)/(L_hi−L_lo)) activates only in mid-to-high lightness and the Gaussian targets the blue hue region. This fixes the blue→white purple shift with zero impact on achromatic colors or other hue regions. Invertible via Halley iteration (cubic convergence, 8 iterations).

Key properties:

• 360/360/360 valid cusps in sRGB, Display P3, and Rec.2020 (OKLab: 299/308/360)
• Zero monotonicity violations and zero invalid cusps across all gamuts
• Blue→White gradient: sky blue midpoint (G/R = 1.51), no lavender shift
• Achromatic: C* < 10⁻¹⁵ (structural guarantee — uniform transfer × orthogonal M₂)
• Munsell Value uniformity: 0.16% (OKLab: 2.80% — 18x better)
• Adaptive gamut clipping with cusp-finding (Ottosson-style L0 calculation)
• Piecewise-linear L correction with 19 breakpoints (analytically invertible)

ColorBench evaluation (83 metrics, 3,038 gradient pairs, 3 gamuts):

| Category | GenSpace wins | OKLab wins | Tie | |----------|-------------|------------|-----| | Gamut geometry | 25 | 0 | 2 | | Application | 10 | 0 | 2 | | Gradient quality | 5 | 3 | 2 | | Perceptual accuracy | 5 | 0 | 0 | | Structural | 4 | 2 | 2 | | Other (hue, achromatic, banding, special, accessibility, advanced, numerical) | 10 | 3 | 8 | | Total | 60 | 8 | 15 |

Known trade-offs: Slightly reduced round-trip precision in sRGB (~5.6×10⁻⁸ vs OKLab's ~1.6×10⁻¹⁵, due to enrichment Halley iteration — invisible in 8-bit pipelines), minor primary hue discontinuity at exact primary vertices, and reduced near-achromatic gradient uniformity in very low chroma regions.

Blue-region gamut fold: All power-law based M1→f→M2 spaces exhibit tiny non-contiguous gamut regions near h≈260° in sRGB due to cubic polynomial roots in the inverse. OKLab has 46 such holes; GenSpace has 5, each ~0.001 chroma wide (sub-pixel, invisible). See color.js#81.

Benchmarks

Perceptual Distance (MetricSpace)

STRESS on COMBVD (3,813 pairs). Lower is better.

| Method | COMBVD STRESS | vs CIEDE2000 | |--------|--------------|-------------| | Helmlab v20b | 23.30 | -20.1% | | CIEDE2000 | 29.18 | — | | CIE94 | 33.59 | +15.1% | | CAM16-UCS (Euclid.) | 33.90 | +16.2% | | ΔE CMC | 34.04 | +16.6% | | IPT (Euclid.) | 41.21 | +41.3% | | CIE Lab ΔE76 | 42.80 | +46.7% | | Oklab (Euclid.) | 47.46 | +62.7% |

STRESS (Standardized Residual Sum of Squares) is the CIE-standard metric for evaluating color difference formulas. COMBVD is a combined visual-difference dataset of 3,813 color pairs from 6 independent psychophysical experiments (Luo & Rigg 1986, RIT-DuPont, Witt, Leeds, BFD, He et al. 2022), containing 64,000+ individual human judgments.

For each pair i, let ΔVᵢ = human visual difference, ΔEᵢ = predicted distance. STRESS finds the optimal scale F minimizing residuals:

STRESS = 100 × √( Σ(ΔEᵢ − F·ΔVᵢ)² / Σ(ΔEᵢ)² )

Scale: 0 = perfect, 100 = no correlation. Full methodology: arXiv:2602.23010.

Gradient Quality (GenSpace)

Helmlab GenSpace vs OKLab — head-to-head on ColorBench (83 metrics, 3,038 gradient pairs across sRGB, Display P3, and Rec.2020 gamuts):

| Category | GenSpace wins | OKLab wins | Tie | |----------|-------------|------------|-----| | Gamut geometry | 25 | 0 | 2 | | Application | 10 | 0 | 2 | | Gradient quality | 5 | 3 | 2 | | Perceptual accuracy | 5 | 0 | 0 | | Structural | 4 | 2 | 2 | | Hue | 2 | 0 | 0 | | Achromatic | 2 | 0 | 0 | | Advanced | 2 | 0 | 4 | | Banding | 1 | 0 | 1 | | Special | 2 | 1 | 0 | | Accessibility | 1 | 1 | 0 | | Numerical | 0 | 1 | 2 | | Total | 60 | 8 | 15 |

Gradient Uniformity

CV (coefficient of variation of CIEDE2000 step sizes). Lower is better.

| Method | Red→Blue | Orange→Cyan | Black→White | Technique | |--------|----------|-------------|-------------|-----------| | Helmlab gradient() | ≈ 0% | ≈ 0% | ≈ 0% | arc-length reparam. | | Helmlab GenSpace | 30.3% | 26.5% | 40.7% | linear interpolation | | Oklab | 31.5% | 41.4% | 41.2% | linear interpolation | | CIE Lab | 44.8% | 52.3% | 61.5% | linear interpolation |

Note: gradient() achieves ≈ 0% via CIEDE2000 arc-length reparameterization. This redistributes steps to equal perceptual spacing — an algorithm that could be applied to any space. Helmlab ships it built-in.

Project Structure

src/helmlab/
├── helmlab.py              # Main API (Helmlab class)
├── spaces/
│   ├── metric.py           # MetricSpace — 72-param enriched pipeline
│   ├── gen.py              # GenSpace — depcubic + enrichment pipeline
│   ├── base.py             # Abstract base class
│   └── ...                 # Baseline spaces (CAM16, IPT, Oklch, etc.)
├── metrics/
│   ├── delta_e.py          # Color difference formulas
│   ├── stress.py           # STRESS computation
│   └── benchmarks.py       # Cross-method benchmarking
├── utils/
│   ├── srgb_convert.py     # sRGB/Display P3 conversions
│   ├── gamut.py            # Gamut mapping (binary search + adaptive clipping)
│   └── ...                 # Converters, I/O, visualization
├── data/
│   ├── metric_params.json  # MetricSpace params (v20b, STRESS 23.30)
│   ├── gen_params.json     # GenSpace params (v0.11.1, depcubic + enrichment)
│   └── ...                 # Dataset loaders (COMBVD, Munsell, etc.)
├── export.py               # Token export (CSS, Android, iOS, Tailwind)
└── feedback/               # Human feedback collection tools

packages/helmlab-js/        # npm package (TypeScript)
packages/postcss-helmlab/   # PostCSS plugin
colorbench/                 # ColorBench evaluation suite (83 metrics)
tests/                      # 609+ tests (413 Python + 196 JavaScript)

Tests

python -m pytest tests/ -q              # 413 Python tests
cd packages/helmlab-js && npx vitest run # 196 JS tests

Research

The optimization experiments, checkpoints, and analysis scripts that led to the current GenSpace v0.11.1 are available in a separate repository:

helmlab-experimental — 480+ experiments across 4 transfer functions, 3 M₁ variants, and systematic grid searches. Includes all checkpoints, optimization scripts, and the full experiment report.

Citation

@article{yildiz2025helmlab,
  title={Helmlab: A Data-Driven Analytical Color Space for UI Design Systems},
  author={Y{\i}ld{\i}z, G{\"o}rkem},
  journal={arXiv preprint arXiv:2602.23010},
  year={2025},
  url={https://arxiv.org/abs/2602.23010}
}

Author

Gorkem Yildiz — helmlab.space

License

MIT