Warping is fundamental to multiple algorithms in computer vision and medical imaging such as image and volume registration. Warping is performed by determining a continuous deformation map and applying it to a given image or volume. In registration the deformation map is determined based on correspondence between two images. It is often the case that the deformation map can only be determined at discrete locations and so has to be interpolated. The discrete locations where the deformation map is determined form irregular sampling of the unknown continuous deformation map. Thin-plate splines are commonly used to perform the interpolation and provide an optimal solution in the sense of bending energy minimization. Assuming N samples of the deformation map and n2 image pixels, thin plate splines require solving a N