Downsampling and storage of pre-computed gradients for volume rendering

Abstract

The way in which gradients are computed in volume datasets influences both the quality of the shading and the performance obtained in rendering algorithms. In particular, the visualization of coarse datasets in multi-resolution representations is affected when gradients are evaluated on-the-fly in the shader code by accessing neighbouring positions. This is not only a costly computation that compromises the performance of the visualization process, but also one that provides gradients of low quality that do not resemble the originals as much as desired because of the new topology of downsampled datasets. An obvious solution is to pre-compute the gradients and store them. Unfortunately, this originates two problems: First, the downsampling process, that is also prone to generate artifacts. Second, the limited bit size of storage itself causes the gradients to loss precision. In order to solve these issues, we propose a downsampling filter for pre-computed gradients that provides improved gradients that better match the originals such that the aforementioned artifacts disappear. Secondly, to address the storage problem, we present a method for the efficient storage of gradient directions that is able to minimize the minimum angle achieved among all representable vectors in a space of 3 bytes. We also provide several examples that show the advantages of the proposed approaches.