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Contrast (formula)

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Various definitions of contrast are used in different situations. Below, luminance contrast is used as an example, but the formulas can also be applied to other physical quantities. In many cases, the definitions of contrast represent a ratio of the type

\frac{\mbox{Luminance difference}}{\mbox{Average luminance}}.

The rationale behind this is that a small difference is negligible if the average luminance is high, while the same small difference matters if the average luminance is low (cf. Weber-Fechner law). Below, two of the most common definitions are given.

Weber contrast

The Weber contrast is defined as

\frac{I-I_\mathrm{b}}{I_\mathrm{b}},

with I and Ib representing the luminance of the features and the background luminance, respectively. It is commonly used in cases where small features are present on a large uniform background, i.e. the average luminance is approximately equal to the background luminance.

Michelson contrast

The Michelson contrast is commonly used for patterns where both bright and dark features are equivalent and take up similar fractions of the area. The Michelson contrast is defined as

\frac{I_\mathrm{max}-I_\mathrm{min}}{I_\mathrm{max}+I_\mathrm{min}},

with Imax and Imin representing the highest and lowest luminance. The denominator represents twice the average of the luminance.

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