Geometry Compression

1
Geometry Compression

• Michael Deering, Sun Microsystems
• SIGGRAPH (1995)
• Presented by Michael Chung

2
Geometry CompressionWhat is it?

• Lossy technique for reducing the size of geometry
  representation.

3
Motivation

• Save bandwidth and transmission time in graphics
  accelerators and networks.
• Save storage space in main memory and on disk.

4
Proposed Contributions

• Technique for lossy compression ratios of between
  6 and 10 to 1
• Claims only slight losses in object quality
• Depends on original representation format and
  final quality level desired

5
Geometry CompressionWhat is it?

• Trade-off between quality (subjective) and amount
  of compression.
• Compression steps can be reversed for
  decompression

6
Geometry CompressionWhat is it?

• Goal represent geometry with geometry
  compression instructions

7
Insights

• Reduce size of geometry representation in several
  ways.
• Reuse vertices in triangle strip via reference
• Bit shaving
• Geometry is local, encode deltas
• Normals as indices

8
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

9
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

10
Step 1 Conversion to Generalized Triangle Mesh

• generalized triangle strip ? generalized triangle
  mesh
• Generalized triangle strip
• Specifies vertices with four vertex replacement
  codes (2 bits)
• Replace oldest
• Replace middle
• Restart clockwise
• Restart counterclockwise

11
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

12
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

13
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

14
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

15
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

16
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

17
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

18
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

19
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle strip (example)

20
Geometry Compression Instruction Set
21
Geometry Compression Instruction Set
22
Geometry Compression Instruction Set
23
Step 1 Conversion to Generalized Triangle Mesh

• generalized triangle strip ? generalized triangle
  mesh
• Generalized triangle mesh
• Generalized triangle strip
• Mesh buffer
• 16 slot queue
• 4 bit index
• Explicitly push vertices onto mesh buffer for
  reuse.
• We save because only 4 bits are required to
  reference old vertex.

24
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

25
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

26
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

27
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

28
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

29
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

30
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

31
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

32
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

33
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

34
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

35
Step 1 Conversion to Generalized Triangle Mesh

• Generalized triangle mesh (example)

36
Step 1 Conversion to Generalized Triangle Mesh
37
Step 1 Conversion to Generalized Triangle Mesh
38
Geometry Compression Instruction Set
39
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

40
Step 2 Quantization
41
Step 2 Quantization
42
Step 2 Quantization

• Some parts of the geometry may require more or
  less precision than others.

43
Step 2 Quantization

• Some parts of the geometry may require more or
  less precision than others.
• So, the amount of quantization we perform per
  position, normal, and color is variable.

44
Step 2 Quantization

• Position
• 32-bit floating-point coordinates are wasteful.
• 8-bit exponent allows an unnecessary range of
  values.
• 24-bit fixed-point mantissa offers unnecessary
  precision.

45
Step 2 Quantization

• Position
• Based on empirical visual tests, allow at most 16
  bits per component (X, Y, Z)

46
Step 2 Quantization

• Color
• Linear reflectivity values R, G, B, (optional) A
• Range from 0.0 to 1.0 per component
• cap state bit sets alpha ON and OFF
• At most 12 unsigned fraction bits per component

47
Geometry Compression Instruction Set
48
Step 2 Quantization

• Normal
• 96 bits can represent up to 296 different normals
• We dont need so many
• Angular density of 0.01 radians between normals
  visually indistinguishable
• This is about 100,000 normals distributed over a
  unit sphere
• 48 bits to represent a normal (16 bits per X, Y,
  Z)
• We can do better than 48 bits per normal
• Use clever indexing to represent 100,000 normals
  with 18 bits

49
Step 2 Quantization

• Normal
• 96 bits can represent up to 296 different normals
• We dont need so many
• Angular density of 0.01 radians between normals
  visually indistinguishable
• This is about 100,000 normals distributed over a
  unit sphere
• 48 bits to represent a normal (16 bits per X, Y,
  Z)
• We can do better than 48 bits per normal
• Use clever indexing to represent 100,000 normals
  with 18 bits

50
Step 2 Quantization

• Normal
• 96 bits can represent up to 296 different normals
• We dont need so many
• Angular density of 0.01 radians between normals
  visually indistinguishable
• This is about 100,000 normals distributed over a
  unit sphere
• 48 bits to represent a normal (16 bits per X, Y,
  Z)
• We can do better than 48 bits per normal
• Use clever indexing to represent 100,000 normals
  with 18 bits

51
Step 2 Quantization

• Normal
• Take advantage of symmetry
• About 100,000 unit normals distributed across
  unit sphere
• Split unit sphere into 48 symmetrical parts

52
Step 2 Quantization

• 3 bits to specify octant
• 3 bits to specify sextant within octant
• All normals in sextant (2000) stored in a table
• Two orthogonal angular addresses index into table
• At most 6 bits per angular index
• Grand total 6 18 bit index per normal

53
Step 2 Quantization

• 3 bits to specify octant
• 3 bits to specify sextant within octant
• All normals in sextant (2000) stored in a table
• Two orthogonal angular addresses index into table
• At most 6 bits per angular index
• Grand total 6 18 bit index per normal

