Prefiltering and reconstruction filters in the volume rendering

This paper deals with reconstruction filters and appropriate prefiltering techniques in the volume rendering. Sampling, resampling and reconstruction of continuous functions are used in many different fields. To satisfy conditions of Shannon's theorem, prefiltering of images or data volumes is usually required before sampling. The usual approach is to use a Gaussian prefilter, where the cutoff frequency is determined by the sampling rate, and one of the different reconstruction schemes is then applied. The problem is to determine a prefilter so that the reconstruction will reproduce the original object as accurately as possible. If the combination of prefiltering and reconstruction in the volumetric space is not adequate, aliasing artifacts will appear. Aliasing artifacts project from the three-dimensional space onto the projection plane and superpose to the artifacts caused by sampling and reconstruction in two dimensions. We present a methodology for designing filters based on optimization of combined operation of prefiltering and reconstruction postfiltering. This methodology offers a framework for comparing different reconstruction schemes in equal circumstances. The correct choice of reconstruction will also influence the derivative reconstruction which is used for shading. We demonstrate our results on examples in two- and three-dimensional space.