Inevitable camera motion during exposure does not augur well for free-hand photography. Distortions introduced in images can be of different types and mainly depend on the structure of the scene, the nature of camera motion, and the shutter mechanism of the camera. In this paper, we address the problem of registering images taken from global shutter and rolling shutter cameras and reveal the constraints on camera motion that admit registration, change detection, and rectification. Our analysis encompasses degradations arising from camera motion during exposure and differences in shutter mechanisms. We also investigate conditions under which camera motions causing distortions in reference and target image can be decoupled to yield the underlying latent image through RS rectification. We validate our approach using several synthetic and real examples.