Weighting by Interpolation Error

The algorithm presented in this section is combining the approach of the weighted distance reduction with the interpolation error calculated for the input data locations. In this case, the distance weights

W = {W1, W2Winp} (33)

are equal to the error of interpolated deformation vectors AXinp.

The basic scheme of the algorithm looks like:

• Select start base point set Xs with corresponding deformation vectors AXs by equidistant reduction

• Do nEWSteps times:

– Interpolate deformations at input points X^p, by using the sets Xs and AXs, to get the deformation vectors AXinp

– Calculate weights Wi by comparing AXmp to AXinp

– Add further base points and deformation vectors by weighted distance reduc­tion to Xs and AXs, respectively.

The type of greedy algorithm, which recalculates the exact interpolation error in each step, is also proposed in [2, p.9].

To interpolate the input points X^p in each step, a new interpolation matrix Hk has to be created from the already chosen base points Xs and inverted in every iteration step. Then the error can be calculated by interpolating the deformation vectors AXs of these base points to the input set Xinp to get the interpolated data set
and taking the pairwise difference to the input deformation vector set AXmp to com­pute the weights

wi — ||Axmp, i Axmp, i||27 i — 1 2:-": ninp.