 Inverse consistency is necessary for good image registration but it is not sufficient, since a mapping can be perfectly consistent but not register the images at all.Image registration is the process of establishing a common coordinate system between two images, and given two images
registering a source image formula_2 to a target image formula_3 consists of determining a transformation formula_4 that maps points from the target space to the source space.An ideal registration algorithm should not be sensitive to which image in the pair is used as source or target, and the registration operator should be antisymmetric such that the mappings
produced when registering formula_2 to formula_3 and formula_3 to formula_2 respectively should be the inverse of each other, i.e.