| Colour | I | P | T | CIPT | hIPT° |
|---|---|---|---|---|---|
| Primary | — | — | — | — | — |
| Comparison | — | — | — | — | — |
| Colour | J | C | h° | M | s | Q |
|---|---|---|---|---|---|---|
| Primary | — | — | — | — | — | — |
| Comparison | — | — | — | — | — | — |
| Colour | L* | a* | b* | C* | h° |
|---|---|---|---|---|---|
| Primary | — | — | — | — | — |
| Comparison | — | — | — | — | — |
Compare ΔEIPT, CIEDE2000, and ΔE₇₆ across average, dim, and dark surround conditions for the current colour pair.
| Surround | ΔEIPT | CIEDE2000 | ΔE₇₆ | IA | IB | JA | JB |
|---|
iCAM06 — Image Colour Appearance Model (Fairchild & Johnson 2007)
iCAM06 is the image-scale extension of CIECAM02 designed for spatially-varying adaptation in complex scenes. It applies local CAT02 chromatic adaptation using a spatially-filtered white-point estimate, then maps adapted XYZ into the IPT colour space via Hunt-Pointer-Estevez LMS and a power-law (γ=0.43) compression. For single colour patches (as in this tool), the spatial stage collapses to a global CAT02 step, making it equivalent to CIECAM02 input fed through the IPT nonlinearity.
Key features: perceptually uniform hue angles, simple Euclidean ΔEIPT that rivals CIEDE2000, fully invertible transform chain (M_IPT−1 exists), and HDR-capable tone reproduction.
IPT Colour Space (Ebner & Fairchild 1998)
The IPT colour space was purpose-built for perceptually uniform hue angles. It begins from XYZ D65, applies the HPE matrix to reach LMS cone space, compresses each channel with a sign-preserving power law (γ=0.43, fitted against cross-media colour-matching data), then applies the IPT rotation matrix. I (Intensity) correlates with lightness [0,1]. P (Protan) encodes the red–green opponent axis. T (Tritan) encodes the blue–yellow axis.
Munsell constant-hue lines map to nearly straight radii in the PT plane — unlike CIELAB where blue hue lines curve significantly. This property makes IPT ideal for gamut mapping along constant-hue rays.
CIE 159:2004 — CAT02 Chromatic Adaptation Transform
CAT02 (CIE Technical Report 159) is the von-Kries chromatic adaptation transform used in both CIECAM02 and iCAM06. It models the visual system’s colour constancy mechanism by converting XYZ to a sharpened cone space, applying diagonal scaling to simulate adaptation, and converting back. The degree-of-adaptation D (∈ [0,1]) controls how much the observer adapts to the illuminant, with the automatic formula linking D to adapting luminance and surround factor.
CIECAM02 — CIE Colour Appearance Model (Moroney et al. 2002)
CIECAM02 (CIE 159:2004) defines six appearance correlates: J (lightness), C (chroma), h (hue angle), M (colourfulness), s (saturation), Q (brightness). It uses CAT02 for chromatic adaptation, HPE for opponent-channel formation, and a sigmoidal compression function. iCAM06 uses CIECAM02’s viewing-condition framework (LA, Yb, surround) but replaces the final nonlinearity with IPT’s power law for improved hue uniformity.
ΔEIPT vs CIEDE2000 vs ΔE₇₆
All three metrics predict perceived colour difference via different routes:
CIEDE2000: weighted ΔL′/ΔC′/ΔH′ with 5 correction terms — best psychophysical fit, not invertible
ΔE₇₆: √(ΔL*² + Δa*² + Δb*²) — simple, fair hue uniformity
Fairchild & Johnson showed ΔEIPT predicts observer colour-difference judgements as well as CIEDE2000 across the RIT-DuPont, Witt, and Luo–Rigg datasets, while being simpler and fully invertible.
