Advanced interactive preintegrated volume rendering with a power series

Preintegrated volume rendering produces high-quality renderings without increased sampling rates. However, a look-up table of a conventional preintegrated volume rendering requires a dimensionality of two, which disturbs interactive renderings when the transfer function is changed. Furthermore, as the resolution of the volume data set increases, the memory space required is impractical or inefficient, especially on GPUs. In the past, several approximation methods have been proposed to reduce the complexity of both the time and memory requirement, but most of them do not correctly present thin opaque structures within slabs and ignore the self-attenuation. We propose an advanced interactive preintegrated volume rendering algorithm that achieves not only high-quality renderings comparable to the conventional ones, but also $(O(n))$ time and memory space requirements even with the self-attenuation within the slabs applied. The algorithm proposed in this paper decomposes the exponential term of the ray integration equation into a power series of a finite order in the form of a linear combination to build a one-dimensional look-up table. Moreover, the proposed algorithm effectively applies the self-attenuation that is caused by fully opaque isosurfaces, by introducing an opaque prediction table. Experimental results demonstrate that the proposed algorithm offers renderings visibly identical to existing preintegrated volume renderings without degrading rendering speed.