On The Simplification Of Radial Basis Function Fields For Volume Rendering: Some Practical Insights

Volume rendering with splatting most commonly decomposes a volume dataset into a field of overlapping radial basis function (RBF) kernels, such as Gaussians. The rendering effort is directly related to the number of RBFs in the volume and the degree of RBF overlap in the rasterization phase. Much work has been done that seeks to lower the number of RBFs by replacing a neighborhood of kernels with a single, wider kernel of the same family. The most regular decomposition for this is the octree. We argue in this paper that this simplification can adversely change the characteristics of the volume, as this substitution results in a different reconstruction of the local volume function. To cope, we propose a special kernel, called AG-splat (AGglutinative splat), which is designed to faithfully encode the local set of RBFs it seeks to replace. At the same time, AG-splats are amenable to the same expedient rendering mechanisms than the regular RBFs. Apart from the rendering primitive itself, we also give a local algorithm, based on statistical fitting, for its encoding of homogenous and ramp-like volume areas.