Catheter Navigation Deformable Registration

The patent transforms the coordinate system from a simple affine transformation to a deformable registration using thin plate splines. This changes the mathematical parameters from linear transformation coefficients to a set of control points and spline weights that can model non-linear distortions. The system uses fiducial pairs to establish correspondence between localization system coordinates and image coordinates, then applies thin plate spline interpolation to compute the deformation field, thereby achieving accurate position transformation while accounting for non-linearities and inhomogeneities in the localization field.

The patent introduces thin plate splines as an intermediary mathematical tool to bridge the gap between the localization system coordinate space and the image coordinate space. Instead of directly computing a complex non-linear transformation, the system uses fiducial pairs as intermediate reference points to define the deformation field. The thin plate spline function acts as a smooth interpolating surface that passes through these fiducial correspondences, providing an elegant solution that balances accuracy with computational tractability.

The patent employs fiducial pairs as pre-established reference points that define the correspondence between localization system coordinates and image coordinates. These fiducial correspondences are collected during an initial registration phase, and the thin plate spline mapping function is pre-computed based on these references. Once the mapping function is established, subsequent catheter position transformations can be performed rapidly using the pre-computed deformation field, thereby reducing the time penalty of the more accurate registration method.