Variational Reconstruction and GPU Ray-Casting of Non-Uniform Point Sets using B-Spline Pyramids

In this work, we focus on the problem of reconstructing a volume (scalar 3D field) based on non-uniform point samples and then rendering the volume by exploiting the processing power of GPUs. In the first part involving the reconstruction, we motivate our choice of tensor-product uniform B-splines for the discretized representation of the continuous volume. They allow for highly efficient, scalable and accurate reconstruction at multiple scales (resolution levels) at once. By subdividing the volume into blocks and reconstructing them independently, current desktop PCs are able to reconstruct large volumes and multiple CPU cores can be efficiently exploited. We focus on linear and cubic B-splines and on how to eliminate otherwise resulting block discontinuities. Once we have reconstructed the volume at multiple scales, we can derive different Levels of Detail (LoDs) by subdividing the volume into blocks and selecting a suitable scale for each block. We present a fusion scheme which guarantees global C continuity for linear LoDs and C continuity for cubic ones. The challenge here is to minimize visual block interscale discontinuities. A LoD, consisting of a hierarchical spatial subdivision into blocks and an autonomous B-spline coefficient grid for each block, is then rendered via a GPU ray-caster. We achieve interactive frame-rates for qualitative Direct Volume Renderings (DVRs) and real-time frame-rates for iso-surface renderings.