Description of Registration Method for Jamal Atif, X. Ripoche, A. Osorio

We extend the work of Principe and al. [2] based on the use of Renyi entropy with Gaussian kernel density estimator, to the multimodal registration problem. The quadratic mutual information is formulated using the Cauchy-Schwartz inequality; we use its normalization form which we call NQMI (Normalized Quadratic Mutual Information). In parallel, we introduce a new reduced adaptive kernel density estimator which uses a small set of local bandwidths rather than a single global one as in the standard kernel estimator or a high number of bandwidths as in the classical adaptive kernel estimator. To compute the adaptive bandwidths we proceed first in estimating the joint histogram with a Mixture of Gaussians at the coarse resolution level. The resulting Gaussians are then used as filtering functions which determine the extent of influence of the local bandwidths.

Thanks to Renyi entropy (smooth entropy), the resulting similarity measure presents interesting smoothness properties , and it less suffers of local maxima compared to the Shannon mutual information. The approach is set in a multi-resolution framework; the optimisation procedure is The Marquardt-Levenberg strategy. The registration takes 30 seconds on a PIV-1GHz.

[1] J. Atif, X. Ripoche, A. Osorio, ½ Non-rigid medical image registration by maximisation of quadratic mutual information ©, in IEEE 29th Annual Northeast Bioengineering Conference, Newark NJ, USA, 22-23 March 2003.

[2] Principe, J., Fisher III, J., & Xu, D. (2000). Information theoretic learning. In S. Haykin (Ed.), Unsupervised adaptive filtering. New York, NY: Wiley.

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