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I am wondering whether one can simply convert the intensity of a color in HSI space to the luminosity value in Lab space. I am referring to te CIELab color space as discussed here: https://en.wikipedia.org/wiki/Lab_color_space#CIELAB-CIEXYZ_conversions

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According to Poynton’s FAQ,

Intensity is a measure over some interval of the electromagnetic spectrum of the flow of power. Lighntess is the perceptual response to luminance (which is radiant power weighted by a spectral sensitivity function that is characteristic of vision).

That is, intensity is an objective measurement of the amount of light, whereas lighntess is how bright we perceive the light.

Intensity does not distinguish different wavelengths of light (ie colors), they each contribute equally to the measurement, and is linear in the amount of light. But our perceived lightness is different for each color, and is non-linear.

Thus it is not possible to map one to the other without knowing the color composition of the light. If you have the complete HSI triplet, then you can compute lightness from the Lab triplet.

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The intensity of HSI is linear combination of the rgb values.
The L of lab is non linear. hence the relationship are not well defined, you can move from one to to other. For assessing the brightness level you can go with I, if you want to check similarity of intensity between 2 pixels, got with L.

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