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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. | ||||||||
CAM16 Colour Appearance Model
Li et al. (2017): CAM16 is a comprehensive colour appearance model proposed as a successor to CIECAM02. It uses CAT16 as its chromatic adaptation step — the first stage converts XYZ tristimulus values to sharpened cone-like responses via the CAT16 matrix, which eliminates the negative LMS values that plagued CAT02 for saturated blues.
Adaptation step: In CAM16, 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.
Key improvement: CAT16 corrects the hue rotation defect documented in CAT02 (Brill & Süsstrunk, 2008), providing physically plausible cone responses for all spectral stimuli while maintaining adaptation accuracy.
CIECAM02 and CAT02 — Predecessor Model
CIE 159:2004: CIECAM02 is the CIE-recommended colour appearance model using CAT02 as its chromatic adaptation step. CAT02 provides good adaptation for most stimuli but has a documented defect for highly saturated blue stimuli near 460 nm.
CAT02 defect: The CAT02 matrix can produce negative cone responses (R_c, G_c, B_c) for spectral stimuli near 460 nm when adapting between certain illuminant pairs. This causes hue rotation artefacts. CIE TC 1-99 is evaluating CAM16 as a correction.
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 for ICC compliance; CAT16 is recommended for appearance-based calculations and new workflows.
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.
CAT16 Transform Matrix (CAM16, Li et al. 2017):
| 0.401288 0.650173 -0.051461 |
|-0.250268 1.204414 0.045854 |
|-0.002079 0.048952 0.953127 |
CAM16 adaptation degree (same formula as CIECAM02):
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
Key advantage over CAT02: All cone responses remain
positive for all spectral stimuli — no hue rotation
defect for saturated blues near 460 nm.
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):
| 0.401288 0.650173 -0.051461 |
|-0.250268 1.204414 0.045854 |
|-0.002079 0.048952 0.953127 |
CAT02 (CIECAM02):
| 0.7328 0.4296 -0.1624 |
|-0.7036 1.6975 0.0061 |
| 0.0030 0.0136 0.9834 |
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
- CAT16 advantage: Unlike CAT02, CAT16 produces positive cone responses for all spectral stimuli — no hue rotation defect for saturated 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 (CAM16 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.
CAM16, CAT16, and Colour Appearance Models
[2] CIE (2004). A colour appearance model for colour management systems: CIECAM02. CIE Publication 159:2004.
[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 CAT16 as the default (CAM16 standard — corrects the CAT02 blue defect), 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 CAM16, the chromatic adaptation degree D is not a simple percentage but a function of the adapting luminance L_A and surround condition F (same formula as CIECAM02):
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 CAM16 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.
CAT16 was specifically designed to correct the hue rotation defect in CAT02 for saturated blue stimuli. This section documents the improvement:
Symptom: Negative R_c values after adaptation
Impact: Hue rotation artefacts in adapted colours
CAT16 solution: Redesigned matrix by Li et al. (2017)
ensures all cone responses remain positive for all
spectral stimuli. The matrix coefficients were optimized
to provide better cone separation while maintaining
physical plausibility.
Recommendation: Use CAT16 as default for all workflows.
Use CAT02 only when strict CIECAM02 compliance is needed.
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.