| Attribute | Primary (A) | Comparison (B) |
|---|---|---|
| J (lightness) | — | — |
| C (chroma) | — | — |
| h (hue angle) | — | — |
| M (colourfulness) | — | — |
| s (saturation) | — | — |
| Q (brightness) | — | — |
| D (adaptation) | — | — |
| FL | — | — |
| Aw | — | — |
| Coordinate | Primary (A) | Comparison (B) |
|---|---|---|
| J′ (lightness) | — | — |
| a′ (red–green) | — | — |
| b′ (yellow–blue) | — | — |
| M′ (colourfulness) | — | — |
| h′ (hue angle) | — | — |
| Variant | c₁ | c₂ | J′(A) | M′(A) | J′(B) | M′(B) | ΔE | Quality |
|---|---|---|---|---|---|---|---|---|
| Loading… | ||||||||
| Coordinate | Primary (A) | Comparison (B) |
|---|---|---|
| L* | — | — |
| a* | — | — |
| b* | — | — |
| C*ab | — | — |
| hab | — | — |
| Channel | Primary (A) | Comparison (B) |
|---|---|---|
| X | — | — |
| Y | — | — |
| Z | — | — |
Compare all three CAM02-UCS variants (UCS, LCD, SCD) side-by-side. Shows J′, M′, ΔE for each variant plus CIEDE2000 and ΔE₇₆ reference values.
| Variant | c₁ | c₂ | ΔE(CAM02) | J′(A) | M′(A) | J′(B) | M′(B) | ΔE₀₀ | ΔE₇₆ | Best |
|---|---|---|---|---|---|---|---|---|---|---|
| Click "Compare UCS / LCD / SCD" to run analysis. | ||||||||||
Enter two hex codes to compute ΔE across all three CAM02-UCS variants plus CIEDE2000 and ΔE₇₆.
CIECAM02 — CIE 159:2004
CIE 159:2004 specifies the CIECAM02 colour appearance model. The forward model takes CIE XYZ tristimulus values plus viewing condition parameters (LA, Yb, surround) and outputs six perceptual correlates: lightness J, chroma C, hue angle h, colourfulness M, saturation s, and brightness Q.
The chromatic adaptation step uses the CAT02 matrix to convert XYZ to sharpened LMS-like cone responses, applies a degree-of-adaptation D, then converts through Hunt-Pointer-Estevez (HPE) matrix to post-adaptation LMS for the non-linear response compression stage.
Surround parameters: Average (F=1.0, c=0.69, Nc=1.0), Dim (F=0.9, c=0.59, Nc=0.9), Dark (F=0.8, c=0.525, Nc=0.8).
CAM02-UCS — Luo, Cui & Li (2006)
Luo, Cui & Li (2006) derived a perceptually uniform colour space from CIECAM02, published in Color Research and Application 31(4):320–330. The transform applies a non-linear compression to J and M, then projects to Cartesian coordinates:
J′ = (1 + 100c₁) × J / (1 + c₁ × J)
M′ = ln(1 + c₂ × M) / c₂
a′ = M′ × cos(h)
b′ = M′ × sin(h)
Three variants were optimised for different ΔE scales:
- UCS: c₁=0.007, c₂=0.0228 — general purpose.
- LCD: c₁=0.0053, c₂=0.0158 — large colour differences.
- SCD: c₁=0.0102, c₂=0.0228 — small colour differences.
ΔE in the uniform space is Euclidean: ΔE = √(ΔJ′² + Δa′² + Δb′²).
Perceptual Uniformity and Colour Metrics
A colour space is perceptually uniform when equal Euclidean distances correspond to equal perceived colour differences. CIELAB (1976) was the first major attempt, but has known non-uniformities especially in the blue region.
CAM02-UCS improves on CIELAB by deriving the uniform space from a full colour appearance model (CIECAM02) rather than from tristimulus values alone, and by optimising the uniformity parameters against large-scale visual assessment datasets (BFD, Leeds, Witt, RIT-DuPont).
CIEDE2000 — CIE 142-2001
CIE 142-2001: CIEDE2000 (ΔE₀₀) is the recommended colour-difference formula. It adds corrections for lightness, chroma, hue, and a rotation term RT that addresses the problematic blue region. ΔE₀₀ <1 is imperceptible, 1–2 just noticeable, 2–5 visible, 5–10 large, >10 very large.
CIE Standard Illuminants
- D65 (6504 K): Standard daylight, sRGB reference white.
- D50 (5003 K): ICC PCS standard, printing industry.
- D55 (5503 K): Mid-morning/afternoon daylight.
- D75 (7504 K): North sky daylight.
- A (2856 K): Tungsten/incandescent (Planckian radiator).
- B (4874 K): Direct noon sunlight (deprecated).
- C (6774 K): Average daylight (deprecated, superseded by D65).
- E: Equal-energy, all wavelengths equal power.
- F2 (4230 K): Cool white fluorescent.
- F7 (6500 K): Broadband fluorescent.
- F11 (4000 K): Narrow tri-phosphor fluorescent.
CIE 15:2004 — Colorimetry
CIE 15:2004 is the fundamental reference for colorimetric computation. It defines the CIE 1931 standard observer, illuminant SPDs (A, D50, D65, etc.), the XYZ colour space, CIELAB, and chromatic adaptation procedures. All calculations in this tool conform to CIE 15:2004 specifications.
