Gamma correction

Gamma correction, or often simply gamma, is a nonlinear operation used to encode and decode luminance or tristimulus values in video or still image systems. Gamma correction is, in the simplest cases, defined by the following power-law expression: Gamma correction, or often simply gamma, is a nonlinear operation used to encode and decode luminance or tristimulus values in video or still image systems. Gamma correction is, in the simplest cases, defined by the following power-law expression: where the non-negative real input value V in {displaystyle V_{ ext{in}}} is raised to the power γ {displaystyle gamma } and multiplied by the constant A, to get the output value V out {displaystyle V_{ ext{out}}} . In the common case of A = 1, inputs and outputs are typically in the range 0–1. A gamma value γ < 1 {displaystyle gamma <1} is sometimes called an encoding gamma, and the process of encoding with this compressive power-law nonlinearity is called gamma compression; conversely a gamma value γ > 1 {displaystyle gamma >1} is called a decoding gamma and the application of the expansive power-law nonlinearity is called gamma expansion. Gamma encoding of images is used to optimize the usage of bits when encoding an image, or bandwidth used to transport an image, by taking advantage of the non-linear manner in which humans perceive light and color. The human perception of brightness, under common illumination conditions (not pitch black nor blindingly bright), follows an approximate power function (note: no relation to the gamma function), with greater sensitivity to relative differences between darker tones than between lighter ones, consistent with the Stevens power law for brightness perception. If images are not gamma-encoded, they allocate too many bits or too much bandwidth to highlights that humans cannot differentiate, and too few bits or too little bandwidth to shadow values that humans are sensitive to and would require more bits/bandwidth to maintain the same visual quality. Gamma encoding of floating-point images is not required (and may be counterproductive), because the floating-point format already provides a piecewise linear approximation of a logarithmic curve. Although gamma encoding was developed originally to compensate for the input–output characteristic of cathode ray tube (CRT) displays, that is not its main purpose or advantage in modern systems. In CRT displays, the light intensity varies nonlinearly with the electron-gun voltage. Altering the input signal by gamma compression can cancel this nonlinearity, such that the output picture has the intended luminance. However, the gamma characteristics of the display device do not play a factor in the gamma encoding of images and video—they need gamma encoding to maximize the visual quality of the signal, regardless of the gamma characteristics of the display device. The similarity of CRT physics to the inverse of gamma encoding needed for video transmission was a combination of coincidence and engineering, which simplified the electronics in early television sets. The concept of gamma can be applied to any nonlinear relationship. For the power-law relationship V out = V in γ {displaystyle V_{ ext{out}}=V_{ ext{in}}^{gamma }} , the curve on a log–log plot is a straight line, with slope everywhere equal to gamma (slope is represented here by the derivative operator): That is, gamma can be visualized as the slope of the input–output curve when plotted on logarithmic axes. For a power-law curve, this slope is constant, but the idea can be extended to any type of curve, in which case gamma (strictly speaking, 'point gamma') is defined as the slope of the curve in any particular region. When a photographic film is exposed to light, the result of the exposure can be represented on a graph showing log of exposure on the horizontal axis, and density, or log of transmittance, on the vertical axis. For a given film formulation and processing method, this curve is its characteristic or Hurter–Driffield curve. Since both axes use logarithmic units, the slope of the linear section of the curve is called the gamma of the film. Negative film typically has a gamma less than 1; positive film (slide film, reversal film) typically has a gamma with absolute value greater than 1.