Invertibility and transitivity analysis for nonrigid image registration

We present a new method for evaluating the perfor- mance of nonrigid image registration algorithms by analyzing the invertibility and transitivity properties of the transformations that they produce. The invertibility and transitivity of transformations com- puted using a unidirectional and a consistent linear-elastic registra- tion algorithm are evaluated. The invertibility of the transformations is evaluated by comparing the composition of transformations from images A to B and B to A to the identity mapping. The transitivity of the transformations is evaluated by measuring the difference be- tween the identity mapping and the composition of the transforma- tions from images A to B, Bt o C, and C to A. Transformations are generated by matching three computer-generated phantoms, three computed tomography (CT) data of infant heads, and 23 magnetic resonance imaging (MRI) data of adult brains. In all cases, the in- verse consistency constraint (ICC) algorithm out-performs the unidi- rectional algorithm by producing transformations that have less in- verse consistency error and less transitivity error. For the MRI brain data, the ICC algorithm reduced the maximum inverse consistency error by 205 times, the average transitivity error by 50%, and the maximum transitivity error by 37% on average compared to the uni- directional algorithm. © 2003 SPIE and IS&T. (DOI: 10.1117/1.1526494)

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