A Coherent Grid Traversal Algorithm for Volume Rendering

1
A Coherent Grid Traversal Algorithm for Volume
Rendering
UCL Department of Computer Science

• Ioannis Makris
• Supervisors Philipp Slusallek, Céline Loscos
• Computer Graphics Lab, Universität des
  Saarlandes

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Overview
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• Introduction
• Previous work in software Direct Volume Rendering
• Introduction to the Cell Broadband Engine
• The Coherent Grid Traversal Algorithm
• Parallelisation Schemes

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Introduction to Direct Volume Rendering

• Technique of displaying a 2D projection of a 3D
  sampled dataset (volume), by accumulating samples
  across lines of sight with some transfer
  function.
• Several types of sampled data. We will only deal
  with rectilinear grids.

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Direct Volume Rendering
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• Ray Casting (Levoy 1988, 1990)
• Image order algorithm
• Splatting (Westover 1990)
• Object order
• Shear Warp (Lacroute 1994, 1996)
• Hybrid order

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Ray Casting
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• Cast a ray from the viewpoint to the volume for
  all pixels
• Obtain samples from the volume in equal
  intervals, by trilinearly interpolating
  neighbouring voxels. Accumulate with some
  operator to get final colour.
• Several acceleration techniques have been
  suggested (early ray termination (Levoy 1990),
  adaptive sampling, octrees (Ogata et al. 1998),
  kd-trees(Wald et al 2005)

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Shear-Warp
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• Considered the fastest known Direct Volume
  Rendering algorithm.
• Steps
• Transform volume to sheared object space
• Project sheared slices on an intermediate image
• Transform the intermediate image to image space
• Requires 3 copies of the data, for every
  principal axis, but RLE compression can help.

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Characteristics of modern x86 processors

• Deep instruction pipeline.
• Very sophisticated hardware branch prediction
• 2 levels of cache, supports software prefetching
• Rich SIMD instruction set

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The CELL processor
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• Developed jointly by IBM, Sony and Toshiba
• Combines a PowerPC general purpose processor with
  8 separate SIMD execution units (SPUs).
• Exceptional FLOPS / cost ratio and more powerful
  than the Itanium!
• Needs fast memory, which is relatively expensive

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Notable Characteristics of the SPUs
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• Software managed local store (i.e. no caches)
• No branch prediction, expensive branch misses
• SIMD loads/stores ONLY
• Favors streaming code

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Motivation for a new algorithm
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• Ray Casting algorithms are typically not cache
  friendly. Performance depends on viewing axis.
• Acceleration structures may produce non-streaming
  code and several overheads.
• Shear Warp may require too much memory for
  certain data.

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A Coherent Grid Traversal Algorithm for Volume
Rendering (1)
UCL Department of Computer Science

• Original idea from Ray Tracing Animated Scenes
  using Coherent Grid Traversal (Wald et al,
  SIGGRAPH 2006).
• Bundles (frustums) of coherent rays are traced in
  grid space, by incrementaly computing the overlap
  with grid slices. The overlap of the frustum is
  computed with a SIMD addition and a SIMD
  truncation only

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A Coherent Grid Traversal Algorithm for Volume
Rendering (2)
UCL Department of Computer Science

• The volume rendering version of the algorithm
  uses a bricked volume (Sakas et al 1994),
  bricks replace the grid elements.
• Bricks are referenced by 3 maps, one for each
  principal axis.
• Compression is achieved by not storing empty
  bricks.

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A Coherent Grid Traversal Algorithm for Volume
Rendering (3)
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A Coherent Grid Traversal Algorithm for Volume
Rendering (4)
UCL Department of Computer Science

• Traversal is performed on the principal axis,
  using the corresponding map.
• Indices are computed incrementally.
• If all the overlapping bricks of a slice are
  empty, the slice is skipped.
• If some bricks are empty, they are associated
  with a locally stored empty brick and processed
  redundantly (but not fetched).

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A Coherent Grid Traversal Algorithm for Volume
Rendering (examples)
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Bundle Parallelisation
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• Bundle Parallelisation is trivial. On a x86 C
  OpenMP implementation, it only required 1 line of
  code.
• It is possible to have some blocks fetched
  multiple times from neighbouring bundles.

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Slice Parallelisation
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• A slice parallelisation is less likely to exhibit
  this problem, but traversal of brick slices is
  not incremental!
• So, how would the processing element know which
  bundles to process for a given slice?

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Slice Parallelisation
UCL Department of Computer Science

• Most bundles will start on k0, or end on kkmax
  (or both).
• During tracing, we create 2 vectors of references
  to bundles, we shall call them A and D, along
  with 2 index tables for the corresponding slices
  we shall call P and Q .
• The bundles that run through a given slice s can
  be expressed as
• Only 2 memory reads are required for that, or no
  memory reads if the bundles are large enough for
  A and D to fit in the cache/local store.

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Slice Parallelisation
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• Remaining bundles can take up to 33 (they are
  about 14 average).
• We use two more lists, we shall call S and E with
  index tables M and N. S holds references to the
  remaining bundles sorted by the first slice they
  intersect, and E sorted by the last.
• Remaining bundles that run through s are
• We need to run through both these lists to find
  that out, but this does not hit performance.

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A notable problem of the CGT algorithm as
described in Wald 2006

• When the roll angle of the bundles to the
  respective angle of the volume is close to p/4,
  the number of blocks fetches can be double than
  the number required.
• There is a good solution to that (not yet
  published).

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Results
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• First results demonstrated an speed increase of
  up to 2 orders of magnitude from ray-casting.
• This may increase with further optimisations

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Conclusion

• We have developed a scalable algorithm for
  coherent volume traversal with performance on-par
  with the Shear Warp, with reduced memory
  requirements.
• We demonstrated parallel implementations.

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Future Work

• Investigate mixed parallelisation schemes
• Optimise the computation performed per brick.

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The End
UCL Department of Computer Science

• Thank you for your attention
• Questions?