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| # | Src | Dst | Src Hex | Adapted | dE00 | dE76 | dE94 | Shift | Gamut |
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Compare all 8 CAT methods against the same patch set and illuminant pair. Shows mean/median/min/max dE00, matrix condition number, and determinant side-by-side.
| Method | Mean dE00 | Median | Min | Max | Std Dev | k(M) | det(M) | Best |
|---|---|---|---|---|---|---|---|---|
| Click "Compare all 8 methods" to run analysis. | ||||||||
CIECAM02 Colour Appearance Model
CIE 159:2004: CIECAM02 is the CIE-recommended colour appearance model. It uses CAT02 as its chromatic adaptation step — the first stage converts XYZ tristimulus values to sharpened RGB (LMS-like) cone responses via the CAT02 matrix.
Adaptation step: In CIECAM02, the degree of adaptation D is computed as D = F × [1 − (1/3.6) × e^(−(L_A + 42)/92)] where F = 1.0 (average surround), 0.9 (dim), 0.8 (dark). L_A is the adapting luminance in cd/m².
Known issues: CAT02 has a documented hue rotation defect for highly saturated blue stimuli (Brill & Süsstrunk, 2008), which CAT16 corrects.
CAM16 and CAT16 — Successor Model
CAM16 (Li et al., 2017) corrects the hue rotation defect in CAT02 and uses an improved CAT16 transform matrix. CIE TC 1-99 is evaluating CAM16 as a potential successor to CIECAM02.
CAT16 matrix: Provides sharper cone separation than CAT02 while maintaining physical plausibility. The improved matrix eliminates negative LMS values for spectral stimuli.
ICC Profile Connection Space (PCS)
ICC v4 Specification: The International Color Consortium mandates the Bradford chromatic adaptation transform for converting between device colour spaces and the Profile Connection Space (PCS), defined under D50 illuminant.
PCS: CIE XYZ or CIELAB under D50 (5003 K). When adapting to/from D50, Bradford is required; CAT02 is used within CIECAM02 appearance calculations but not for ICC PCS conversion.
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 the chromatic adaptation procedures used when converting between illuminants.
CIE Technical Report 159:2004 and CIE 160:2004 provide further guidance on chromatic adaptation transforms and evaluations of the Von Kries coefficient law and its extensions.
CIEDE2000 — Colour Difference Standard
CIE 142-2001: CIEDE2000 (dE00) is the current recommended colour-difference formula. It includes corrections for lightness, chroma, hue, and an interaction term (rotation term RT) that addresses the blue region problematic in earlier metrics.
Guideline ranges: dE00 <1 imperceptible, 1-2 perceptible only by trained observers, 2-5 visible, 5-10 large, >10 very large difference.
CIE Standard Illuminants
- Illuminant A (2856 K): Tungsten/incandescent. Defined by Planckian radiator.
- Illuminant B (4874 K): Direct noon sunlight (deprecated in CIE 2004).
- Illuminant C (6774 K): Average daylight (deprecated, superseded by D65).
- D50 (5003 K): ICC PCS standard, printing industry.
- D55 (5503 K): Mid-morning/afternoon daylight.
- D65 (6504 K): Standard daylight, sRGB reference white.
- D75 (7504 K): North sky daylight.
- E (equal-energy): Theoretical, equal power at all wavelengths.
- FL series (F1-F12): Fluorescent lamp spectral types.
ISO 3664:2009 — Viewing Conditions
ISO 3664 specifies viewing conditions for colour evaluation in graphic technology. It mandates D50 illumination for print evaluation and D65 for comparison with electronic displays. Chromatic adaptation transforms bridge the gap between these viewing conditions.
CAT02 Transform Matrix (CIECAM02, CIE 159:2004):
| 0.7328 0.4296 -0.1624 |
|-0.7036 1.6975 0.0061 |
| 0.0030 0.0136 0.9834 |
CIECAM02 adaptation degree:
D = F * [1 - (1/3.6) * exp(-(L_A + 42)/92)]
F = 1.0 (average), 0.9 (dim), 0.8 (dark)
L_A = adapting field luminance (cd/m^2)
Adapted cone response:
R'_c = D * (Y_w * R_w_d / R_w_s) * R_s + (1 - D) * R_s
G'_c = D * (Y_w * G_w_d / G_w_s) * G_s + (1 - D) * G_s
B'_c = D * (Y_w * B_w_d / B_w_s) * B_s + (1 - D) * B_s
Known defect: Negative RGB values for highly saturated blue
stimuli near 460 nm (Brill & Susstrunk 2008). CAT16 fixes this.
Chromatic Adaptation Transform — General Form:
[L, M, S]T = M * [X, Y, Z]T
Step 2: Diagonal scaling (von Kries law):
D = diag(d1, d2, d3)
where di = 1 + D_adapt * (dst_LMSi / src_LMSi - 1)
D_adapt = adaptation degree (0 = none, 1 = full)
Step 3: LMS to XYZ via inverse transform:
[X', Y', Z']T = M-inv * D * M * [X, Y, Z]T
Full adaptation matrix: A = M-inv * D * M
This single 3x3 matrix adapts any XYZ vector.
