Gamma and Perceptual Uniformity: Why 50 Percent Grey Is Not Half as Bright

Two different nonlinearities, one in the display and one in you, and what happens when you forget which is which.

Short answer: an sRGB code value of 128 emits about 22 percent of the light that 255 emits, yet its CIE lightness is about 54, roughly half way up the perceptual scale. That is not a contradiction, it is two separate nonlinearities that happen to nearly cancel. The encoding nonlinearity, gamma, spends code values where the eye needs them. The perceptual nonlinearity, roughly a cube root, is how lightness relates to luminance. Confuse them and you get muddy gradients, wrong blends and a mid grey that is not the middle of anything you meant.

Three different meanings of "half"

Ask for the grey half way between black and white and there are at least three defensible answers.

Notice how far apart 119, 128 and 188 are, and how close 119 and 128 look on screen. That closeness is not an accident: the encoding was designed so that the middle of the code range lands near the middle of the perceptual range. It is the light that has been pushed out of shape, and the light is what physics and image processing care about.

Why gamma is there

The usual story is historical. Cathode ray tubes had a naturally nonlinear response, roughly a power law with an exponent near 2.4, so encoding the signal with the inverse power meant a display needed no correction. That is true, and it is not the reason the arrangement survived flat panels.

The real reason is perceptual coding efficiency. Human sensitivity to a small change in light is roughly proportional to the light already present, so a fixed step in the dark is far more visible than the same step in the highlights. A linear code spreads its values evenly across light and therefore wastes most of them where the eye cannot use them, while starving the shadows where it can. Poynton's long-standing treatment of the subject makes the point directly: matching the perceptual performance of an 8-bit nonlinear channel with linear coding takes on the order of eleven bits. Gamma is not a legacy wart. It is compression that happens to have started as physics.

This connects straight to Mach bands and banding. Banding is what you see when the code values run out, and the reason it appears in shadows rather than highlights is exactly this allocation.

The other nonlinearity: how lightness relates to light

Sensation does not grow in proportion to stimulus intensity. Stevens argued in 1957 that perceived magnitude across many sensory modalities follows a power function of physical intensity, with an exponent characteristic of the modality, and for brightness that exponent is well below one. Whatever your view of the details, the qualitative claim is robust: doubling the light does not double the apparent brightness.

The colorimetric version of this is the CIE lightness scale, L star, defined on roughly the cube root of luminance relative to a reference white, with a short linear segment near black to keep it well behaved. It runs 0 to 100 and is constructed so that equal steps are intended to look equally spaced. That is the scale in the table above, and it is the reason 21.6 percent of the light reads as a middle grey rather than a dark one.

Once you have that, a lot of otherwise mysterious behavior becomes predictable. Two swatches that differ by 5 in L star look about equally different whether they sit in the shadows or the highlights, but they differ by very different amounts of actual light, which is why a fixed numeric step in code values does not produce a smooth ramp.

Where it goes wrong in practice

Blending by averaging codes. The midpoint between a code value of 0 and 255 is not 128 in any physical sense. Averaging encoded values averages the wrong quantity, and the result is systematically too dark, most visibly when mixing a saturated color with white. Do the arithmetic in linear light, or in a space built for perceptual interpolation, and the midpoint stops looking muddy.

Resizing and blurring. Any operation that averages neighboring pixels inherits the same problem. Downscaling an image with fine bright detail on a dark ground in encoded values loses brightness that linear-light downscaling preserves.

Alpha compositing. Semi-transparent overlays are averages too, so a 50 percent black overlay does not halve the light unless the compositing is done in linear light.

Gradients. A gradient with evenly spaced code values is even in neither light nor lightness, strictly speaking, though it is much closer to even in lightness. A gradient with evenly spaced linear values looks badly bunched at the top.

Contrast checking. Accessibility contrast ratios are defined on relative luminance, which means the code values have to be linearised before the ratio is computed. Doing it on the raw codes gives a confidently wrong answer, as our page on color contrast and accessibility explains.

"Perceptually uniform" is a goal, not a fact

It is worth being careful with the phrase. CIELAB was designed as a perceptually uniform space and it is a great deal better than working in raw device values, but its uniformity is approximate. Work evaluating the uniform color spaces proposed after CIELAB put the average visual threshold in that space at roughly 2.3 units, while noting that the actual threshold varies considerably across the space. The response of the color science community was telling: rather than replacing the space, the current color-difference recommendation keeps CIELAB and adds weighting functions for lightness, chroma and hue plus a correction term for the blue region. That is a patch, and it is honest about being one.

The lineage of attempts to do better, and what the web finally adopted, is covered in OKLCH and modern color spaces. The short version is that a space can be uniform for small differences or for large ones, for surface colors or for emitted light, and no single space is best at all of them.

What this means for the games

Huetween asks for the color halfway between two others, and everything above is why that question needs a definition before it has an answer. The midpoint in code values, in linear light and in a perceptual space are three different colors. We use a perceptual definition, because that is the one that matches what people mean when they say halfway.

Huespan asks you to reproduce an interval rather than a single color, which makes the choice of scale even more visible: an interval that is constant in lightness is not constant in luminance, and vice versa. Our page on color midpoint and interval perception goes into what that does to the task.

Huesort asks for a smooth ordering, and smoothness is scale-dependent in exactly the same way. A sequence that is even in one space will look slightly bunched in another, which is one reason we do not treat a single misplacement as a real error.

The practical takeaway for a player is smaller than all this theory suggests: keep your display's brightness and any automatic tint adjustment steady, because both of them move the transfer function under your feet, and a shifted transfer function changes which differences are visible at all.

Keep reading

• OKLCH and modern color spaces: what came after CIELAB, and what the web adopted.
• Mach bands and banding: what happens when the code values run out.
• Color contrast and accessibility: why the ratio has to be computed on linear light.

Sources: Poynton, C., Frequently asked questions about gamma; Poynton, C. (1998), Rehabilitation of gamma, Proceedings of SPIE 3299, 232; Stevens, S. S. (1957), On the psychophysical law, Psychological Review 64(3), 153; International Commission on Illumination, CIE 015:2018 Colorimetry, 4th edition; W3C, A standard default color space for the internet: sRGB; Mahy, M., Van Eycken, L. and Oosterlinck, A. (1994), Evaluation of uniform color spaces developed after the adoption of CIELAB and CIELUV, Color Research & Application 19(2), 105.