We develop a multi-pole type method to form fast approximations of thin-plate spline fitting problems. Thin-plate splines, and generalizations of them, arise in the context of computer vision through a regularization or interpolation/approximation process.
David Suter,
"Multipole methods for visual reconstruction", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); doi: 10.1117/12.146628; https://doi.org/10.1117/12.146628