Color Similarity/distance In RGBA Color Space

Answer :

Finally, I've found it! After thorough testing and experimentation my conclusions are:

• The correct way is to calculate maximum possible difference between the two colors.
  Formulas with any kind of estimated average/typical difference had room for discontinuities.

• I was unable to find a working formula that calculates the distance without blending RGBA colors with some backgrounds.

• There is no need to take every possible background color into account. It can be simplified down to blending maximum and minimum separately for each of R/G/B channels:

  1. blend the channel in both colors with channel=0 as the background, measure squared difference
  2. blend the channel in both colors with channel=max as the background, measure squared difference
  3. take higher of the two.

Fortunately blending with "white" and "black" is trivial when you use premultiplied alpha.

The complete formula for premultiplied alpha color space is:

rgb *= a // colors must be premultiplied max((r₁-r₂)², (r₁-r₂ - a₁+a₂)²) + max((g₁-g₂)², (g₁-g₂ - a₁+a₂)²) + max((b₁-b₂)², (b₁-b₂ - a₁+a₂)²) 

C Source including SSE2 implementation.

Several principles:

1. When two colors have same alpha, rgbaDistance = rgbDistance * ( alpha / 255). Compatible with RGB color distance algorithm when both alpha are 255.
2. All Colors with very low alpha are similar.
3. The rgbaDistance between two colors with same RGB is linearly dependent on delta Alpha.

double DistanceSquared(Color a, Color b) {     int deltaR = a.R - b.R;     int deltaG = a.G - b.G;     int deltaB = a.B - b.B;     int deltaAlpha = a.A - b.A;     double rgbDistanceSquared = (deltaR * deltaR + deltaG * deltaG + deltaB * deltaB) / 3.0;     return deltaAlpha * deltaAlpha / 2.0 + rgbDistanceSquared * a.A * b.A / (255 * 255); }