Welcome to Scicomp! You might be interested in the Field of (multimodal) medical image registration. In medical contexts one often wants to register a CT image with an MR or PET-Scan. The amplitudes of these modalities may vary considerably and differ in their physical meaning. Nonetheless they show the same spatial features.

In order to register these images one needs to calculate a similarity between them to iterate the optimizer. One approach that worked well was using local gradient information instead of amplitudes ("mutual information").

A good starting point may be the list of available similarity metrics implemented in the (wonderful) itk library:

https://itk.org/Doxygen/html/group__RegistrationMetrics.html