Lossless Compression of FloatingPoint Geometry

1
Lossless CompressionofFloating-Point Geometry
Martin Isenburg UNCChapel Hill
Peter Lindstrom LLNLLivermore
Jack Snoeyink UNCChapel Hill
2
Overview

• Motivation
• Geometry Compression
• Predictive Schemes
• Corrections in Floating-Point
• Results
• Conclusion

3
Meshes and Compression
146 MB
3 MB
UNCpower-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 Compressionof 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 GeometryCompression 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 Compressionfor 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 compressionfor 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 forMesh
Encoding Sorkine et al., 03
19
Overview

• Motivation
• Geometry Compression
• Predictive Schemes
• Corrections in Floating-Point
• Results
• Conclusion

20
Predictive Coding

• quantize positions with b bits
• predict from neighbors
• compute difference
• compress with entropy coder

21
Predictive Coding

• quantize positions with b bits
• predict from neighbors
• compute difference
• compress with entropy coder

22
Predictive Coding

• quantize positions with b bits
• predict from neighbors
• compute difference
• compress with entropy coder

23
Predictive Coding

• quantize positions with b bits
• predict from neighbors
• compute difference
• 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 vectorwith 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
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
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!
• ?????????,????!