Streaming Compression of Triangle Meshes

1
Streaming Compressionof Triangle Meshes
Martin Isenburg University of Californiaat
Berkeley
Jack Snoeyink University of North Carolina at
Chapel Hill
Peter Lindstrom Lawrence LivermoreNational Labs
2
Compression
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Compression

• physical
• sleeping bags
• compressed air

4
Mesh Compression
Geometry Compression Deering, 95

• Efficient Rendering
• Progressive Transmission
• Maximum Compression

5
Current Schemes
Triangle Mesh Compression Touma Gotsman 98
Cut-Border Machine Gumhold Strasser 98
Edgebreaker Rossignac 99
Face Fixer Isenburg Snoeyink 00
Angle Analyzer Lee, Alliez Desbrun 02
Degree Duality Coder Isenburg 02
Out-of-Core Compression Isenburg Gumhold 03
FreeLence Kälberer et al. 05
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Current Approach
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Current Approach
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Underlying Assumption

• original ordering of vertices and triangles is
  not important
• no need to preserve it
• compressor is allowed to re-order

• impose canonical ordering
• only encode connectivity graph
• re-order mesh based on some deterministic
  traversal

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Original Orderings
rendering the first 20to 40 percent of
thetriangle array
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Connectivity Traversal
Entire Mesh As Input
vertices
triangles
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Large Meshes
3D scans
isosurfaces
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Large Meshes
3D scans
isosurfaces
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Limited Main Memory

• impossible to construct / store data structures
  for mesh traversal

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Out-of-Core Compression

• OoC-Mesh
• on-disk clustering
• construct in advance
• cache LRU clusters
• OoC-Compressor
• make few queries

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Out-of-Core Compression

• OoC-Mesh
• on-disk clustering
• construct in advance
• cache LRU clusters
• OoC-Compressor
• make few queries
• Decompression
• streaming

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Streaming
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Streaming

• physical
• water in a pipe
• drip coffee

• triangle meshes

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Two Types of Streaming

• progressive

?
?
?
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Non-Progressive Streaming

• consume immediately
• potentially without end
• keep small buffer
• delete data if no longer needed

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Streaming Mesh Formats

• interleave introduce finalize

Streaming Meshes Isenburg and Lindstrom 05
v 1.32 0.12 0.23v 1.43 0.23 0.92v
0.91 0.15 0.62f 1 2 3done 2 v
0.72 0.34 0.35f 4 1 3done 1 v
0.72 1.03 0.35 ? ? ? ?
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Outputting Streaming Meshes

• isosurface
• 235 million vertices
• 469 million triangles

over8 Gigabyte

• marching cubes
• extract layer by layer
• output elements as extracted
• finalize vertices of previous layer

Richtmeyer-Meshkov instability simulation at LLNL
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Streaming Simplification
Stream Algorithm for Wu Kobbelt 03
Large Mesh Simplification Isenburg et al.
03
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Streaming Compression
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Streaming Compression (1)

• streaming API

bool open(FILE file, int bits) bool
write_vertex(float position)bool
write_triangle(int index, bool finalize) bool
close()
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Streaming Compression (2)

• when writing a vertex
• insert in hash

• when writing a triangle
• look-up active vertices
• determine configuration
• compress triangle
• positions of new vertices
• remove finalized data structures

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Possible Configurations
written triangle
start
add
fill
start1
end
join
active elements
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Compressing a Triangle

• configuration

• specify active vertex
• log2(width) bits
• better use cache

add

• specify other active vertices
• use local edge lists

• position of new vertices
• parallelogram prediction

• finalization flags

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Demo

• compress triangles immediately

• use delay buffer

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Greedy Local Reordering
Improving connectivity compression by reordering
triangles in a delay buffer
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lucy
16
14
(original)
12
(spectral)
10
bpv
(geometric)
8
(breadth)
6
4
(depth)
2
st. matthew
0
(original)
25
50
1K
5K
100
250
500
10K
50K
(spectral)
none
(geometric)
delay buffer size
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out-of-core
344 MB
compressed
(coordinates uniformly quantized to 18 bits)
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Example Processing Pipeline
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Pipelined Stream-Processing

• conventional processing

• super-linear speedup
• minimal end-to-end I/O delay
• optimal disk caching

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Demo Pipeline
regular volume grid
v 1.32 0.12 0.23v 1.43 0.23 0.92v
0.91 0.15 0.62f 1 2 3done 2 v
0.72 0.34 0.35f 4 1 3done 1 ?
? ? ?
256
256
256
smextract smclean smsimp smcompress
P2
P3
P1
P4
grid.raw
mesh.smc
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Conclusion
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Current Schemes do not Scale
9 GB
1 MB
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Problems of Current Schemes
entire mesh as input
IO-inefficient for large data
186 million vertices(2 GB)
dedicated out-of-core data structure(11
GB) global reordering ofmesh
duringcompression
372 milliontriangles(4 GB)
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Streaming Approach
bool open(FILE file, int bits) bool
write_vertex(float position)bool
write_triangle(int index, bool finalize) bool
close()
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out-of-core
344 MB
compressed
(coordinates uniformly quantized to 18 bits)
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Alternate Approaches

• different re-ordering strategy
• higher correlation
• deterministic growing strategy
• let compressor choose correct
• degree-based coding
• need to relax max delay constraint
• geometry
• local coordinate system, angles,

• connectivity

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Compressing Volume Meshes
standard
streaming
2.14 bpt
3.88 bpt
rate
torso
7 min
8 sec
time
115 MB
3 MB
memory
1.81 bpt
3.56 bpt
rate
fighter
11 min
12 sec
time
140 MB
6 MB
memory
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Current/Future Work

• implement more stream modules
• streaming surface reconstruction
• streaming stripification
• streaming re-meshing
• streaming smoothing
• streaming segmentation
• streaming feature extraction
• streaming

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Acknowledgements

• meshes
• Stanford University, Cyberware
• support
• NSF grant 0429901
• "Collaborative Research Fundamentalsand
  Algorithms for Streaming Meshes."
• U.S. DOE / LLNL W-7405-Eng-48
• Max Planck Institute für Informatik

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Thank You
streaming compression API http//www.cs.unc.edu/
isenburg/smc
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Stream-Processing Modules

• tasks that process mesh elements one at a time
• e.g. for each triangle t
• tasks that only require access to local neighbors
• e.g. for each triangle t of vertex v
• tasks that are order independent
• e.g. collapse edges shorter than ?

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triceratops.obj 2832 vertices 2834
polygonsv 3.661 0.002 -0.738v 3.719
0.347 -0.833v 3.977 0.311 -0.725v 4.077
0.139 -0.654 ? ? ? ? f 2806 2810
2815 2821f 2797 2801 2811 2805f 2789
2793 2802 2796f 2783 2794 2788 ? ?
? ?
2832! permutations
2806
2834! permutations