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Lossless Compression of Floating-Point Geometry

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Lossless Compression of Floating-Point Geometry Martin Isenburg UNC Chapel Hill Peter Lindstrom LLNL Livermore Jack Snoeyink UNC Chapel Hill Overview Motivation ... – PowerPoint PPT presentation

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Title: Lossless Compression of Floating-Point Geometry


1
Lossless Compression of Floating-Point Geometry
Martin Isenburg UNC Chapel Hill
Peter Lindstrom LLNL Livermore
Jack Snoeyink UNC Chapel Hill
2
Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

3
Meshes and Compression
146 MB
3 MB
UNC power-plant
127 MB
12,748,510 triangles 11,070,509 vertices
25 MB
4
Floating-Point Numbers
  • have varying precision
  • largest exponent ? least precise

0
128
64
32
16
8
4
x - axis
- 4.095
190.974
5
Samples per Millimeter
16 bit
18 bit
20 bit
22 bit
24 bit
6
No quantizing possible
  • stubborn scientists / engineers
  • Do not touch my data !!!
  • data has varying precision
  • specifically aligned with origin
  • not enough a-priori information
  • no bounding box
  • unknown precision
  • streaming data source

7
Mesh Compression
  • Geometry Compression Deering, 95
  • Fast Rendering
  • Progressive Transmission
  • Maximum Compression

Geometry Compression Deering, 95
Maximum Compression
8
Mesh Compression
  • Geometry Compression Deering, 95
  • Fast Rendering
  • Progressive Transmission
  • Maximum Compression
  • Connectivity
  • Geometry

Geometry Compression Deering, 95
Maximum Compression
Geometry
9
Mesh Compression
  • Geometry Compression Deering, 95
  • Fast Rendering
  • Progressive Transmission
  • Maximum Compression
  • Connectivity
  • Geometry
  • lossy
  • lossless

Geometry Compression Deering, 95
Maximum Compression
Geometry
lossless
10
Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

11
Geometry Compression
  • Classic approaches 95 98
  • linear prediction

Geometry Compression Deering, 95
Geometric Compression through topological
surgery Taubin Rossignac, 98
Triangle Mesh Compression Touma Gotsman, 98
12
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

13
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

Spectral Compression of Mesh Geometry Karni
Gotsman, 00
14
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

Progressive Geometry Compression Khodakovsky et
al., 00
15
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

Geometric Compression for interactive
transmission Devillers Gandoin, 00
16
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

Vertex data compression for triangle meshes Lee
Ko, 00
17
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

Angle-Analyzer A triangle- quad mesh
codec Lee, Alliez Desbrun, 02
18
Geometry Compression
  • Classic approaches 95 98
  • linear prediction
  • Recent approaches 00 03
  • spectral
  • re-meshing
  • space-dividing
  • vector-quantization
  • angle-based
  • delta coordinates

High-Pass Quantization for Mesh
Encoding Sorkine et al., 03
19
Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

20
Predictive Coding
  1. quantize positions with b bits
  2. predict from neighbors
  3. compute difference
  4. compress with entropy coder

21
Predictive Coding
  1. quantize positions with b bits
  2. predict from neighbors
  3. compute difference
  4. compress with entropy coder

22
Predictive Coding
  1. quantize positions with b bits
  2. predict from neighbors
  3. compute difference
  4. compress with entropy coder

23
Predictive Coding
  1. quantize positions with b bits
  2. predict from neighbors
  3. compute difference
  4. compress with entropy coder

24
Arithmetic Entropy Coder
  • for a symbol sequence of t types

t
1
?
Entropy pi log2( ) bits
pi
i 1
of type t
pi
total
25
Deering, 95
  • Prediction Delta-Coding
























processed region

unprocessed region





26
Taubin Rossignac, 98
  • Prediction Spanning Tree

processed region
unprocessed region
27
Touma Gotsman, 98
  • Prediction Parallelogram Rule

processed region
unprocessed region
28
Talk Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

29
Corrective Vectors ?
compute difference vector with integer arithmetic
30
32-bit IEEE Floating-Point
X
X X X X X X X X
X X X X X X X X X X X X X X X X X X X X X X X
1 bit sign
8 bit exponent
23 bit mantissa
0

½
- 1
1
- 2.0
2.0
- 4.0
4.0
- 8.0
8.0
16.0
-16.0
31
32-bit IEEE Floating-Point
X
X X X X X X X X
X X X X X X X X X X X X X X X X X X X X X X X
1 bit sign
8 bit exponent
23 bit mantissa
0

½
- 1
1
- 2.0
2.0
- 4.0
4.0
- 8.0
8.0
16.0
-16.0
01999a
82
1
75c284
7a
1
49999a
82
0
32
Floating-Point Corrections (1)
position
prediction
33
Floating-Point Corrections (2)
position
prediction
1
82
01999a
1
81
7ccccd
34
Floating-Point Corrections (3)
position
prediction
1
7a
75c284
0
7c
0f5c29
35
Talk Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

36
Results bpv
model
buddha david power plant lucy
raw
gzip -9
55.8 56.1 23.7 78.7
96.0 96.0 96.0 96.0
37
Percentage of Unique Floats
82.4
77.2
y
z
53.4
49.0
42.0
x
40.2
37.6
x
z
28.9
x
y
22.2
y
z
4.4
2.0
1.5
x
z
y
buddha
david
powerplant
lucy
38
Completing, not competing !!!
model
buddha david power plant lucy
16 bit
21.8 12.5 11.6 14.6
39
Simpler Scheme (Non-Predictive)
A
40
Simpler Scheme (Predictive)
A
41
Talk Overview
  • Motivation
  • Geometry Compression
  • Predictive Schemes
  • Corrections in Floating-Point
  • Results
  • Conclusion

42
Summary
  • efficient predictive compression of
    floating-point in a lossless manner
  • predict in floating-point
  • break predicted and actual float into several
    components
  • compress differences separately
  • use exponent to switch contexts
  • completing, not competing

43
Current / Future Work
  • investigate trade-offs
  • compression versus throughput
  • optimize implementation
  • run faster / use less memory
  • improve scheme for sparse data
  • quantize without bounding box
  • guarantee precision
  • learn bounding box

44
Acknowledgments
  • funding
  • LLNL
  • DOE contract No. W-7405-Eng-48
  • models
  • Digital Michelangelo Project
  • UNC Walkthru Group
  • Newport News Shipbuilding

45
  • Thank You!
  • ?????????,????!
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