Why Converting SDR to HDR Involves More Than Just Brightening the Image

Introduction

The ASC StEM2 test material provides three aligned data layers for the same 18,580‑frame sequence: 16‑bit Float EXR source (ACES AP0), a standard‑dynamic‑range (SDR) DCI‑P3 master (Gamma 2.6, 48 cd/m², 12‑bit JPEG 2000) and a high‑dynamic‑range (HDR) master (PQ, 300 cd/m², 12‑bit JPEG 2000). This enables a pixel‑wise statistical study of SDR‑to‑HDR mapping.

Data and Methods

Analysis proceeds in four steps:

Log‑luminance scatter plots of corresponding SDR and HDR pixels.

Isotonic (monotonic) regression to fit a non‑decreasing mapping. The regression objective is shown in

; goodness‑of‑fit is quantified by

.

Gradient‑domain Pearson correlation (ρ) using Sobel‑derived gradients to assess structural consistency.

ICtCp‑based perceptual colour difference ΔE_ITP for colour analysis.

Brightness Structure Relationship

Scatter analysis reveals a clear monotonic SDR‑to‑HDR relationship (Figure 2). Isotonic regression yields R² > 0.99 for more than 85 % of frames, with an average of 0.9986; the lowest R² (0.917) occurs in a single frame with extreme lighting. Gradient correlation ρ exceeds 0.96, confirming preservation of geometric structure.

Residuals are defined as the deviation of HDR luminance from the isotonic baseline (Equation 4):

Three residual clusters are identified:

Type I – self‑luminous highlights: high residual energy, spatially aligned with bright emitters.

Type II – material & texture: moderate energy, high structural scores.

Type III – negative control: low energy and structure, fully explained by the global mapping.

Statistically, Type III occupies ~50 % of pixels but only 0.8 % of residual energy, while Types I and II together cover ~50 % of pixels and account for >99 % of the energy (Table 2).

Color Structure Relationship

After Bradford white‑point adaptation to DCI‑P3, both SDR and HDR frames are transformed to ICtCp. Four metrics are computed:

Mean hue shift (Mean Δh) = 2.38°; 95th‑percentile Δh = 6.52°.

Chroma Pearson correlation – high, indicating structural consistency of colour saturation.

Proportion of pixels with increased saturation in the mid‑tone range (20–100 cd/m²) ≈ 66.9 % (average ΔS ≈ +0.003).

In dark (<20 cd/m²) and bright (>100 cd/m²) ranges, saturation change is negative (‑0.039 and ‑0.008 respectively) with lower increase proportions (30.8 % and 34.4 %).

These results show overall hue stability and a luminance‑dependent redistribution of saturation.

Behaviour Classification Using Physical Reference

EXR (ACES AP0) is converted to XYZ (D65) and gain‑aligned to the mid‑tone of SDR/HDR. For each pixel x, perceptual distances ΔE_ITP(SDR) and ΔE_ITP(HDR) are computed (Equation 5):

Decision rule:

If ΔE_ITP(HDR) < ΔE_ITP(SDR) → classify as *physical restoration*.

If ΔE_ITP(HDR) > ΔE_ITP(SDR) → classify as *semantic adjustment*.

A 3 JND threshold (≈ 3 ΔE_ITP) filters insignificant differences. Decision maps (Figure 6) show physical restoration covering 82.4 % of frame area (Table 5); semantic adjustments concentrate in extreme highlights, high‑saturation emissive objects, and specular materials.

Conclusion and Outlook

The empirical study confirms a stable global monotonic SDR‑to‑HDR mapping with high structural fidelity, while localized residuals (Types I and II) require targeted semantic tweaks. This “restrained restoration” mechanism—global monotonic scaling plus selective compensation—provides a quantitative basis for AI‑driven HDR conversion, metadata generation compatible with SMPTE ST 2094, and optimisation of domestic LED‑screen workflows.

Code example

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