A Coherent Grid Traversal Algorithm for Volume Rendering Ioannis Makris Supervisors: Philipp...

A Coherent Grid Traversal Algorithm for Volume Rendering

Ioannis Makris

Supervisors: Philipp Slusallek*, Céline Loscos

*Computer Graphics Lab, Universität des Saarlandes

UCL Department of Computer Science

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Overview

• 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

• 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

• 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

• 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

• 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

• 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

• 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)

• 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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• 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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Original Volume Sparse Blocks

Pointer array fortraversal along y axis

Pointer array fortraversal along x axis

x

y ±y ±x

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• 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

• 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

• 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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• Most bundles will start on k=0, or end on k=kmax (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.


sQkPk DAks

0max

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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.


sNkMk ESks 0\max

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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 π/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

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

Thank you for your attention

Questions?


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