| Colour | Jz | az | bz | Cz | hz° | Iz |
|---|---|---|---|---|---|---|
| Primary | — | — | — | — | — | — |
| Comparison | — | — | — | — | — | — |
| Colour | J | Qz | Mz | Cz | hz° | Sz |
|---|---|---|---|---|---|---|
| Primary | — | — | — | — | — | — |
| Comparison | — | — | — | — | — | — |
| Colour | Reinhard | ACES | Hable | BT.2446A | Log |
|---|---|---|---|---|---|
| Primary | — | — | — | — | — |
| Comparison | — | — | — | — | — |
| Colour | L* | a* | b* | C* | h° |
|---|---|---|---|---|---|
| Primary | — | — | — | — | — |
| Comparison | — | — | — | — | — |
Compare all 5 tone mapping operators on the current colour pair. Shows tone-mapped output values and post-mapping ΔEz side-by-side.
| Operator | TM(A) | TM(B) | ΔEz post-TM | Quality |
|---|---|---|---|---|
| Click “Compare all 5 TMOs” to run analysis. | ||||
ITU-R BT.2100 — HDR Television
BT.2100 defines Perceptual Quantizer (PQ, ST 2084) and Hybrid Log-Gamma (HLG) transfer functions for HDR television. PQ encodes absolute luminance from 0 to 10 000 cd/m² using a perceptual model derived from Barten’s contrast sensitivity function.
PQ reference: SMPTE ST 2084:2014, ITU-R BT.2100-2 (2018).
Jzazbz (Safdar, Hardeberg, Ronnier Luo 2017)
Jzazbz is a perceptually uniform colour space using PQ-encoded absolute luminance. It covers 0.001 to 10 000 cd/m² with near-constant JND steps. Designed as an HDR replacement for CIELAB’s cube-root compression which is only valid for relative colorimetry.
Key achievement: ΔEz thresholds are scale-invariant across SDR and HDR — a ΔEz of 1 is roughly a JND at both 1 nit and 1000 nits.
ZCAM (Safdar, Ciu, Kim, Luo 2021)
ZCAM extends Jzazbz with CAM-style appearance correlates incorporating viewing conditions: adapting luminance Lw, background Yb, and surround factor Fs. It is the first HDR colour appearance model built on an absolute uniform colour space.
Reference: Safdar et al. (2021), Optics Express 29(4), 6036-6052.
ITU-R BT.2446 — HDR to SDR Conversion
BT.2446 defines standardised methods for converting HDR content to SDR for backward-compatible distribution. Method A uses a power-law curve with peak-luminance mapping. Methods B and C address scene-referred and display-referred workflows respectively.
CIEDE2000 & CIE 15:2004
CIEDE2000 (CIE 142-2001) is the recommended SDR colour-difference formula with corrections for lightness, chroma, hue, and the blue rotation term. CIE 15:2004 defines CIELAB and the standard observer. For HDR work, ΔEz from Jzazbz is preferred.
ICC.2 HDR Colour Management
ICC.2 (iccMAX) extends the ICC profile format for HDR and wide colour gamut workflows. Jzazbz is used as the Profile Connection Space (PCS) for HDR profiles, replacing PCSLAB/PCSXYZ for wide-gamut targets. ZCAM may serve as the appearance model for cross-media viewing condition adaptation.
HDR Industry Applications
- HDR10 / Dolby Vision QC: ΔEz allows comparing HDR master vs. compressed deliverable across the full 0–10 000 nit range.
- Tone mapping evaluation: ZCAM correlates assess whether a TMO preserves appearance relative to the HDR master.
- Display characterisation: ZCAM predicts appearance changes as display peak luminance varies (500 nit vs. 2000 nit).
- Perceptual gradient generation: Jzazbz interpolation produces visually smooth transitions at any luminance level.
Jzazbz Forward Model (Safdar et al. 2017):
X′ = b·Xabs − (b−1)·Zabs
Y′ = g·Yabs − (g−1)·Xabs
Step 2 — M1 linear matrix → [L, M, S]
M1 = [[0.41479, 0.58000, 0.01465],
[−0.20151, 1.12025, 0.07626],
[−0.01660, 0.26480, 0.66848]]
Step 3 — PQ transfer (normalised to 10 000 cd/m²):
PQ(x) = ((c₁+c₂·xm₁)/(1+c₃·xm₁))m₂
c₁=0.836, c₂=18.852, c₃=18.688, m₁=0.1593, m₂=78.844
Step 4 — M2 matrix → [Iz, az, bz]
M2 = [[0.5, 0.5, 0],
[3.524, −4.067, 0.543],
[0.199, 1.097, −1.296]]
Step 5 — Jz compression:
Jz = (1+d)·Iz / (1+d·Iz) (d = −0.56)
ΔEz = √(ΔJz² + Δaz² + Δbz²)
ZCAM Forward Model (Safdar et al. 2021):
Fb = √(Yb / Yw) — background factor
FL = luminance adaptation (CIECAM02-style, f(Lw))
Qz = (1.6 / Fs0.12) · Iz(Fs²/2.69) — brightness
Jz = 100 · (Qz / Qz,w)α — lightness
hz = atan2(bz, az) — hue angle
Mz = 100·(az²+bz²)0.37 · FL0.2 — colorfulness
Cz = Mz / Fb — chroma
Sz = 100·√(Mz/Qz) — saturation
Perceptual Quantizer (SMPTE ST 2084):
Y = 10000 · ((max(V1/m2 − c1, 0)) / (c2 − c3·V1/m2))1/m1
OETF (linear to PQ):
V = ((c1 + c2·Ym1) / (1 + c3·Ym1))m2
Constants:
m1 = 2610/16384 = 0.1593...