54
Step 2 Quantization

• 3 bits to specify octant
• 3 bits to specify sextant within octant
• All normals in sextant (2000) stored in a table
• Two orthogonal angular addresses index into table
• At most 6 bits per angular index
• Grand total 6 18 bit index per normal

55
Step 2 Quantization

• What about the 26 normals at the shared corners
  of each sextant?
• These normals belong to more than one sextant,
  but should be represented only once
• 3-bit indices 110 and 111 have not been assigned
  to a sextant
• Use one of these indices to represent the unique
  collection of these 26 normals

56
Step 2 Quantization

• What about the 26 normals at the shared corners
  of each sextant?
• These normals belong to more than one sextant,
  but should be represented only once
• 3-bit indices 110 and 111 have not been assigned
  to a sextant
• Use one of these indices to represent the unique
  collection of these 26 normals

57
Step 2 Quantization

• Angular indices represent a regular grid of
  coordinates in angular space

58
Step 2 Quantization

• Angular indices represent a regular grid of
  coordinates in angular space

59
Step 2 Quantization

• Angular indices represent a regular grid of
  coordinates in angular space

60
Step 2 Quantization

• Summary
• Position 16 bits or less per component
• Color 12 bits or less per component
• Normal 6 18 bits total
• 6 bits to take advantage of symmetry
• 0 12 bits to index table of normals per sextant

61
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

62
Step 3 Delta Encoding

• Represent components with deltas between neighbors

63
Step 3 Delta Encoding
64
Step 3 Delta Encoding

• Represent components with deltas between neighbors

65
Step 3 Delta Encoding

• Represent components with deltas between
  neighbors
• Store histogram of delta group bit lengths
• One histogram per group type (position, normal,
  color)

66
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

67
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

68
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

69
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

70
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

71
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

72
Huffman Encoding

• Huffman encoding assigns shorter tags to more
  frequently encountered data.

73
Step 4 Huffman Tag-Based Variable-Length Encoding

• Assign a Huffman tag to each delta encoded
  position, normal, or color.
• The tag encodes the bit length of the associated
  delta data.

74
Compression Steps

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

75
Geometry Compression Instruction Set
76
Geometry Compression Instruction Set

• Binary output
• Series of geometry compression instructions.
• Initialize Huffman table first, then describe
  geometry.
• Header must be placed in stream before the body
  of the previous instruction
• H1 B0 H2 B1 H3 B2
• This gives hardware time to process header

77
Compression StepsAny Questions?

• Convert triangle data to generalized triangle
  mesh
• Quantization of positions, colors, normals
• Delta encoding of quantized values
• Huffman tag-based variable-length encoding of
  deltas
• Output binary output stream with Huffman table
  initializations and geometry compression
  instructions

78
Results

• Software implementation
• Compression speed 3000 triangles / second
• Decompression speed 10,000 triangles / second
• No information about machine used for evaluation

79
Results
80
Results
81
Results
82
Response

• The technique is supposed to be lossy.
• It would be nice to see example images of this.
• Only one image of an original model is shown.
• For the other model examples, there is no
  original to compare to.
• Paper claims that compression speed is not
  important.
• Is this true for virtual worlds?

83
Response

• The technique is supposed to be lossy.
• It would be nice to see example images of this.
• Only one image of an original model is shown.
• For the other model examples, there is no
  original to compare to.
• Paper claims that compression speed is not
  important.
• Is this true for virtual worlds?

84
Response

• The technique is supposed to be lossy.
• It would be nice to see example images of this.
• Only one image of an original model is shown.
• For the other model examples, there is no
  original to compare to.
• Paper claims that compression speed is not
  important.
• Is this true for virtual worlds?

85
Response

• The technique is supposed to be lossy.
• It would be nice to see example images of this.
• Only one image of an original model is shown.
• For the other model examples, there is no
  original to compare to.
• Paper claims that compression speed is not
  important.
• Is this true for virtual worlds?

86
Summary

• First paper on geometry compression
• Lossy compression of 3D geometry
• Reuse vertices in triangle strip using mesh
  buffer
• Shave bits via variable levels of quantization
• 18-bit indices to reference 48-bit normals
• Delta compression saves bits since geometry tends
  to be local
• Compressed result is 6 to 10 times fewer bits
  than original geometry data

87
Summary

• First paper on geometry compression
• Lossy compression of 3D geometry
• Reuse vertices in triangle strip using mesh
  buffer
• Shave bits via variable levels of quantization
• 18-bit indices to reference 48-bit normals
• Delta compression saves bits since geometry tends
  to be local
• Compressed result is 6 to 10 times fewer bits
  than original geometry data

88
Summary

• First paper on geometry compression
• Lossy compression of 3D geometry
• Reuse vertices in triangle strip using mesh
  buffer
• Shave bits via variable levels of quantization
• 18-bit indices to reference 48-bit normals
• Delta compression saves bits since geometry tends
  to be local
• Compressed result is 6 to 10 times fewer bits
  than original geometry data

89
Summary

• First paper on geometry compression
• Lossy compression of 3D geometry
• Reuse vertices in triangle strip using mesh
  buffer
• Shave bits via variable levels of quantization
• 18-bit indices to reference 48-bit normals
• Delta compression saves bits since geometry tends
  to be local
• Compressed result is 6 to 10 times fewer bits
  than original geometry data