Using Kriging to Interpolate Spatially Distributed Volumetric Medical Data

Abstract

Routine cases in diagnostic radiology require the interpolation of volumetric medical imaging data sets. Inaccurate renditions of interpolated volumes can lead to the misdiagnosis of a patient\u27s condition. It is therefore essential that interpolated modality space estimates accurately portray patient space. Kriging is investigated in this research to interpolate medical imaging volumes. Kriging requires data to be spatially distributed. Therefore, magnetic resonance imaging (MRI) data is shown to exhibit spatially regionalized characteristics such that it can be modeled using regionalized variables and subsequently be interpolated using kriging. A comprehensive, automated, three-dimensional structural analysis of the MRI data is accomplished to derive a mathematical model of spatial variation about each interpolated point. Kriging uses these models to compute estimates of minimal estimation variance. Estimation accuracy of the kriged, interpolated MRI volume is demonstrated to exceed that achieved using trilinear interpolation if the derived model of spatial variation sufficiently represents the regionalized neighborhoods about each interpolated voxel. Models of spatial variation that assume an ellipsoid extent with orthogonal axes of continuity are demonstrated to insufficiently characterize modality space MRI data. Model accuracy is concluded to be critical to achieve estimation accuracies that exceed those of trilinear interpolation