Grayscale image

This page is a solution to the task Grayscale image in the Rosetta Code, written in Fōrmulæ.

Many image processing algorithms are defined for grayscale (or else monochromatic) images. Task Extend the data storage type defined on this page to support grayscale images. Define two operations, one to convert a color image to a grayscale image and one for the backward conversion. To get luminance of a color use the formula recommended by CIE: L = 0.2126 × R + 0.7152 × G + 0.0722 × B When using floating-point arithmetic make sure that rounding errors would not cause run-time problems or else distorted results when calculated luminance is stored as an unsigned integer.

Note the use of the dot product in the calculation of the gray level, because the above formula can be seen as $\text{[math]}$

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