Comparing four Display-P3 to sRGB gamut-mapping methods

Summary

This report compares four ways to move ideal Display-P3 colors into ideal sRGB. The experiment changes one design decision at a time: first the radial coordinate space, then the mapping algorithm. That separation reveals a result that a single score would hide.

Changing CIELAB radial mapping to OkLCh radial mapping reduced the severe P3-yellow displacement from 23.928 to 5.523, but raised the 125-color grid mean from 2.857 to 2.947 and moved the worst case to red. Keeping OkLCh and changing only the algorithm to Local MINDE lowered the mean to 2.323 and the maximum to 7.602, while increasing the 90th-percentile IPT hue-coordinate change from 3.368° to 4.806°.

No method wins every reported criterion. The useful result is the location and shape of the trade-offs.

Where the question came from

An earlier color-management course project reproduced fine-art prints through a profiled workflow. Its gamut-mapping choice was a setting inside commercial software: the rendered result could be measured, but the rule that decided how out-of-gamut colors moved could not be inspected.

This study revisits that practical question at the algorithm level. Instead of asking only whether a print or screen result differs, it implements declared rules and records which property each rule preserves, what it changes, and where it fails.

Experiment design

Input and destination

The input table is a five-level cube in encoded Display-P3 with component levels 0, 0.25, 0.5, 0.75, and 1.0. It contains 125 colors; 94 fall outside ideal sRGB. The cube gives deterministic coverage of axes, corners, neutrals, and mixed colors. It is not sampled from photographs and carries no frequency interpretation.

Both RGB spaces use their ideal D65 primaries and the shared piecewise transfer curve. Mapping is evaluated in unclipped destination-linear RGB. A color is in gamut only when all three channels lie in [0,1] within the declared numerical tolerance.

Controlled comparisons

This structure prevents a coordinate-space effect from being attributed to an algorithm change, or vice versa.

Four declared methods

For CIELAB radial mapping, a color is represented at fixed L* and hue h:

a(C) = C cos(h)
b(C) = C sin(h)

If the input is outside sRGB, its chroma is reduced to the first sRGB boundary connected to neutral. OkLCh radial mapping uses the same rule at fixed OkLab lightness and OkLCh hue.

Local MINDE follows the Binary Search Gamut Mapping with Local MINDE algorithm in the 28 July 2026 CSS Color 4 Candidate Recommendation Draft. It searches in OkLCh and compares a candidate with its clipped sRGB color using ΔEOK. The implementation records the draft’s 0.02 local difference threshold and 0.0001 search epsilon. Those constants define this dated algorithm; they do not turn this experiment into an observer study.

The experimental soft method protects a core below K = 0.75D, where D is the connected destination boundary, then maps input chroma C by:

C' = K + (D - K)(C - K) / ((D - K) + (C - K))

The curve is continuous with unit slope at the knee, strictly increasing, and approaches D without crossing it. It intentionally moves in-gamut shoulder colors above K.

Why the boundary solver matters

At fixed CIELAB L* and hue, the inverse-Lab calculation makes each destination linear-RGB channel a piecewise cubic function of chroma. The solver partitions the ray at Lab breakpoints, finds channel extrema, enumerates crossings of the 0 and 1 channel surfaces, and refines the first in-gamut to out-of-gamut transition.

Taking the first exit is important because a ray can leave sRGB, re-enter, and leave again. A test color at L*=96.23856 and hue 1.80124 radians briefly exits near C*=57.64. A coarse membership scan can step across that excursion and select a later boundary. The analytic crossing search detects the first transition.

The OkLCh solver uses the same channel-surface idea. At fixed OkLab lightness and hue, the inverse transform is cubic in chroma without the CIELAB piecewise breakpoint.

Results

Aggregate displacement

The full sample tables are published for CIELAB radial, OkLCh radial, Local MINDE, and the soft knee.

Secondary hue-coordinate diagnostic

Preserving a hue coordinate in one space does not guarantee constant hue in another. Each modified input and output with defined IPT hue was therefore also compared by its absolute IPT hue-angle difference.

The coordinate change lowered the median and maximum IPT hue difference while slightly increasing the 90th percentile and count above 3°. Local MINDE lowered the CIEDE2000 aggregates and worst IPT hue difference, but widened the IPT hue tail. These are model-to-model diagnostics, not visibility thresholds.

The P3-yellow counterexample

P3 yellow explains most clearly why the CIELAB result cannot be summarized as “radial clipping removes excess chroma.” Its input C* is 127.63, but the first neutral-connected Display-P3 boundary on that constant-L*, constant-hue ray is only 28.48; the first sRGB boundary is 22.74. The legal source color lies in a later, disconnected high-chroma interval.

CIELAB radial mapping therefore removes 104.89 C* and produces the largest displacement in the grid. OkLCh radial mapping changes the ray geometry and retains substantially more chroma. That fixes this counterexample, but the higher grid mean and new red worst case show why it is not a universal result.

Tests

The public C++ test exercises the transform matrices, common-gamut identity, the P3-red boundary at C*=93.86561347147861 within 2e-9, the narrow leave-and-re-enter ray, the Local-MINDE P3-yellow output against an independent oracle, and rejection of invalid domains or unresolved boundaries.

It also maps a deterministic set of 3,229 legal Display-P3 inputs through all four methods: a 9 × 9 × 9 component cube containing transfer-function neighbors and extrema, 2,000 fixed-seed samples, and 500 near-neutral samples. For that set:

• every result must be finite and independently inside sRGB;
• the CIELAB radial and soft methods may not increase Lab chroma and must preserve L*;
• their Lab-hue bound is 2e-7 radians only when both input and output chroma exceed 1e-6, because an angle is not meaningful at a vanishing radius;
• OkLCh radial mapping may not increase mapping chroma, must preserve OkLab lightness, and must hold OkLCh hue within 1e-8 degrees when hue is defined; and
• all three hard intents must preserve destination-gamut inputs.

These tests establish numerical behavior and rejection boundaries. They do not establish image preference, device characterization, or observer response.

Limitations and next experiment

• The source and destination are ideal encoding spaces, not measured devices.
• The 125-color cube is a stress grid, not an image-color distribution.
• CIEDE2000, ΔEOK, and IPT hue angle answer different numerical questions; none is treated as a universal quality score.
• Fixed CIELAB or OkLCh hue is a coordinate constraint, not perceptual-hue validation.
• Local MINDE is tied to a dated draft algorithm for individual SDR colors.
• The soft knee is an experimental baseline and was not tested for observer preference.

The resolving extension is an image-and-observer study on characterized source and destination devices. It would retain the algorithm outputs shown here, add representative photographs and difficult synthetic colors, control viewing conditions, and ask task-specific questions about preserved distinctions, artifacts, and preference. Until then, the defensible conclusion is the numerical trade-off—not a winning rendering intent.