Modelling and rendering large volume data with gaussian radial basis functions

Implicit representations have the potential to represent large volumes succinctly. In this paper we presenta multiresolution and progressive implicit representation of scalar volumetric data using anisotropic
Gaussian radial basis functions (RBFs) defined over an octree. Our representation lends itself well to
progressive level-of-detail representations. Our RBF encoding algorithm based on a Maximum Like-
lihood Estimation (MLE) calculation is non-iterative, scales in a O(nlogn) manner, and operates in a
memory-friendly manner on very large datasets by processing small blocks at a time. We also present
a GPU-based ray-casting algorithm for direct rendering from implicit volumes. Our GPU-based im-
plicit volume rendering algorithm is accelerated by early-ray termination and empty-space skipping
for implicit volumes and can render volumes encoded with 16 million RBFs at 1 to 3 frames/second.
The octree hierarchy enables the GPU-based ray-casting algorithm to efficiently traverse using location
codes and is also suitable for view-dependent level-of-detail-based rendering.