printing – How can I compare histograms between a digital image and it’s print

I want to compare color histograms between a digital photo and its physically printed in cloth (like a tshirt) version. The process is simple:

  1. Printing a digital image (with good resolution) in a tshirt
  2. Take a picture of that printed tshirt in proper aligment and crop
  3. Compare histograms

As one might expect, the color histogram of the photo of the printed tshirt is very different from the original image, as it should be. What I want to know is if there is any known method to achieve one of the following:

  1. From original digital image, transform colors so to be closer to printed colorspace histogram.
  2. From printed tshirt photo, try to normalize or transform in some way to achieve back original colors.

I am aware that the color distribution of the printed tshirt depend also on the camera that captures it. Right now I am thinkig of training a ML model to try to learn the color transformation between two colors distributions (original and physically printed).

However, I wonder if there is some literature about that or some procedure I can perform using my camera to try to find that color transformation so I can apply to other prints.

My goal is to generalize (predict) the printed color distribution transformation from original digital image. As I’m always using the same printer for print, and the same camera for the photo of the tshirt, I guess this should be feasible.

Thanks in advance.