m2 = 2523/32 = 78.84375
c1 = 3424/4096 = 0.8359375
c2 = 2413/128 = 18.8515625
c3 = 2392/128 = 18.6875
Y normalised to [0, 1] representing [0, 10000] cd/m²
Tone Mapping Operators:
| Operator | Formula / key property |
|---|---|
| Reinhard | v·(1+v/W²)/(1+v) — smooth, highlights asymptote at W |
| ACES | Narkowicz 2015 — S-shaped, preserves mid-tone contrast |
| Hable | Uncharted 2 filmic — strong shoulder and toe |
| BT.2446A | ITU-R standard HDR→SDR, power-law with peak mapping |
| Log | log₂(1+v) — preserves shadow detail |
Colour Difference Metrics:
ΔEz = √(ΔJz² + Δaz² + Δbz²)
Scale-invariant across full HDR-SDR range.
CIEDE2000 (ΔE00):
Full CIEDE2000 with G, T, SL, SC, SH, RT corrections.
Only valid for relative colorimetry (SDR).
ΔE76:
ΔE = √(ΔL*² + Δa*² + Δb*²)
Simple Euclidean in CIELAB.
- ΔEz <1: Imperceptible across the HDR range.
- ΔEz 1–3: Small — very slight tonal shift.
- ΔEz 3–10: Moderate — perceptible tonal/chromatic difference.
- ΔEz >10: Large difference (often luminance-dominated).
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|
|Y| = |0.2126729 0.7151522 0.0721750| |G|
|Z| |0.0193339 0.1191920 0.9503041| |B|
Absolute XYZ (cd/m²):
X_abs = X_rel × nits
Y_abs = Y_rel × nits
Z_abs = Z_rel × nits
- sRGB Gamut: Input colours are clipped to sRGB [0,255]. Real HDR content may exceed sRGB gamut (BT.2020).
- Absolute vs Relative: Jzazbz uses absolute luminance. CIELAB uses relative. Comparing ΔEz and ΔE00 directly is not meaningful — they measure different things.
- ZCAM approximation: The ZCAM correlates use a simplified adaptation model; full compliance requires additional chromatic adaptation steps not implemented here.
- Tone mapping is per-channel: Real TMOs may include colour grading, saturation adjustment, and gamut mapping not captured by simple per-Y curves.
- Display dependent: Results assume ideal PQ display. Actual appearance varies with monitor gamma, viewing conditions, and ambient light.
HDR Colour Appearance
[2] Safdar, M., Cui, G., Kim, Y.J., Luo, M.R. (2021). ZCAM, a colour appearance model based on a high dynamic range uniform colour space. Optics Express, 29(4), 6036-6052. DOI: 10.1364/OE.413659
[3] Fairchild, M.D. (2013). Color Appearance Models, 3rd Ed. Wiley-Blackwell. ISBN: 978-1-119-96703-3
HDR Standards and Transfer Functions
[5] ITU-R BT.2100-2 (2018). Image parameter values for high dynamic range television for use in production and international programme exchange.
[6] ITU-R BT.2446-1 (2021). Methods for conversion of high dynamic range content to standard dynamic range content and vice versa.
Tone Mapping Operators
[8] Narkowicz, K. (2015). ACES Filmic Tone Mapping Curve. Blog post.
[9] Hable, J. (2010). Filmic Tonemapping Operators. GDC presentation (Uncharted 2).
Colorimetry and Colour Difference
[11] Sharma, G., Wu, W., Dalal, E.N. (2005). The CIEDE2000 color-difference formula. Color Res. App., 30(1), 21-30. DOI: 10.1002/col.20070
[12] IEC 61966-2-1:1999. sRGB colour space specification.
About this tool
This tool implements Jzazbz absolute colorimetry, ZCAM appearance correlates, 5 tone mapping operators, ΔEz/CIEDE2000/ΔE76 metrics, and CIE 1931 chromaticity — entirely client-side (zero network). Not a substitute for calibrated measurement or official CIE software.
Enter hex colours (one per line or comma-separated). Computes pairwise ΔEz at the current scene luminance settings, plus CIEDE2000 for SDR reference. Full statistics and histogram.
Research note: Jzazbz exhibits improved hue linearity over CIELAB in the blue region (∼270°), where CIELAB’s a*b* plane shows significant hue non-linearity. This makes ΔEz more reliable for blue-heavy HDR content (e.g., sky gradients, neon lighting).
Jzazbz hue error (blues): <3° across 0.1–10000 cd/m²
For critical blue evaluation, always prefer ΔEz over CIEDE2000.
Future: reconstruct full spectral reflectance from sRGB, compute Jzazbz from spectral data via CIE 1931 observer integration, and compare with tristimulus-derived values for metamerism analysis.