Exclusion Blend Mode on Identical Images in GIMP

When you blend an image with an identical copy of itself using the Exclusion blend mode in GIMP, the software executes a specific quadratic transformation on each pixel's color channel. This operation maps the image through an inverted parabola where both pure black and pure white become black, while midtones retain moderate brightness, producing a solarized effect that caps the maximum brightness of the output at 50% gray.

The standard formula for the Exclusion blend mode between a base layer pixel value (\(A\)) and a blend layer pixel value (\(B\)) in normalized color space (where values range from \(0.0\) to \(1.0\)) is:

\[f(A, B) = A + B - 2AB\]

Because both layers are identical, \(B\) equals \(A\). Substituting \(A\) for \(B\) simplifies the equation to:

\[f(A) = A + A - 2A^2 = 2A - 2A^2 = 2A(1 - A)\]

In an 8-bit color channel system where values range from \(0\) to \(255\), this formula translates to:

\[\text{Output} = \frac{2A(255 - A)}{255}\]

This transformation alters the tonal distribution of the image in several distinct ways:

  • Blacks remain black: When an input channel is pure black (\(A = 0\)), the formula yields \(2(0) - 2(0)^2 = 0\). Shadow areas with zero luminance remain untouched.
  • Whites invert to black: When an input channel is pure white (\(A = 1.0\) or \(255\)), the calculation yields \(2(1.0) - 2(1.0)^2 = 0\). Extreme highlights lose all luminance and collapse into black.
  • Midtones peak at 50% gray: The vertex of the parabola occurs at \(A = 0.5\) (or \(127.5\) in 8-bit). Substituting \(0.5\) into the formula produces \(2(0.5) - 2(0.5)^2 = 1.0 - 0.5 = 0.5\). Midtones represent the brightest elements in the composite image.
  • Dynamic range is halved: Because the peak output value cannot exceed \(0.5\), the resulting image will contain no values brighter than 50% neutral gray. The overall tonal range is compressed into the lower half of the histogram (\(0\) to \(128\) in 8-bit space).

The transformation creates a symmetrical, non-linear tonal inversion commonly associated with the Sabattier effect (solarization), removing high-key highlights and flattening overall image contrast.