Biorthogonal Wavelet Filters for Frequency Domain Volume Rendering

Abstract

Rendering images from three-dimensional discrete data sets usually involves interpolation between samples. In terms of signal processing theory, common interpolation methods like trilinear and cubic interpolation are equivalent to the convolution of the sampled data with a suitably chosen reconstruction filter. Frequency domain volume rendering is a technique based on the Fourier projection-slice theorem for the efficient generation of line integral projections without absorption. The quality of the images relies almost completely on the quality of the interpolation filter for the extraction of a 2D slice from the 3D frequency domain representation of the volume. This paper presents experiences we obtained when implementing frequency domain volume rendering and investigates the use of scaling functions of biorthogonal wavelets as reconstruction filters that exhibit the required compact support in space and fast decay in the frequency domain. This method generates X-ray-like images with good quality and short rendering times. In order to accelerate the rendering process without much loss of image quality we introduce wavelets as a subband filtering scheme generating a hierarchical representation of the volume data with the potential for interactive data exploration.