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

Martin Kinkelin
Variational Reconstruction and GPU Ray-Casting of Non-Uniform Point Sets using B-Spline Pyramids
[Thesis]

Information

Abstract

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 C0 continuity for linear LoDs and C2 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.

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BibTeX

@mastersthesis{Kinkelin-2011-VR,
  title =      "Variational Reconstruction and GPU Ray-Casting of
               Non-Uniform Point Sets using B-Spline Pyramids",
  author =     "Martin Kinkelin",
  year =       "2011",
  abstract =   "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 C0 continuity for linear LoDs and C2
               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.",
  month =      may,
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2011/Kinkelin-2011-VR/",
}