All CAT Transform Matrices (M):
| 0.7328 0.4296 -0.1624 |
|-0.7036 1.6975 0.0061 |
| 0.0030 0.0136 0.9834 |
CAT16 (CAM16):
| 0.401288 0.650173 -0.051461 |
|-0.250268 1.204414 0.045854 |
|-0.002079 0.048952 0.953127 |
Bradford (ICC):
| 0.8951 0.2664 -0.1614 |
|-0.7502 1.7135 0.0367 |
| 0.0389 -0.0685 1.0296 |
Von Kries:
| 0.40024 0.70760 -0.08081 |
|-0.22630 1.16532 0.04570 |
| 0.00000 0.00000 0.91822 |
Sharp:
| 1.2694 -0.0988 -0.1706 |
|-0.8364 1.8006 0.0357 |
| 0.0297 -0.0315 1.0018 |
CMCCAT2000:
| 0.7982 0.3389 -0.1371 |
|-0.5918 1.5512 0.0406 |
| 0.0008 0.0239 0.9753 |
HPE (Hunt-Pointer-Estevez):
| 0.38971 0.68898 -0.07868 |
|-0.22981 1.18340 0.04641 |
| 0.00000 0.00000 1.00000 |
XYZ Scaling: Identity matrix I3
sRGB to/from XYZ (IEC 61966-2-1, D65):
if C_srgb <= 0.04045: C_lin = C_srgb / 12.92
else: C_lin = ((C_srgb + 0.055) / 1.055)^2.4
Linear RGB to XYZ (D65):
|X| |0.4124564 0.3575761 0.1804375| |R_lin|
|Y| = |0.2126729 0.7151522 0.0721750| |G_lin|
|Z| |0.0193339 0.1191920 0.9503041| |B_lin|
XYZ to Linear RGB (D65):
|R_lin| | 3.2404542 -1.5371385 -0.4985314| |X|
|G_lin| = |-0.9692660 1.8760108 0.0415560| |Y|
|B_lin| | 0.0556434 -0.2040259 1.0572252| |Z|
sRGB Gamma (linear to companding):
if C_lin <= 0.0031308: C_srgb = 12.92 * C_lin
else: C_srgb = 1.055 * C_lin^(1/2.4) - 0.055
XYZ to CIELAB (CIE 15:2004):
f(t) = (29/6)^2*t/3 + 4/29 otherwise
L* = 116 * f(Y/Yn) - 16
a* = 500 * [f(X/Xn) - f(Y/Yn)]
b* = 200 * [f(Y/Yn) - f(Z/Zn)]
where (Xn, Yn, Zn) = white-point reference.
LCH (cylindrical):
C* = sqrt(a*^2 + b*^2)
h = atan2(b*, a*) [0-360 degrees]
Colour Difference Metrics:
dE*ab = sqrt[(dL*)^2 + (da*)^2 + (db*)^2]
CIE94 (dE*94):
dE*94 = sqrt[(dL*/SL)^2 + (dC*/SC)^2 + (dH*/SH)^2]
SL = 1, SC = 1 + 0.045*C1*, SH = 1 + 0.015*C1*
CIEDE2000 (dE00):
G = 0.5 * [1 - sqrt(C_bar^7 / (C_bar^7 + 25^7))]
a'i = ai * (1 + G)
C'i = sqrt(a'i^2 + bi^2), h'i = atan2(bi, a'i)
dH' = 2*sqrt(C'1*C'2) * sin(dh'/2)
SL = 1 + 0.015*(L_bar'-50)^2 / sqrt(20+(L_bar'-50)^2)
SC = 1 + 0.045 * C_bar'
SH = 1 + 0.015 * C_bar' * T
T = 1 - 0.17cos(h_bar'-30) + 0.24cos(2h_bar')
+ 0.32cos(3h_bar'+6) - 0.20cos(4h_bar'-63)
RT = -sin(2*dTheta) * RC (rotation term)
dE00 = sqrt[(dL'/SL*KL)^2 + (dC'/SC*KC)^2
+ (dH'/SH*KH)^2 + RT*(dC'/SC*KC)*(dH'/SH*KH)]
- dE < 1: Imperceptible to most observers.
- dE 1-2: Perceptible on close inspection by trained observers.
- dE 2-5: Clearly noticeable difference.
- dE > 5: Colors appear distinctly different.
Spectral Power Distribution Generation:
M(lambda,T) = 2hc^2 / lambda^5 * 1/(e^(hc/lambda*kT) - 1)
h = 6.626e-34, c = 2.998e8, k = 1.381e-23
CIE Daylight (D-series, >=4000 K):
S(lambda) = S0(lambda) + M1*S1(lambda) + M2*S2(lambda)
where S0, S1, S2 are CIE basis vectors (300-830 nm)
xD computed from CCT via Kang et al. (2002) approximation
yD = -3*xD^2 + 2.87*xD - 0.275
CCT to xy chromaticity (Kang et al. 2002):
T <= 4000 K: x = -0.2661e9/T^3 - 0.2344e6/T^2 + 877.7/T + 0.180
T > 4000 K: x = -3.0258e9/T^3 + 2.1070e6/T^2 + 222.6/T + 0.240
- CAT02 Blue Defect: CAT02 can produce negative cone responses for highly saturated blue stimuli near 460 nm. This is a known defect (Brill & Süsstrunk 2008). Use CAT16 for problematic blues.
