Adaptive parametrization of multivariate B-splines for image registration

We present an adaptive parametrization scheme for dynamic mesh refinement in the application of parametric image registration. The scheme is based on a refinement measure ensuring that the control points give an efficient representation of the warp fields, in terms of minimizing the registration cost function. In the current work we introduce multivariate B-splines as a novel alternative to the widely used tensor B-splines enabling us to make efficient use of the derived measure. The multivariate B-splines of order n are C ^n-1 smooth and are based on Delaunay configurations of arbitrary 2D or 3D control point sets. Efficient algorithms for finding the configurations are presented, and B-splines are through their flexibility shown to feature several advantages over the tensor B-splines. In spite of efforts to make the tensor product B-splines more flexible, the knots are still bound to reside on a regular grid. In contrast, by efficient non-constrained placement of the knots, the multivariate B-splines are shown to give a good representation of inhomogeneous objects in natural settings. The wide applicability of the method is illustrated through its application on medical data and for optical flow estimation.