ΔE-ITP (Delta E ITP) — HDR/WCG Colour-Difference Feature Extractor¶

Feature name: delta_e_itp Provided feature key: delta_e_itp ADR: ADR-1110 References:

• ITU-R BT.2124-0 (01/2019), Objective metric for the assessment of the potential visibility of colour differences in television — Annex 1 (normative pipeline), Annex 4 (normative worked example).
• ITU-R BT.2100, Image parameter values for high dynamic range television — RGB↔LMS matrix, PQ (ST-2084) transfer function, ICtCp definition.
• SMPTE ST 2084:2014 — Perceptual Quantizer (PQ) EOTF.

Overview¶

delta_e_itp is a full-reference, per-pixel colour-difference metric for HDR / wide-colour-gamut video, defined by ITU-R BT.2124-0. It measures the perceptual visibility of colour differences between a reference and a distorted frame in the ITP colour space (a scaled form of ICtCp).

A ΔE-ITP value of approximately 1.0 corresponds to one just-noticeable colour difference under the most critical adaptation state. Higher values mean a larger (more visible) colour error. An identical reference/distorted pair yields exactly 0.0.

This fills the fork's HDR/WCG colour-fidelity gap: ciede (ΔE2000) is an SDR / BT.709 metric, and ssimulacra2 is a perceptual structural metric; neither is appropriate for measuring colour error on PQ HDR content.

What it measures¶

Per pixel, both frames are converted to the ITP colour space and the scaled Euclidean distance is taken:

ΔE_ITP = 720 * sqrt( (ΔI)^2 + (ΔT)^2 + (ΔP)^2 )

The per-frame score is the mean per-pixel ΔE-ITP over the frame (sum / (width * height)).

Pipeline (ITU-R BT.2124-0 Annex 1)¶

For each pixel of both reference and distorted frames:

1. YUV → non-linear R'G'B' [0, 1] — dequantize by bit depth using the configured quantization range and apply the inverse matrix.
2. PQ EOTF — decode the non-linear PQ signal to linear, display-referred RGB (0–10 000 cd/m²).
3. RGB → LMS — BT.2100 integer matrix (rows ÷ 4096).
4. PQ inverse EOTF — re-encode LMS luminance to the non-linear L'M'S' domain that ICtCp is defined on.
5. L'M'S' → ICtCp — BT.2100 integer matrix (rows ÷ 4096).
6. ITP scaling — I = I, T = 0.5·Ct, P = Cp.

All per-pixel math is done in double precision (matching the ciede precedent). Out-of-gamut negative LMS / ICtCp values are not clamped, so out-of-gamut colour errors remain measurable (BT.2124 Annex 4).

Chroma planes of 4:2:0 / 4:2:2 input are upsampled to luma resolution before conversion; 4:4:4 input is used directly. 4:0:0 (luma-only) input is rejected with an error, since a colour-difference metric requires chroma.

Scope: PQ transfer only (this release)¶

Important: This release implements the PQ (SMPTE ST-2084) transfer function only.

VmafPicture carries no transfer-function or colorimetry metadata, so the extractor must assume a transfer function. The default — and the only accepted value in this release — is transfer=pq. Feeding non-PQ content (SDR, HLG) to this metric produces meaningless numbers.

The HLG and BT.1886/SDR transfer paths defined in BT.2124-0 (Annex 3 / Conversion 5) are deferred follow-ups: their constants are single-sourced in the standard and were not independently cross-validated, so they are intentionally not shipped here. Requesting transfer=hlg or transfer=bt1886 returns an error at initialisation. See ADR-1110 for the rationale.

Options¶

Usage¶

# Default: PQ transfer, BT.2020 NCL matrix, limited (narrow) range.
vmaf --reference ref.yuv --distorted dist.yuv \
     --width 1920 --height 1080 --pixel_format 420 --bitdepth 10 \
     --feature delta_e_itp --output out.xml

# With explicit options. The CLI feature-option syntax is
# `name=key=val:key2=val2` (first '=' separates the name; ':' separates
# subsequent key=value pairs).
vmaf --reference ref.yuv --distorted dist.yuv \
     --width 1920 --height 1080 --pixel_format 444 --bitdepth 10 \
     --feature "delta_e_itp=matrix=bt2020:range=full" --output out.xml

No build flag is required: delta_e_itp is compiled unconditionally.

Interpreting the score¶

• 0.0 — reference and distorted frames are identical.
• ~1.0 — about one just-noticeable colour difference (the threshold of visibility under critical viewing).
• larger — proportionally larger, more visible colour error.

Implementation notes¶

• CPU scalar only for now. AVX2 / AVX-512 / NEON SIMD twins and CUDA / SYCL / HIP / Metal GPU twins are out of scope for this release (the same staging ciede and ssimulacra2 followed). A future GPU twin computing the PQ EOTF in fp32 should target a places=4–5 parity bound, not bit-exactness (ADR-0214 / ADR-0220).
• No model assets. ΔE-ITP is a fully analytic, standardised metric with no trained weights or lookup tables. The constants come directly from ITU-R BT.2124-0 / BT.2100.
• PQ transfer functions live in core/src/feature/delta_e_itp_math.h, mirroring the ssimulacra2_math.h deterministic-math-helper pattern. A committed deterministic PQ LUT for byte-exact cross-host reproducibility is deferred to the SIMD/snapshot follow-up.

Test coverage¶

core/test/test_delta_e_itp.c:

1. Blue-patch ITP oracle — the BT.2124-0 Annex 4 normative worked example (58 % PQ BT.709-blue patch, 10-bit full-range RGB [296, 201, 582]) converts to the full-precision ITP triple [0.355721, 0.134647, -0.161395], asserted at places=4.
2. Identity — a pixel compared with itself yields exactly 0.0.
3. Synthetic pair — a fully-specified linear-RGB pair yields the reference ΔE-ITP 8.037360 (places=4).
4. Documentation cross-check — the standard's pre-rounded ITP triples reproduce its printed pooled 2.363 (places=3). (This is a documentation cross-check only; the standard's 2.363 is computed from rounded intermediates and is not used as the extractor oracle.)
5. PQ transfer round-trip — EOTF(EOTF⁻¹(L)) == L; the blue-patch blue channel decodes to ~181.318 cd/m².
6. End-to-end — the registered extractor loads, scores an identical frame as 0.0, and a distorted frame as a finite positive value.
7. Scope guard — transfer=hlg is rejected at init with -EINVAL.