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3D Mesh Compression in Open3DGC
Khaled MAMMOU
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1, 3, 7 1, 7, 6 1, 6, 2 1, 2, 4 1, 4, 5
Connectivity
‒ Indexed Face Set
‒ Geometry: positions
‒ Connectivity: list of triangles
‒ Redundancy
‒ Indexes repeated multiple times
‒ No need to preserve triangles and vertices order
‒ No need for 32-bit precision for positions/attributes
‒ Neighbour vertices exhibit high geometry correlations
Requires 192 bits per vertex!
1 2 3 4 5 6 7
X1, Y1, Z1 X2, Y2, Z2 X3, Y3, Z3 X4, Y4, Z4 X5, Y5, Z5 X6, Y6, Z6 X7, Y7, Z7
Geometry
X3, Y3, Z3 X7, Y7, Z7 X6, Y6, Z6 X2, Y2, Z2 X4, Y4, Z4 X5, Y5, Z5 X1, Y1, Z1
7, 5, 6 7, 4, 5 7, 3, 4 7, 1, 2 7, 2, 3
Reordered geometry
Reordered Connectivity
Lossy geometry compression and lossless connectivity encoding reduce the stream size to 10-20 bpv
V2
V6
V7
V3
V1
V4
V5
OPPORTUNITIES FOR COMPRESSION
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Connectivity
Encoder
Arithmetic or ASCII
Encoding
[Mammou’09] K. Mammou, T. Zaharia, F. Prêteux, “TFAN: A low complexity 3D mesh compression algorithm” Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009
TFAN-based Connectivity Encoding
Prediction Uniform
Quantization Geometry
Compressed
stream
‒ Algorithm based on TFAN codec [Mammou’09]
‒ Triangular meshes with attributes
‒ Arbitrary topologies (e.g., manifold or not, open/closed, oriented or not, arbitrary genus, holes…)
‒ MPEG-SC3DMC (Scalable Complexity 3D Mesh Coding) published in 2010
ENCODER OVERVIEW
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Connectivity
Encoder
Arithmetic or ASCII
Encoding
[Mammou’09] K. Mammou, T. Zaharia, F. Prêteux, “TFAN: A low complexity 3D mesh compression algorithm” Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009
TFAN-based Connectivity Encoding
Prediction Uniform
Quantization Geometry
Compressed
stream
‒ Algorithm based on TFAN codec [Mammou’09]
‒ Triangular meshes with attributes
‒ Arbitrary topologies (e.g., manifold or not, open, closed, holes…)
‒ MPEG-SC3DMC (Scalable Complexity 3D Mesh Coding) published in 2010
ENCODER OVERVIEW
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ENCODER OVERVIEW
‒ Uniform quantization
‒ Map real numbers to integers
‒ Maximum quantization error
Uniform quantization reduces the number of bits per vertex for positions
from 96 bpv to 24 bpv
q=8 q=6 q=4 q=10 Original
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Connectivity
Encoder
Arithmetic or ASCII
Encoding
[Mammou’09] K. Mammou, T. Zaharia, F. Prêteux, “TFAN: A low complexity 3D mesh compression algorithm” Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009
TFAN-based Connectivity Encoding
Prediction Uniform
Quantization Geometry
Compressed
stream
‒ Algorithm based on TFAN codec [Mammou’09]
‒ Triangular meshes with attributes
‒ Arbitrary topologies (e.g., manifold or not, open, closed, holes…)
‒ MPEG-SC3DMC (Scalable Complexity 3D Mesh Coding) published in 2010
ENCODER OVERVIEW
![Page 7: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/7.jpg)
‒ Geometry prediction
‒ Exploit connectivity information
‒ Differential and “parallelogram” prediction
ENCODER OVERVIEW
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‒ Geometry prediction
‒ Exploit connectivity information
‒ Differential and “parallelogram” prediction
‒ Adaptively choose the best predictor
Geometry prediction reduces the number of bits per vertex for positions
from 24 bpv to 10.3 bpv
ENCODER OVERVIEW
![Page 9: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/9.jpg)
Connectivity
Encoder
Arithmetic or ASCII
Encoding
[Mammou’09] K. Mammou, T. Zaharia, F. Prêteux, “TFAN: A low complexity 3D mesh compression algorithm” Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009
TFAN-based Connectivity Encoding
Prediction Uniform
Quantization Geometry
Compressed
stream
‒ Algorithm based on TFAN codec [Mammou’09]
‒ Triangular meshes with attributes
‒ Arbitrary topologies (e.g., manifold or not, open, closed, holes…)
‒ MPEG-SC3DMC (Scalable Complexity 3D Mesh Coding) published in 2010
ENCODER OVERVIEW
![Page 10: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/10.jpg)
‒ Triangle FAN
‒ Each two successive triangles share a common edge
‒ All triangles share a common vertex (i.e., center of the TFAN)
‒ All the triangles have the same orientation
‒ Described by enumerating the vertices in their traversal order
7 indices instead of 15 for IFS
(1,3,7,6,2,4,5)
Implicitly encodes adjacency information
ENCODER OVERVIEW
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‒ TFAN-based connectivity compression
‒ Decompose the mesh into a set of TFANs ‒ Traverse the vertices from neighbour to neighbour
‒ Rename vertices according to the traversal order
‒ For each vertex, group its incident non-visited triangles into TFANs
V’7
V’8
V’9
V’10
V’1
V’2 V’3
V’5
V’6
V’4
V1
