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Summary and Conclusions

Inverse consistency and transitivity are two important properties that should be satisfied by any set of transformations that define correspondence between a collection of similar images. It was shown that registration error measured by intensity mismatch alone is not sufficient to determine the performance of an image registration algorithm.

The invertibility and the transitivity error analysis demonstrated that there are two primary sources of inverse consistency errors. The first type of error occurs at the image edges and is due to the linear-elastic regularization preventing the registration algorithm to completely match the borders. The second source of error occurs away from the image edges and is due to the smoothing induced by the linear-elastic regularization. The second type of error is reduced by jointly estimating the forward and reverse transformations while using the inverse consistency constraint.

The consistent linear-elastic algorithm produces transformations with improved pointwise invertibility correspondence and pointwise transitivity compared to the unidirectional linear-elastic algorithm. The inverse consistent registration algorithm reduced the maximum inverse consistency error by 60 times for the phantom data, 8.6 times for the CT data, and 205 times on average for the MRI data. The inverse consistent registration algorithm also reduced the maximum transitivity error by 60 % for the phantom data, 30% for the CT data, and 37 % on average for the MRI data compared to the unidirectional algorithm. Likewise, the average transitivity error was reduced by 50% for the phantom data, 70 % for the CT data, and 50 % on average for the MRI data.

Next: Acknowledgments Up: index Previous: Transitivity Error

Gary E. Christensen 2002-07-04