This is the fifteenth in a series of posts on color reproduction. The series starts here.

It’s fine to be able to describe of the color errors of each of the 24 patches in the Macbeth color checker, but is also useful to be able to say something about the overall color accuracy. One of the areas in which cameras and profiles differ significantly is whether the actual chroma of the patches are on average reproduced accurately, or if there is a significant increase or decrease in average chroma.

Imatest has a module for analyzing photographs of Macbeth color checkers. This module has an overall “saturation” metric that is expressed as a percentage value. Imatest’s explanation of this measure doesn’t mention the word saturation (although that’s the word used on the graph): “The mean camera chroma (the average of all camera chroma values) relative to the mean ideal chroma is displayed on the upper right.” That’s plain enough, but I don’t think that’s a particularly good measure.

First off, taking a ratio like that means that small errors in not-very-chromatic samples will not affect the result much; the measure weights the samples with large chromas highly. Second, chroma errors from the 6 gray patches are lumped in with the other 18 patches. I think they should be treated differently.

Therefore, I’ve devised an aggregate chroma error measure:

The first applies to the 18 non-gray patches. It is the mean chroma error of all 18 patches (each patch’s chroma error added together and the total divided by 18). Positive numbers mean that on average, the camera/profile/raw developer combination produces results that are oversaturated. Negative numbers mean that on average, the camera/profile/raw developer combination produces results that are undersaturated. Quite imaginatively, I call this measure the **mean chroma error**. The standard deviation of the 18 chroma errors I call the **mean chroma sigma.**

Calculating a similar measure for the 6 gray patches wouldn’t be any more useful than calculating the Euclidean chromaticity error distance, since the target’s chroma for the 6 gray squares is close to zero.

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