 formula_10 and formula_11 or, equivalently, formula_12 and formula_13, where formula_14 denotes the function composition operator.Real algorithms are not perfect, and when swapping the role of source and target image in a registration problem the so obtained transformations are not the inverse of each other.Inverse consistency can be enforced by adding to the loss function of the registration a symmetric regularisation term that penalises inconsistent transformations

Inverse consistency can be used as a quality metric to evaluate image registration results.