V4 V6
V5 V7
V3
V8
V10 V2
V9
ENCODER OVERVIEW
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‒ TFAN-based connectivity compression
‒ Decompose the mesh into a set of TFANs ‒ Traverse the vertices from neighbour to neighbour
‒ Rename vertices according to the traversal order
‒ For each vertex, group its incident non-visited triangles into TFANs
‒ Encode TFANs ‒ Distinguish 10 topological configurations
‒ Use local indices instead of absolute ones
ENCODER OVERVIEW
![Page 13: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/13.jpg)
‒ TFAN-based connectivity compression
‒ Decompose the mesh into a set of TFANs ‒ Traverse the vertices from neighbour to neighbour
‒ Rename vertices according to the traversal order
‒ For each vertex, group its incident non-visited triangles into TFANs
‒ Encode TFANs ‒ Distinguish 10 topological configurations
‒ Use local indices instead of absolute ones
‒ Entropy encoding ‒ Exploit statistical redundancy
TFAN-based connectivity compression reduces the number of bits per vertex for
connectivity from 96 bpv to 3.1 bpv
0%
20%
40%
60%
80%
100%
1 2 3 4 5 6 7 8 9 10 Fr
eq
ue
ncy
TFAN configurations
ENCODER OVERVIEW
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Vertex re-ordering
Neighbors list
Bitstream
10
CONNECTIVITY ENCODING EXAMPLE
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10 1,(7,1)
Vertex re-ordering
Neighbors list
V1 → V1 {}
Bitstream
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V4}
V6 → V2
V4 → V3
Bitstream
10 1,(7,1) 2,(4,1)
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V4, V5}
V6 → V2
V4 → V3
V5 → V4
Bitstream
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
10 1,(7,1) 2,(4,1),(7,2)
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V5, V2, V9, V7}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V9}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1)
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V7,V10}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
V10 → V8
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2)
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V7,V10,V8}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
V10 → V8
V8 → V9
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1)
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
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Vertex re-ordering
Neighbors list
V1 → V1 {V3}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0
V10 → V8
V8 → V9
V3 → V10
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
![Page 24: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/24.jpg)
Vertex re-ordering
Neighbors list
V1 → V1 {V8}
V6 → V2
V4 → V3
V5 → V4
V2 → V5
V9 → V6
V7 → V7
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0
V10 → V8
V8 → V9
V3 → V10
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY ENCODING EXAMPLE
![Page 25: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/25.jpg)
Neighbors list
{}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
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Neighbors list
{V3}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 27: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/27.jpg)
Neighbors list
{V3, V4}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
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Neighbors list
{V4}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 29: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/29.jpg)
Neighbors list
{}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 30: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/30.jpg)
Neighbors list
{V6}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 31: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/31.jpg)
Neighbors list
{V7, V8}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 32: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/32.jpg)
Neighbors list
{V7, V8, V9}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
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Neighbors list
{V9}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 34: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/34.jpg)
Neighbors list
{V10}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 35: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/35.jpg)
Neighbors list
{}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
C1
C2
C3
C6
C7
C8
C4
C5
C9
C10
CONNECTIVITY DECODING EXAMPLE
![Page 36: 3D Mesh Compression in Open3DGC - GitHub · Computer Animation and Virtual Worlds, Vol. 20(2-3), pp. 343–354, 2009 TFAN-based Connectivity Uniform Quantization Geometry Compressed](https://reader034.vdocument.in/reader034/viewer/2022050522/5fa58de6aa11e50b134ab269/html5/thumbnails/36.jpg)
Neighbors list
{}
Bitstream
10 1,(7,1) 2,(4,1),(7,2) 0 0 1,(4, 1) 2,(6,2),(4,1) 0 0 0 0
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CONNECTIVITY DECODING EXAMPLE