Analysis of the HDAF for Interpolation and Noise Suppression in Volume Rendering

Abstract

In this paper, we evaluate the HDAF (Hermite Distributed Approximating Functionals) family of interpolation and derivative functions, with respect to their accuracy for reliable volume rendering, and compare them with other interpolation and derivative estimation filters. We utilize several different evaluation methods, both analytical and experimental. The former includes the order of decay of the global error, the local spatial error, and the behavior of the filters in the frequency domain. In the experimental part, visualizations of both synthetic and medical data are produced and studied. We show that the HDAFs exhibit superior behavior if the volumetric data are distorted by high frequency noise, and perform well under noise free conditions. This due to their ability to adjust the range of recovered frequencies.