The registrations of functions and images is a widely-studied problem that has seen a variety of solutions in the recent years. Most of these solutions are based on objective functions that fail to satisfy two most basic and desired properties in registration: (1) invariance under identical warping: since the registration between two images is unchanged under identical domain warping, the cost function evaluating registrations should also remain unchanged; (2) inverse consistency: the optimal registration of image A to B should be the same as that of image B to A. We present a novel registration approach that uses the L~2 norm, between certain vector fields derived from images, as an objective function for registering images. This framework satisfies symmetry and invariance properties. We demonstrate this framework using examples from different types of images and compare performances with some recent methods.
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