Colour correction with colour chart

@fotoseb1207! the accepted tried and true method for this is to use a really good ICC profile.

I have worked with fine art copy photographers (such as Christie's the auctioneers) some of whom make a new ICC capture profile for every setup and say they get an excellent match (this is done using a colorchecker SG and basICColor input profiling software in much of the art capture world)

I do not know of a method that looks at the captured chart and algorithmically corrects it - other than an ICC profile which was designed to do pretty much exactly that.

D Fosse writes

"chasing a perfect colorimetric match is futile. Even if you could get there, the result wouldn't necessarily look good or credible. A digital file is not the same as a physical object. What you should aim for is equivalent color, not identical color."

I agree, the profiling software manufacturers are generally not sdekign. an exact coltimetric match but a good equivalent appearance. 

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

I usually just pin the contrast curve manually, using the gray patches to get the numbers close - and then adjust individual colors visually.

Each patch has standardized Lab values. These can be translated into any other color space - or Lightroom %.

IME, chasing a perfect colorimetric match is futile. Even if you could get there, the result wouldn't necessarily look good or credible. A digital file is not the same as a physical object. What you should aim for is equivalent color, not identical color.

For shooting artworks, I use cross-polarized light to eliminate reflections. But this in itself alters color relationships, and renders the color checker less of a reliable reference. So I do it by eye (and a good accurate monitor).

Another complication is print. In that case you can't go by numbers - you have to allow for paper color and maximum ink. This will in itself compress the tonal range, and so you have to "reverse-expand" to make sure the final result gives the same visual experience as the original.

And of course a colorchecker is only valid for perfectly flat objects. Any 3-dimensionality, and all bets are off.