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Assume I have m x n pixels of an RGB image. If I calculate 3mn, what is the name of quantity for this value?

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    $\begingroup$ Wikipedia calls them subpixels $\endgroup$ – MBaz Apr 9 at 22:15
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number of channel per pixel

This is typically referred to as colour depth or bit depth and expressed as bits or 'bits per pixel' (bpp)

number of pixels

There is no special terminology for this, it's just "Pixel count" or similar. It's unusual to need to refer to the total pixel count of an image without any other context, the dimensions are usually used instead.

If I calculate 3mn, what is the name of quantity for this value?

There is no special word for this quantity, but the units would typically be bits or bytes, for example

1024 x 768 x 32bpp

= 3,145,728 bytes (3Mb)

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A comment states "subpixels" but that name is only used for the single-color physical display areas making up the pixels on a screen. The corresponding data item does not have an official name of its own. You can use "primary color values" for it. Note that the light sensitive "pixel" areas of a rectangular photo sensor matrix under a Bayer matrix (or other color filter matrix) are called "sensels". Proper 3-value pixels are extrapolated from them using a demosaicing algorithm like "AMaZE" ("Aliasing Minimization and Zipper Elimination").

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