Using kriging for 3D medical imaging

We describe our implementation of kriging for interpolation of scalar values in three-dimensional medical image surface rendering and for slice interpolation. Kriging is an interpolation technique developed in the geosciences for estimating ore deposit spatial distributions. Kriging has been mathematically proven to be the best (statistically optimal) linear unbiased estimation technique for spatially distributed data. As a byproduct of the kriging technique, kriging can calculate the estimation error for the interslice interpolated values. Kriging also offers the potential for quantifying the interpolation error in slices computed by the estimation technique. This paper presents the initial results obtained using kriging for the pre-processing operations of slice interpolation by slice-value interpolation and interpolating voxel values during iso-surface extraction. We found that kriging is an accurate interpolation technique for surface rendering and for slice interpolation. Our results indicate that kriging can duplicate the rendering results obtained with other interpolation techniques and it offers the potential for providing visually "better" images than are obtained using the other interpolation techniques we tested.