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Spline Pyramids for Inter-Modal Image Registration Using Mutual Information

P. Thévenaz, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing V, San Diego CA, USA, July 30-August 1, 1997, vol. 3169, pp. 236-247.



We propose a new optimizer for multiresolution image registration. It is adapted to a criterion known as mutual information and is well suited to inter-modality. Our iteration strategy is inspired by the Marquardt-Levenberg algorithm, even though the underlying problem is not least-squares. We develop a framework based on a continuous polynomial spline representation of images. Together with the use of Parzen histogram estimates, it allows for closed-form expressions of the gradient and Hessian of the criterion. Tremendous simplifications result from the choice of Parzen windows satisfying the partition of unity, also based on B-splines. We use this framework to compute an image pyramid and to set our optimizer in a multiresolution context. We perform several experiments and show that it is particularly well adapted to a coarse-to-fine optimization strategy. We compare our approach to the popular Powell algorithm and conclude that our proposed optimizer is faster, at no cost in robustness or precision.


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