Thin-Plate Splines
•
•
•
A function, f, R2 -> R2 is a thin-plate spline if:
• Constraint: Given corresponding points: X1…Xn and U1…Un, f(Xi)=Ui.
• Energy: f minimizes the following:
If we think of this as the amount of bending produced by f.  Allows arbitrary affine transformation.