Assuming that the color in each sensor channel averages to gray over the entire image (field of view) is one of the most common assumptions made when trying to estimate the spectral distribution of the illuminant. Typically, each sensor channel is averaged independently (von Kries adaptation).

Here is the experimental data, after it has been averaged to a gray of (RGB: 0.38, 0.431, 0.32) :

Two dimensional histograms of the corrected images are available: chromaticity and Red vs. Blue

Color Corrected Test Images

Gamut	Illuminant A	Illuminant B	Illuminant C
All

Problem arise, however, when the objects don't average to gray :

Gamut	Illuminant A	Illuminant B	Illuminant C
Little Blue
Little Red

Here are examples of the original images, for comparison...

Illuminant A	Illuminant B	Illuminant C

A differing assumption commonly used for spectral normalization is the White world assumption.

The simple Isis script used to average the images to gray is gray.isis.