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Summary and Conclusions

This paper presented a new algorithm for jointly estimating a consistent set of transformations that map one image to another and vice versa. A new parameterization based on the Fourier series was presented and was used to simplify the discretized linear-elasticity constraint. The Fourier series parameterization is simpler than our previous parameterizations and each basis coefficient can be interpreted as the weight of a harmonic component in a single coordinate direction. The algorithm was tested on both MRI and CT data. It was found that the unconstrained estimation leads to singular or near singular transformations. It was also shown that the linear-elastic constraint alone is not sufficient to guarantee that the forward and reverse transformations are inverses of one another. Results were presented that suggest that even though the inverse consistency constraint is not guaranteed to generate nonsingular transformations, in practice it may be possible to use the inverse consistency as the only constraint. Finally, it was shown that the most consistent transformations were generated using both the inverse consistency and the linear-elastic constraints.

Next: Acknowledgments Up: index Previous: Limitations of Diffeomorphic Transformations

Xiujuan Geng 2002-07-04