Fast Interpolation of Dense Motion Fields from Synthetic Phantoms

Abstract

Numerical phantoms are a common tool for the evaluation of registration and reconstruction algorithms. For applications concerning motion, dense deformation fields are of particular interest. Phantoms, however, are often described as surfaces and thus motion vectors can only be generated at these surfaces. In order to create dense motion fields, interpolation is required. A frequently used method for this purpose is the Parzen interpolator. However, with a high number of surface motion vectors and a high voxel count, its run time increases dramatically. In this paper, we investigate different methods to accelerate the creation of these motion fields using hierarchical sampling and the random ball cover. In the results, we show that a 64³ volume can be sampled in less than one second with an error below 0.1mm. Furthermore, we accelerate the interpolation of a 256³ dense deformation field to only $\tilde 6.5$ minutes using the proposed methods from days with previous methods.