Algorithm to check similarity of colors

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RGB distance in the euclidean space is not very similar to “average human perception”.

You can use YUV color space, it takes into account this factor :

 |  Y' |     |  0.299     0.587    0.114   | | R |
 |  U  |  =  | -0.14713  -0.28886  0.436   | | G |
 |  V  |     |  0.615    -0.51499 -0.10001 | | B |

You can also use the CIE color space for this purpose.

EDIT:

I shall mention that YUV color space is an inexpensive approximation that can be computed via simple formulas. But it is not perceptually uniform. Perceptually uniform means that a change of the same amount in a color value should produce a change of about the same visual importance.
If you need a more precise and rigourous metric you must definitely consider CIELAB color space or an another perceptually uniform space (even if there are no simple formulas for conversion).

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