CIE Standard Illuminants (D65, D50, A, E)
CIE 15:2004 defines D-series daylight illuminants and Illuminant A. D65 (6504 K) is the standard for sRGB, Rec. 709, and Display P3. D50 (5003 K) is the ICC PCS white point. Illuminant A (2856 K) represents incandescent tungsten. Equal-energy illuminant E has equal power at all visible wavelengths. Changing the illuminant in this tool alters the CAT02 adaptation state and thus all IPT and CIECAM02 correlates.
Applications: HDR Tone Mapping, Gamut Mapping, Cross-Media Matching
- HDR tone mapping — iCAM06’s spatial pipeline produces naturalistic tone-mapped images by preserving local contrast through spatially adaptive white maps.
- Gamut mapping — compress along constant-hue rays in the PT plane without hue rotation; M_IPT−1 makes this practical in real-time.
- Cross-media colour matching — predict how colours shift from print to display to projection under different whites and surrounds.
- Camera ISP — model observer adaptation state for white-balance and colour correction algorithms.
- Material You (HCT) — Google’s HCT system draws from the same IPT hue-uniformity principles for palette generation.
- Perceptual gradients — straight lines in IPT produce evenly-stepping gradients without hue rotation.
IPT Colour Space (Ebner & Fairchild 1998)
MHPE = [[ 0.38971, 0.68898, -0.07868],
[-0.22981, 1.18340, 0.04641],
[ 0.00000, 0.00000, 1.00000]]
2. Power-law compression (γ = 0.43):
L′ = sign(L) · |L|0.43
M′ = sign(M) · |M|0.43
S′ = sign(S) · |S|0.43
3. IPT rotation matrix:
MIPT = [[ 0.4000, 0.4000, 0.2000],
[ 4.4550, -4.8510, 0.3960],
[ 0.8056, 0.3572, -1.1628]]
[I, P, T] = MIPT · [L′, M′, S′]
CIPT = √(P² + T²)
hIPT = atan2(T, P)
iCAM06 Forward Model (Fairchild & Johnson 2007)
Full spatial pipeline (image-scale):
2. CAT02 adaptation per pixel using local white and D
3. Xadapted → HPE LMS → |·|0.43 → IPT
4. Derive lightness J from I via Stevens-law
5. Tone reproduction to compress dynamic range
Point mode (this tool):
For isolated patches, spatial adaptation collapses to global CAT02.
Equivalent to CIECAM02 input through IPT nonlinearity.
CAT02 Chromatic Adaptation Transform
[-0.7036, 1.6975, 0.0061],
[ 0.0030, 0.0136, 0.9834]]
Degree of adaptation D:
D = F · [1 − (1/3.6) · e−(LA+42)/92]
clamped to [0, 1]
Adapted cone responses:
Rc = (D · YW/RW + 1 − D) · R
Gc = (D · YW/GW + 1 − D) · G
Bc = (D · YW/BW + 1 − D) · B
The adapted XYZ is recovered via MCAT02−1 and fed into the HPE/IPT chain (iCAM06) or the CIECAM02 sigmoidal compression.
CIECAM02 Forward Model (CIE 159:2004)
R′a = 400 · (FL·Rc/100)0.42 / [(FL·Rc/100)0.42 + 27.13] + 0.1
Opponent channels:
a = R′a − 12·G′a/11 + B′a/11
b = (R′a + G′a − 2·B′a) / 9
Correlates:
h = atan2(b, a) — hue angle
J = 100 · (A / AW)c·z — lightness
C = t0.9 · (J/100)0.5 · (1.64 − 0.29n)0.73 — chroma
M = C · FL0.25 — colourfulness
s = 100 · (M / Q)0.5 — saturation
Q = (4/c) · (J/100)0.5 · (AW + 4) · FL0.25 — brightness
sRGB ↔ XYZ (D65, 2° observer)
Clin = C/12.92 if C ≤ 0.04045
Clin = ((C + 0.055)/1.055)2.4 otherwise
sRGB → XYZ (IEC 61966-2-1):
MsRGB = [[0.4124564, 0.3575761, 0.1804375],
[0.2126729, 0.7151522, 0.0721750],
[0.0193339, 0.1191920, 0.9503041]]
ΔE Colour-Difference Formulas
ΔE = √(ΔI² + ΔP² + ΔT²)
ΔE₇₆ (Euclidean):
ΔE = √(ΔL*² + Δa*² + Δb*²)
CIEDE2000:
ΔE₀₀ = √[(ΔL′/SL)² + (ΔC′/SC)² + (ΔH′/SH)² + RT·(ΔC′/SC)·(ΔH′/SH)]
Perceptibility thresholds (approximate):
| ΔE range | Perceptual meaning |
|---|---|
| 0–1 | Imperceptible |
| 1–2 | Just noticeable (trained observer) |
| 2–5 | Acceptable in some industries |
| 5–10 | Clearly different colours |
| >10 | Large / obvious colour difference |
Known Limitations
- Point mode only: This tool operates on isolated colour patches. The full spatially-varying iCAM06 pipeline (requiring image input, Gaussian blur for local white estimation) is not implemented.
