Tim: I do this all the time, both in RGB color space, when we need color correction to a standard RGB image, and in XYZ color space, when we want calibrated color measurements. In theory it's simple, but the code and formulas are way too lengthy to share here. Basically for RGB-to-RGB correction, you make a model of your transform, say linear, quadratic, or cubic, with or without cross terms (RG, RB, R*B^2, etc.). Then you do a least squares model to get a model for Restimated, Gestimated, and Bestimated. Let's look at just the Red. You plug in the standard values for your 24 red chips (that's the "y"), and the values of R, G, B, RG, RB, GB, R^2G, etc. into the "tall" 24 by N matrix, and you do least squares to get the coefficients, alpha. Then repeat to get sets of coefficients beta, and gamma, for the estimated green and blue. Now, for any arbitrary RGB, you plug them into the three equations to get the estimated RGB as if that color was snapped at the same time and color temperature as your standard. If all you have are changes in intensity you probably don't need any cross terms, but if you have changes in the color of the illumination, then including cross terms will correct for that, though sometimes people do white balancing as a separate step before color correction. Here is some code I did to do really crude white balancing (actually too crude and simple for me to ever actually use but simple enough that people can understand it).
I don't have any demo code to share with you - it's all too intricately wired into my projects. Someone on the imaging team at the Mathworks (I think it was Grant if I remember correctly) has a demo to do this. I think it was for the Computer Vision System Toolbox, but might have been for the Image Processing Toolbox. Call them and try to track it down. In the mean time try this: http://www.mathworks.com/matlabcentral/answers/?search_submit=answers&query=color+checker&term=color+checker
