Adaptive free-form deformation for interpatient medical image registration

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Abstract
A number of methods have been proposed recently to solve nonrigid registration problems. One of these involves optimizing a Mutual Information (MI) based objective function over a regularly spaced grid of basis functions. This approach has produced good results but its computational complexity is inversely proportional to the compliance of the transformation. Transformations able to register two high resolution images on a very local scale need a large number of degrees of freedom. Finding an optimum in such a search space is lengthy and prone to convergence to local maxima. In this paper, we propose a modification to this class of algorithms that reduces their computational complexity and improves their convergence properties. The approach we propose adapts the compliance of the transformation locally. Registration is achieved iteratively, from a coarse to a fine scale. At each level, the gradient of the cost function with respect to the coefficients of a set of compactly supported radial basis functions spread over a regular grid is used to estimate a local adaptation of the grid. Optimization is then conducted over the estimated irregular grid one region at a time. Results show the advantage of the approach we propose over a method without local grid adaptation.

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