How to calculate how much two images overlap (pixels?)

I have been working in photoshop to edit two line-drawing images (with transparent backgrounds) and then overlap them on top of each other. But I need to control how much the images overlap (percentage of image space, number of pixels, etc.) and wasn't able to find a way to do this in photoshop. Is it possible to do this in MATLAB/how?

[Image Analyst]

You forgot to attach the two pictures. Also say how they are overlapped. Is it just a rigid translation in x and y? Or is rotation going to be involved?

[AJ]

My apologies! I've attached an example of two images overlapping. Ideally it would be a rigid translation in x and y but I've noticed from doing this in photoshop that a lot of the images will have to be rotated some way.