A Geometric Theory of Symmetric Registration

This paper shows that asymmetry (inverse inconsistency) in L2 and information theoretic (IT) registration objective functions is the result of using standard volume differential forms. A new space with non-standard volume differential forms is identified, and a unique symmetrizing volume differential form is found in it. This form simultaneously symmetrizes the L2 and the IT registration functions. Experimental results supporting the mathematical theory are provided.