- sRGB Gamut: Adapted colours are clipped to [0,255] per channel. Real colours outside sRGB produce clipping artefacts; use dE to assess severity.
- Linear Scaling: All CATs use diagonal (von Kries) scaling in a sharpened space, not full cone-adaptation neural models.
- Incomplete Adaptation: The degree slider is a linear interpolation — real adaptation is non-linear and observer-dependent (CIECAM02 uses the exponential D formula).
- No Surround Effects: CIECAM02/CAM16 model surround luminance, background, and viewing conditions; this tool isolates the CAT step only.
- SPD Approximation: Fluorescent illuminants use Planckian approximation, not the full CIE line-spectrum data.
- Display Dependent: Results depend on monitor gamma, color profile, and ambient lighting. Use ICC-profiled displays for accurate evaluation.
CAT02 and Colour Appearance Models
[2] Li, C., Li, Z., Wang, Z., et al. (2017). Comprehensive color solutions: CAM16, CAT16, and S-decoupled UCS. Color Res. App., 42(6), 703-718. DOI: 10.1002/col.22131
[3] Brill, M.H. & Susstrunk, S. (2008). Repairing gamut problems in CIECAM02. Color Res. App., 33(5), 424-426. DOI: 10.1002/col.20437
[4] Luo, M.R., Hunt, R.W.G. (1998). The structure of the CIE 1997 colour appearance model (CIECAM97s). Color Res. App., 23(3), 138-146.
[5] Fairchild, M.D. (2013). Color Appearance Models, 3rd Ed. Wiley-Blackwell. ISBN: 978-1-119-96703-3
Chromatic Adaptation Transforms
[7] Fairchild, M.D. (1996). Refinement of the RLAB color space. Color Res. App., 21(5), 338-346.
[8] Hunt, R.W.G. & Pointer, M.R. (2011). Measuring Colour, 4th Ed. Wiley.
Colorimetry and Colour Difference
[10] Sharma, G., Wu, W., Dalal, E.N. (2005). The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations. Color Res. App., 30(1), 21-30. DOI: 10.1002/col.20070
[11] CIE (2001). Improvement to industrial colour-difference evaluation. CIE 142-2001.
ICC and Industry Standards
[13] ISO 3664:2009. Graphic technology and photography — Viewing conditions.
[14] IEC 61966-2-1:1999. Colour management — Default RGB colour space — sRGB.
SPD and Illuminant Computation
[16] Judd, D.B., MacAdam, D.L., Wyszecki, G. (1964). Spectral distribution of typical daylight as a function of correlated color temperature. JOSA, 54(8), 1031-1040.
About this tool
This tool implements 8 chromatic adaptation transforms with CAT02 as the default (CIECAM02 standard), full CIEDE2000, CIE76, CIE94 metrics, CIE 1931 chromaticity visualization, SPD spectral analysis, and multi-method comparison — entirely client-side (zero network). Not a substitute for calibrated measurement or official CIE software.
In CIECAM02, the chromatic adaptation degree D is not a simple percentage but a function of the adapting luminance L_A and surround condition F:
where F = 1.0 (average), 0.9 (dim), 0.8 (dark) surround
L_A = adapting luminance (cd/m^2)
Examples:
L_A = 64 cd/m^2 → D ≈ 0.94 (near-complete adaptation)
L_A = 16 cd/m^2 → D ≈ 0.86 (typical office)
L_A = 4 cd/m^2 → D ≈ 0.69 (dim viewing)
L_A = 0.2 cd/m^2 → D ≈ 0.49 (scotopic conditions)
The slider above provides linear 0-100% as a simplified control.
For precise CIECAM02 calculations, compute D from L_A and F.
Reconstructs full spectral reflectance from sRGB, applies chromatic adaptation in spectral domain (rather than tristimulus), and re-renders under destination illuminant. Compares tristimulus and spectral adaptation accuracy.
Enter hex colours (one per line or comma-separated). Adapts all colours using current settings and produces full dE analysis with statistics.
CAT02 is known to produce negative cone responses for highly saturated blue stimuli. This section documents the defect and compares CAT02 vs CAT16 for blue-region patches:
Symptom: Negative R_c values after adaptation
Impact: Hue rotation artefacts in adapted colours
CAT16 fix: Redesigned matrix ensures all cone
responses remain positive for all spectral stimuli.
Recommendation: Use CAT16 for workflows involving
saturated blues. Use CAT02 when CIECAM02 compliance
is required. Use the "Compare all 8 methods" button
in the Actions tab to evaluate both on your data.
Analyses gamut boundary interactions when adapting between illuminants. Shows which patches clip, which channels saturate, and recommends gamut mapping strategies.