- sRGB gamut boundary: Input is sRGB hex (8-bit per channel). Wide-gamut or HDR stimuli cannot be entered directly.
- CAT02 singularity: CAT02 can produce negative adapted cone responses for highly saturated stimuli outside the sRGB gamut. This tool clamps inputs to sRGB, avoiding the issue.
- Single-state adaptation: The model assumes steady-state adaptation. Temporal adaptation dynamics are not modelled.
- No fluorescence model: iCAM06 does not handle fluorescent or phosphorescent stimuli.
- Browser floating-point: All computation uses IEEE 754 double precision. Differences from reference implementations are below 10−10.
Image Colour Appearance Models
[2] Ebner, F. & Fairchild, M.D. (1998). “Development and testing of a color space (IPT) with improved hue uniformity.” IS&T/SID CIC6, 8–13.
[3] Fairchild, M.D. & Johnson, G.M. (2002). “Meet iCAM: A next-generation color appearance model.” IS&T/SID CIC10, 33–38.
CIECAM02 & Chromatic Adaptation
[5] CIE Technical Report 159:2004. “A Colour Appearance Model for Colour Management Systems: CIECAM02.”
[6] Lam, K.M. (1985). Metamerism and Colour Constancy. Ph.D. thesis, University of Bradford.
Colorimetry and Colour Difference
[8] Sharma, G., Wu, W., Dalal, E.N. (2005). “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations.” Color Research & Application, 30(1), 21–30.
[9] IEC 61966-2-1:1999. “Multimedia systems and equipment — Colour measurement and management — Part 2-1: Default RGB colour space — sRGB.”
Industry Standards
[11] ISO 3664:2009. “Graphic technology and photography — Viewing conditions.”
About this Tool
Enter multiple hex colours (comma or newline separated). The engine computes pairwise ΔEIPT, CIEDE2000, and ΔE₇₆ for every combination using the current illuminant, viewing conditions, and D. Minimum 2 colours required.
IPT was specifically engineered to produce perceptually uniform hue angles. For Munsell chips, constant-hue lines map to nearly straight radii in the PT plane. The mean unsigned hue prediction error in IPT is approximately 2° lower than CIELAB across the full Munsell set. The batch analysis above can be used to verify this numerically by computing Δh between model predictions and Munsell renotation data.
The degree-of-adaptation D in iCAM06/CIECAM02 ranges from 0 (no adaptation) to 1 (full adaptation). Under typical viewing (LA≈64, average surround), D≈0.94. The automatic formula D=F·[1−(1/3.6)·e−(LA+42)/92] clamps to [0,1]. This tool exposes D as a slider so researchers can explore partial adaptation effects on IPT and CIECAM02 correlates — useful for modelling mixed illumination scenarios.
Future: implement the full spatially-varying iCAM06 pipeline accepting image input. The image would be Gaussian-blurred to estimate local adaptation whites, enabling per-pixel CAT02 adaptation before the IPT transform. This enables research into local adaptation, HDR tone mapping quality, and cross-media image appearance prediction.