Research-1100: ΔE-ITP (Delta E ITP) — HDR/WCG colour-difference metric feasibility¶

• Status: Closed (ADR-1110 Accepted)
• Workstream: full-reference metric inventory; HDR/WCG colour fidelity
• Last updated: 2026-06-14
• Related ADR: ADR-1110
• Source dossier: .workingdir2/rc/metrics/deltae-itp.md (gitignored planning artifact; this digest is the tracked summary of its verified findings).

Question¶

The fork has SDR colour difference (ciede, ΔE2000, BT.709-hardcoded) and a perceptual structural metric (ssimulacra2), but no HDR/WCG colour-difference metric. Should the fork add ΔE-ITP (ITU-R BT.2124-0), and if so, what scope is safe for the first release given that VmafPicture carries no transfer-function metadata?

Metric summary¶

ΔE-ITP (ITU-R BT.2124-0, "Objective metric for the assessment of the potential visibility of colour differences in television") measures the perceptual visibility of colour differences in HDR (PQ) and HLG video. It is a pure analytic per-pixel metric (no trained model). The pipeline (Annex 1):

YUV -> R'G'B' -> linear RGB (PQ EOTF) -> LMS (BT.2100 /4096 matrix)
    -> L'M'S' (PQ EOTF^-1) -> ICtCp (BT.2100 /4096 matrix)
    -> ITP (I, 0.5*Ct, Cp)
ΔE_ITP = 720 * sqrt((ΔI)^2 + (ΔT)^2 + (ΔP)^2)

≈1.0 corresponds to one just-noticeable colour difference. It maps directly onto the VmafFeatureExtractor interface and mirrors ciede.c's structure (per-pixel kernel, chroma upsampling, 8/16-bit reads, double-precision frame sum, mean pooling).

Constants — adversarial verification¶

Every constant was confirmed against the normative ITU-R BT.2124-0 PDF (read directly) plus at least one independent source. Triple-confirmed:

• RGB→LMS [1688, 2146, 262 / 683, 2951, 462 / 99, 309, 3688] / 4096 — BT.2124-0 Annex 1 + colour-science ictcp.py + Wikipedia ICtCp. The truncated handwiki row-3 [993, 668, 3] is confirmed wrong (canonical ends 3688); the dzone float [0.3592, 0.6976, -0.0358] matrix is a different (Dolby/XYZ-based) LMS matrix — both traps avoided.
• PQ ST-2084 m1 = 2610/16384, m2 = 2523/4096·128, c1 = 3424/4096, c2 = 2413/4096·32, c3 = 2392/4096·32 — BT.2124-0 + colour-science st_2084.py + SMPTE ST 2084.
• L'M'S'→ICtCp [2048, 2048, 0 / 6610, -13613, 7003 / 17933, -17390, -543] / 4096 — BT.2124-0 + colour-science + Wikipedia.
• ITP scaling I, T = 0.5·Ct, P = Cp and ΔE = 720·√Σ — BT.2124-0 Annex 1 Steps 4–5 + colour-science delta_E_ITP.

Single-sourced (deferred): the HLG (Annex 3) OOTF/OETF⁻¹ constants and the HLG-relative scalings 1.823698 / 1.887755, and the BT.1886/SDR Conversion 5 path (Lw=100, E'^2.4 EOTF + BT.709→BT.2100 primaries). These come only from BT.2124-0 itself and were not independently cross-confirmed against BT.2100-2.

Test vector (BT.2124-0 Annex 4 normative worked example)¶

58 % PQ BT.709-blue patch, 10-bit full-range PQ RGB [296, 201, 582]:

The Python pipeline reproduces the standard's printed pooled ΔE = 2.363 from the pre-rounded ITP triples. A full-precision extractor fed the same pair yields ~2.282, not 2.363. Conclusion: assert the full-precision ITP triple at places=4 as the parity gate; use 2.363 only as a documentation cross-check. (Implemented exactly this way in test_delta_e_itp.c.)

Decision (verifier's required fixes applied)¶

• Ship the metric (closes the HDR/WCG colour-fidelity gap). Adversarial verdict: GO-WITH-FIXES.
• PQ-only RC scope — every shipped constant stays double/triple-confirmed. HLG and BT.1886/SDR transfers deferred until independently validated.
• places=4 ITP-triple oracle, not pooled==2.363, as the parity assertion.
• CPU scalar only; SIMD/GPU twins, deterministic PQ LUT deferred (same staging ciede / ssimulacra2 followed).

See ADR-1110 for the decision record.

References¶

• ITU-R BT.2124-0 (01/2019) — Annexes 1–4.
• ITU-R BT.2100; SMPTE ST 2084:2014.
• colour-science/colour (BSD-3-Clause): ictcp.py, st_2084.py, delta_e.py — used for cross-validation only, not ported into the tree.
• Wikipedia "ICtCp" — independent matrix confirmation.