Two shots of the same place: one taken in the morning from a drone, the other in the evening from a satellite. The first shows tree shadows, the second shows glints on the water. It's like two accounts of the same event in different dialects. Image registration is the interpreter that finds common ground between such frames.
The interpreter looks for anchor points: building corners, river bends. Then it matches them, estimates how one image needs to be shifted or rotated to align with the other, and applies that transformation. For images of the same type, the correlation coefficient (a measure of brightness similarity) works; for different types, mutual information (a measure of statistical dependence) is used.
There is no universal interpreter. For simple shifts, markers work; for complex distortions, neural networks and evolutionary algorithms come into play. But when the image is covered by clouds, anchor points are lost, and the problem remains open.
For aligning MRI and PET brain images, mutual information is often used: it finds common patterns in intensities, even if one image shows anatomy and the other shows metabolic activity.