I don't know how to make a specific question, because that's what I don't know and I'm asking for.
I don't even know what tags should I put on this question. If I knew, I would have the answer.
I have a set of 2D data (images), and I want to find the features that are invariant on all images. For example, the same object may be photographed at different resolutions, different sizes, different rotations, different illumination, and different coloration.
I want to know if there is a tool or mathematical theory about invariants in sets of data which I can study.
I once read an article about an astronomer which developed an algorithm which got the same hash from different astronomical photograph (of the same stars), independently of the scale, rotation and light intensity of the photograph.
I cannot find that article again, but I guess that there is an underlying mathematical theory which should be applied.
So the question is where I should be looking for. Which branch of mathematics is what I need to explore?