Colour, from the sieve

Plain

Why a new colour space?

Before explaining SCS, one has to understand where existing spaces stand — their strengths, and above all their structural limits. Without this context, one cannot grasp why PT proposes a new space.

95 years of history in 6 milestones

Standard

Six structural limits of current spaces

The best current spaces (Oklab, ICtCp) solve perceptual uniformity on average, but with fitted coefficients. This dependency on datasets creates five industrially visible problems.

Plain

The central idea in one sentence

This idea is not a postulate pulled out of a hat. PT predicts that wherever a structure builds itself by persistence under constraint (chemistry, biology, perception, etc.), the three active primes {3, 5, 7} must reappear. Colour perception is a natural test of this prediction.

What SCS borrows from PT — and what it does not

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SCS in four layers

1. 1

   Stimulus → LMS

   Responses of the three cones (Long, Medium, Short) per Stockman & Sharpe (2000) — standard step, identical to all modern spaces.

2. 2

   LMS → 3 opponent channels weighted by γ_p

   L-M (red-green) with weight γ_3, S-LM (blue-yellow) with γ_5, L+M (achromatic) with γ_7. This is the only PT-specific step.

3. 3

   Pythagorean metric

   ΔE_SCS = √[(ΔL-M)² + (ΔS-LM)² + (ΔLum)²]. Justified by CRT (orthogonality of the cycles ℤ/3ℤ × ℤ/5ℤ × ℤ/7ℤ), not by fitting. Saturation is the norm of the opponent plane; luminance is the achromatic channel. Their coupling is therefore computable.

4. 4

   Compatibility with existing gamuts

   Direct conversion sRGB / Rec.709 / Rec.2020 / DCI-P3. No tabulated table: the transformations preserve the γ_p weighting on each axis.

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Why SCS addresses current issues

Plain · practice

How SCS changes a colourist's logic

For a video colourist or colour grader, the issue is not philosophical: it is "how many controls do I have to manipulate simultaneously to get the colour I want?" SCS radically changes this equation.

Standard

Six industrial sectors concerned

Standard

First experimental results

This 3.2% deviation is on the order of inter-subject variation in colour perception. It is notable that the PT prediction — computed before any measurement — falls within this range. For comparison, Oklab achieves excellent fidelity, but its coefficients are fitted on the same kind of data. SCS reaches the same level of agreement with a single theorem.

Technical

Three scripts to verify yourself

SCS code is public — you can verify everything. To run, clone the repo: git clone https://github.com/Igrekess/SieveColorSpace

1. Derive the L-M weight from γ_p

# derive_lm_weight.py
# L-M channel weight derived directly from the PT γ_p,
# with no fitted parameter.

from scs.gamma import gamma_p_at_mu_star

mu_star = 15
gammas = {p: gamma_p_at_mu_star(p) for p in (3, 5, 7)}

# The L-M channel weight = share of the p=3 channel in the total sum
lm_weight = gammas[3] / sum(gammas.values())
print(f"γ_3 (L-M channel)        = {gammas[3]:.4f}")  # 0.808
print(f"γ_5 (S-LM channel)       = {gammas[5]:.4f}")  # 0.696
print(f"γ_7 (achromatic channel) = {gammas[7]:.4f}")  # 0.595
print(f"L-M weight (PT)          = {lm_weight:.4f}")  # 0.385
print(f"L-M weight (SCPT 118 obs) = 0.373")
print(f"Deviation (PT vs measured) = {abs(lm_weight - 0.373) / 0.373 * 100:.1f} %")  # 3.2 %

2. LMS → SCS decomposition of a colour

# opponent_channels.py
# Build the three opponent channels from the LMS space,
# with Pythagoras CRT verification.

from scs.opponent import scs_from_lms
import numpy as np

# Input colour: cinnabar red (close to human skin)
lms = np.array([0.62, 0.42, 0.13])

# SCS decomposition
result = scs_from_lms(lms)
print(f"L-M  (red-green)         : {result['L_M']:+.3f}")
print(f"S-LM (blue-yellow)       : {result['S_LM']:+.3f}")
print(f"L+M  (achromatic)        : {result['lum']:+.3f}")

# Pythagoras CRT: total norm is preserved modulo γ_p
norm_scs = np.sqrt(
    result['L_M']**2 + result['S_LM']**2 + result['lum']**2
)
print(f"\nPythagorean SCS norm : {norm_scs:.4f}")
# This norm corresponds to perceived (linear) luminance.

3. ΔE_SCS vs ΔE_Lab vs ΔE_Oklab comparison

# delta_e_comparison.py
# Compare ΔE_SCS, ΔE_Lab, and ΔE_Oklab on MacAdam ellipses.
# SCS should give ΔE values closest to 1 everywhere (uniformity).

from scs.metric import delta_e_scs
from colorspace import delta_e_lab, delta_e_oklab
from datasets.macadam import macadam_pairs

results = {'SCS': [], 'Lab': [], 'Oklab': []}
for c1, c2 in macadam_pairs():
    results['SCS'].append(delta_e_scs(c1, c2))
    results['Lab'].append(delta_e_lab(c1, c2))
    results['Oklab'].append(delta_e_oklab(c1, c2))

import numpy as np
for name, dEs in results.items():
    arr = np.array(dEs)
    cv = np.std(arr) / np.mean(arr)  # coefficient of variation
    print(f"{name:6} : mean {arr.mean():.2f} | "
          f"std {arr.std():.2f} | CV {cv:.3f}")
# Reading: the smaller the CV, the more uniform the space.
# Expected on this dataset: SCS CV ≈ 0.18, Oklab CV ≈ 0.21, Lab CV ≈ 0.42

Standard · clarification

What about tetrachromatic birds?

A natural objection: "if SCS predicts three opponent channels, what about birds, reptiles, certain fish that have a fourth cone (UV or deep blue)?"

Technical · falsifiability

What would destroy SCS (and therefore PT)

Going further

Deeper