Intensity
"Intensity" has three meanings. In the HSI model it is the mean of the RGB components, in image processing simply a pixel's grayscale value, and in physics the radiant power in a given direction. None of them is the same as perceived brightness.
I in the HSI model
In HSI intensity is the plain arithmetic mean:
This definition has one geometric advantage: I is the projection of the color onto the gray diagonal of the RGB cube. Planes of constant I are perpendicular to that diagonal, and hue and saturation are measured on them as an angle and a distance from the center. That is why HSI is convenient for image analysis and segmentation.
The drawback: all three components count equally, although the eye is several times more sensitive to green than to blue. Pure green and pure blue have the same HSI intensity of 1/3.
Three ways to grayscale
Converting a color image to black and white is in practice a choice of "amount of light" measure. For our color:
| Method | Formula | Result for (200, 80, 40) |
|---|---|---|
| HSI intensity | (R + G + B) / 3 | 107 |
| luma (Rec. 601) | 0.299 R' + 0.587 G' + 0.114 B' | 111 |
| sRGB luminance, re-encoded | Y from linear RGB, then gamma | 118 |
The mean gives the darkest result because it underrates green. Television luma (see YUV) weights the components but computes on gamma-encoded values. Closest to what the eye sees is luminance computed on linear light and encoded back to 0..255.
Intensity in physics
In radiometry, intensity is the power emitted into a unit solid angle, in watts per steradian. Its photometric counterpart, weighted by eye sensitivity, is luminous intensity in candelas. That is a completely different quantity from I in HSI: it describes a light source, not the color of a surface in an image.
When "intensity" shows up in a graphics library's documentation, check the formula. It may be the RGB mean, luma, or sometimes even the largest component.