Hitting the colour a meter measured

Twenty-two chart patches, each with the sRGB triple sampled from a real photograph and the CIELAB value a colorimeter implies. Converting between colour spaces is exact arithmetic; deciding what the numbers mean physically is a fit, and this is that fit done by hand.

Try this

Start from the naive route at 9.54 and try to bring the mean down. You can reach about 4 with patience and then it stops — the rest needs the off-diagonal terms of a full 3×3, because the camera's red channel sees some of what the eye calls green.

Where this lab comes from

How Close Is Your Colour to the Real Thing?

Lesson 5 of The Image as Data. Converting between colour spaces is exact arithmetic; deciding what the numbers mean physically is a fit. Checked against a colorimeter on 22 chart patches: treating the developed file as sRGB lands 9.54 ΔE*ab from the light in the room, the camera's own published matrix does no better, and a 3x3 fitted here and scored on patches it never saw reaches 2.41.

More in the image itself