GPU Acceleration of Iterative Clustering

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GPU AccelerationofIterative Clustering

• Jesse D. Hall
• John C. Hart
• University of Illinois, Urbana-Champaign

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Iterative Clustering(aka k-means/Lloyds/LBG
Alg.)
Partitioning Assign eachpoint to
nearestcluster center
Fitting Find newcenter foreach cluster
Initialization Pick (random)collection
ofcluster centers
Cluster bunnies courtesy Nate Carr
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Applications

• Vector quantization
• Image compression (Gersho Gray, VQ Signal
  Compression, 92)
• Light field compression (Levoy Hanrahan, S96)
• Texture synthesis (Wei Levoy, S00)
• Clustered principal component analysis
• Precomputed radiance transfer (Sloan, us
  Snyder, S03)
• Mesh clustering
• Multichart geometry images (Sander et al., SGP03)
• Variational Shape Approx. (Cohen-Steiner et al.,
  S04)

Vector quantization of a light field Levoy
Hanrahan, S96
Vector quantization ofradiance transfer
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Clustering of
Orientation
Illumination
Position
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CPU GPU Approach

• GPU Partitioning
• Metric evaluation independent for each point
• Metric evaluation usually not data dependent
• Ideal for SIMD streaming implementation
• CPU Fitting
• Fitting inherently a reduction operation
• Relies on sophisticated data structures (e.g.
  kd-trees) and processes (e.g. matrix
  eigenstructure)

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GPU Partitioning

• Load cluster center and ID into fragment shader
  constants
• Fragment shader evaluates metric on point data
  stored in (deep) texture
• Distance stored in z-buffer if less than current
  z-value (and ID written to framebuffer)
• After all clusters processed, framebuffer
  contains IDs of nearest cluster for each
  datapoint
• Requires z-buffer readback which will be faster
  with PCI-Express

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Hierarchical GPU Partitioning
or

• Organize cluster centers in a kd-tree
• Point may need to backtrack severaltimes to find
  best cluster
• Nevertheless O(n log k) in practice
• Requires lots of decisions per point whichwould
  hinder GPU implementation
• Instead send group (e.g. previouscluster) of
  datapoints simultaneouslythrough kd-tree
• Traverse based on groups bounding box
• Keep track of individual points closest distance
  and ID
• Groups organized as rectangles in texture memory

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Clustered Principal Components for Precomputed
Radiance Transfer

• Lloyds Algorithm on PRT datasets would take hours
  on John Snyders PC, ran overnight
• Can implement CPCA cluster metric in Cg
• Final result is d2
• VDIM of 4-vectors needed to store a point
• NPCA of PCA basis vectors
• More complex than Euclidean distance, but same
  of texture fetches

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GPU CPU v. CPU
NVIDIA GeForce FX 5900 vs. AMD Athlon XP
2800 16D points, 128 clusters
3x
10
16K points, 128 clusters
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64K 16D points
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Conclusions

• GPU CPU 3x faster than CPU alone
• Slower CPU fared just as well ? process is
  bandwidth limited
• Scales well even with of clusters which
  corresponds to of fragment program state
  changes ? process dominated by floating point
  performance
• GPU valuable for preprocessing