ISO 11664 Series — CIE Colorimetry
The ISO 11664 series (parts 1–6) codifies CIE colorimetric standards into ISO format: standard observers, XYZ tristimulus computation, CIELAB, and colour-difference formulas including CIEDE2000.
CAM02-UCS Transform (Luo et al., 2006)
Given CIECAM02 correlates J (lightness), M (colourfulness), and h (hue angle in degrees), the CAM02-UCS transform computes perceptually uniform J′a′b′ coordinates:
M′ = ln(1 + c₂ × M) / c₂
a′ = M′ × cos(h × π/180)
b′ = M′ × sin(h × π/180)
Variant Parameters
LCD: c₁ = 0.0053, c₂ = 0.0158
SCD: c₁ = 0.0102, c₂ = 0.0228
Colour Difference
The logarithmic compression on M ensures colourfulness differences at high chroma levels are perceptually scaled. UCS is the general-purpose default; LCD was optimised against large colour differences (BFD dataset); SCD was optimised against small colour differences (Witt dataset).
CIECAM02 Forward Model
The CIECAM02 forward model transforms CIE XYZ to perceptual attributes:
D = F × [1 − (1/3.6) × e−(LA+42)/92]
Rc = (D × Yw/Rw + 1 − D) × R
2. RGBc → (HPE) → LMSa (post-adaptation)
f(x) = 400 × (FL|x|/100)0.42 / [(FL|x|/100)0.42 + 27.13] + 0.1
3. LMSa → Correlates:
J = 100 × (A/Aw)cz
h = atan2(b, a) in degrees
C = t0.9 × √(J/100) × (1.64 − 0.29n)0.73
M = C × FL0.25
Q = (4/c) × √(J/100) × (Aw + 4) × FL0.25
s = 100 × √(M/Q)
Parameters: LA = adapting luminance (cd/m²), Yb = background relative luminance, F/c/Nc = surround coefficients.
Colour Difference Formulas
ΔE(CAM02-UCS)
CIEDE2000 (CIE 142-2001)
CIE76
Interpretation: ΔE ≤ 1 imperceptible | 1–2 just noticeable | 2–5 acceptable tolerance | 5–10 clearly different | >10 large difference.
CIELAB (CIE 1976)
a* = 500 × [ f(X/Xn) − f(Y/Yn) ]
b* = 200 × [ f(Y/Yn) − f(Z/Zn) ]
where f(t) = t1/3 if t > (6/29)³
f(t) = t/(3δ²) + 4/29 otherwise
δ = 6/29
C*ab = √(a*² + b*²)
hab = atan2(b*, a*)
sRGB ↔ CIE XYZ (IEC 61966-2-1)
Clinear = C/12.92 if C ≤ 0.04045
Clinear = ((C + 0.055)/1.055)2.4 otherwise
sRGB → XYZ:
[X] [0.4124564 0.3575761 0.1804375] [Rlin]
[Y] = [0.2126729 0.7151522 0.0721750] [Glin]
[Z] [0.0193339 0.1191920 0.9503041] [Blin]
XYZ → sRGB:
[R] [ 3.2404542 −1.5371385 −0.4985314] [X]
[G] = [−0.9692660 1.8760108 0.0415560] [Y]
[B] [ 0.0556434 −0.2040259 1.0572252] [Z]
Known Limitations
- CIECAM02 blue defect: The CAT02 matrix can produce negative cone responses for highly saturated blue stimuli. This affects the J'a'b' output for spectral blues near 460 nm.
- sRGB gamut limitation: This tool operates within the sRGB gamut. Colours outside sRGB are clipped before processing. For wide-gamut workflows, use ICC profiles.
- UCS optimisation scope: The c₁/c₂ parameters were optimised against specific visual datasets (BFD, Leeds, Witt, RIT-DuPont). Performance may vary for colour regions underrepresented in those datasets.
- Viewing conditions: CIECAM02 results are sensitive to viewing conditions. Default LA=64 cd/m², Yb=20 correspond to typical office display viewing. Adjust as needed for your evaluation context.
- CAM16-UCS: Li et al. (2017) proposed an updated CAM16-UCS based on the CAM16 model, which fixes the blue defect. See the CIECAM16-UCS tool for that implementation.
Enter hex colours (one per line or comma-separated). Computes CAM02-UCS J′a′b′ for each colour, builds a full pairwise ΔE matrix, and derives statistics (min, max, mean, median, std dev) plus a histogram.
General-purpose uniform colour space.
Balanced performance across all ΔE scales.
LCD (c₁=0.0053, c₂=0.0158):
Optimised for Large Colour Differences.
Better correlation with visual data for ΔE > 5.
Reference datasets: BFD, Leeds.
SCD (c₁=0.0102, c₂=0.0228):
Optimised for Small Colour Differences.
Better correlation with visual data for ΔE < 5.
Reference datasets: Witt, RIT-DuPont.
Recommendation: Start with UCS. Use LCD for
cross-media comparison or print proofing. Use SCD
for QC tolerance workflows where differences are
known to be small (near JND threshold).
negative cone responses for spectral blues near
460 nm. This produces erroneous J, M, and h values
which propagate into the CAM02-UCS J′a′b′ space.
Li et al. (2017) proposed CAM16 with CAT16 matrix
to fix this defect. CAM16-UCS is the recommended
successor for applications where saturated blues
are critical.
For most practical sRGB workflows, the blue defect
does not manifest as sRGB cannot represent spectral
blues at the problematic saturation levels.