Invertibility and Transitivity Analysis For Nonrigid Image Registration

Gary E. Christensen and Hans J. Johnson

Department of Electrical and Computer Engineering
The University of Iowa, Iowa City, IA, 52242, USA

Abstract:

This paper presents a new method for evaluating the performance of nonrigid image registration algorithms by analyzing the invertibility and transitivity properties of the transformations that they produce. The invertibility and transitivity of transformations computed using a unidirectional and a consistent linear-elastic registration algorithm were evaluated. Invertibility of the transformations was evaluated by comparing the composition of transformations from image $A$-to-$B$ and $B$-to-$A$ to the identity mapping. Transitivity of the transformations was evaluated by measuring the difference between the identity mapping and the composition the transformations from image $A$-to-$B$, $B$-to-$C$, and $C$-to-$A$. Transformations were generated by matching computer three generated phantoms, three CT data of infant heads, and 23 MRI data of adult brains. In all cases, the inverse consistency constraint (ICC) algorithm out performed the unidirectional (UD) algorithm by producing transformations that have less inverse consistency (IC) error and less transitivity error. For the MRI brain data, the ICC algorithm reduced the maximum IC error on average by 205 times, the average transitivity error by 50 percent, and the maximum transitivity error by 37 percent compared to the UD algorithm.

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Questions or Comments: gary-christensen@uiowa.edu