Brightness is one of the most significant pixel characteristics. It is involved in many image-editing algorithms such as contrast or shadow/highlight. Currently, there is no conventional formula for brightness calculation, and the same image-processing tool may employ several different brightness measures. However, stimuli, equibright according to one measure, may differ more, than ten times according to another. This paper suggests using length of a color vector for Brightness and demonstrates with major image editing procedures the advantage of this measure. Suggested definition for Brightness is convenient in terms of software development because it simplifies design of algorithms that perform only intended operations without concurrent unwilling modification some other image parameters. For example, suggested contrast editing algorithm modifies only pixel Brightness and does not change chromatic coordinates. An advantage of the algorithms is especially visible when they are applied to a high dynamic range image.
Sergey Bezryadin, Pavel Bourov, Dmitry Ilinih, "Brightness Calculation in Digital Image Processing" in Proc. Int'l Symp.on Technologies for Digital Photo Fulfillment, 2007, pp 10 - 15, https://doi.org/10.2352/ISSN.2169-4672.2007.1.0.10