Radial basis functions include the Thin Plate Spline, Natural Cubic Spline, Marcov Spline, Exponential Spline, and Rational Quadratic Spline. These methods are best for correcting local distortions. RMS values are not reported when using radial basis function methods as these methods are perfect interpolators at the control points.
The minimum number of control points required for the Thin Plate Spline transformation is four. The equation is of the form:
The left graphic is the file before using the thin plate spline transformation.
The right graphic is the file after using a thin plate spline transformation.