Thin-Plate Spline Interpolation
David C. Wilson, B.A. Mair · Birkhäuser Boston eBooks · 2004
The purpose of this chapter is to present an introduction to thin-plate spline interpolation and indicate how it can be a useful tool in medical imaging applications. After a brief review of the strengths and weaknesses of polynomial and Fourier interpolation, the ideas fundamental to the success of cubic spline interpolation are discussed. These ideas include convergence rates of both the interpolants and the derivatives as well as the fact that the clamped cubic spline is the solution of a minimization problem, where the optimal solution is the one exhibiting the fewest “wiggles.” This measure is important because it helps ensure that if slowly oscillating data is interpolated by a spline technique, then the interpolation will also be reasonable. The classical examples of Runge are presented, which dramatically demonstrate the dangers of polynomial interpolation for even the least oscillatory data. While the Fourier interpolants are more stable than the polynomial ones, they have the problem that while the interpolants converge, their derivatives do not. Thus, the spline approach has definite advantages These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.