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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Seminar

Geometry Compression for 3D Streaming

Paolo Simone Gasparello

Scuola Superiore S. Anna

May 11, 2010

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Outline

1 Concepts

2 Geometry

3 Connectivity

4 Entropy coding

5 Experimental Results

6 Discussion

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Motivations

Data ling3D scanners can produce very large meshes with many millionsof polygons requiring hundreds of Mb of storage.

Data transmissionApplications such as Distibuted VEs often require thetransmission of large 3D models over WANnetwork.

Very high compression ratioNewest algorithms can drastically reduce the memory impringof complex 3D models (over 90%).

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Motivations

Data ling3D scanners can produce very large meshes with many millionsof polygons requiring hundreds of Mb of storage.

Data transmissionApplications such as Distibuted VEs often require thetransmission of large 3D models over WANnetwork.

Very high compression ratioNewest algorithms can drastically reduce the memory impringof complex 3D models (over 90%).

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Motivations

Data ling3D scanners can produce very large meshes with many millionsof polygons requiring hundreds of Mb of storage.

Data transmissionApplications such as Distibuted VEs often require thetransmission of large 3D models over WANnetwork.

Very high compression ratioNewest algorithms can drastically reduce the memory impringof complex 3D models (over 90%).

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Geometry Data

GeometryDescribes where vertices are located inthe 3D world

v i = {x i , y i , z i } i = 1 . . . V

ConnectivityThis information describes the relationsbetween the elements of the mesh:vertices, edges, faces

f i = {v 1 i , . . . , v n i } i = 1 . . . F

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Geometry Data

GeometryDescribes where vertices are located inthe 3D world

v i = {x i , y i , z i } i = 1 . . . V

ConnectivityThis information describes the relationsbetween the elements of the mesh:vertices, edges, faces

f i = {v 1 i , . . . , v n i } i = 1 . . . F

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Geometry Compression

Uniform Quantization of the coordinatesTransmission involves only quantization indices:

Q (x ) =2M x + 0 . 5

2M

Figure: Uniform Quantization

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Geometry Compression

Vertex PredictionParallelogram rule

Figure: Parallelogram predictor

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Valence Based EncodingOverview

Valence of a vertexThe valence of a vertex is the number of incident edges

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Valence Based EncodingConquering the mesh: ADD

Figure: Output: (ADD 6)

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Valence Based EncodingConquering the mesh: Full Focus Vertex

Figure: Output: No Symbol

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3D Geometry

Compression

Paolo SimoneGasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Valence Based EncodingSpecial case: SPLIT

Figure: Output: (SPLIT 11)

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Valence Based EncodingSpecial case: MERGE

Figure: Output: (MERGE l , i )

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Entropy MinimizationArithmetic Encoder

Exployting RedundancyConnectivity symbols are mostly (ADD 6)Prediction errors are mostly 0In general, statistical distribution for symbols is aGaussiancentered at (ADD 6) for connectivity symbols, and at 0 forgeometry symbols

Context-Based Arithmetic Coder

Several contexts with different frequency tables for eachsymbol stream should be used:ConnectivityGeometryOther properties. . .

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Entropy MinimizationArithmetic Encoder

Exployting RedundancyConnectivity symbols are mostly (ADD 6)Prediction errors are mostly 0In general, statistical distribution for symbols is aGaussiancentered at (ADD 6) for connectivity symbols, and at 0 forgeometry symbols

Context-Based Arithmetic Coder

Several contexts with different frequency tables for eachsymbol stream should be used:ConnectivityGeometryOther properties. . .

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Entropy MinimizationArithmetic Encoder

Exployting RedundancyConnectivity symbols are mostly (ADD 6)Prediction errors are mostly 0In general, statistical distribution for symbols is aGaussiancentered at (ADD 6) for connectivity symbols, and at 0 forgeometry symbols

Context-Based Arithmetic Coder

Several contexts with different frequency tables for eachsymbol stream should be used:ConnectivityGeometryOther properties. . .

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

3D Geometry Compressor

In our approach we combine several different techniques toachieve a common goal:Valence Based EncodingGeometry QuantizationVertex Prediction

Arithmetic CodingWe are developing 3D Compression encoders compatibleswith the needs of Virtual Environments characterized by avery high compression ratio (up to 95%).

Raptor Dragon Eros

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3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

3D Geometry Compressor

In our approach we combine several different techniques toachieve a common goal:Valence Based EncodingGeometry QuantizationVertex Prediction

Arithmetic CodingWe are developing 3D Compression encoders compatibleswith the needs of Virtual Environments characterized by avery high compression ratio (up to 95%).

Raptor Dragon Eros

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20/26

3D Geometry

CompressionPaolo Simone

Gasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

3D Geometry Compressor

In our approach we combine several different techniques toachieve a common goal:Valence Based EncodingGeometry QuantizationVertex Prediction

Arithmetic CodingWe are developing 3D Compression encoders compatibleswith the needs of Virtual Environments characterized by avery high compression ratio (up to 95%).

Raptor Dragon Eros

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

3D Geometry Compressor

In our approach we combine several different techniques toachieve a common goal:Valence Based EncodingGeometry QuantizationVertex Prediction

Arithmetic CodingWe are developing 3D Compression encoders compatibleswith the needs of Virtual Environments characterized by avery high compression ratio (up to 95%).

Raptor Dragon Eros

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

Compression Effectiveness

0

5

10

15

20

25

30

35

40

Orig. Quant. Zip Compr. Orig. Quant. Zip Com pr. Orig. Quant . Zip Co mpr .

S i z e

[ 1 0

6 B

y t e s

]

4.96% 4.73% 3.51%

GeometriyConneictvity

Global

Eros 1.1MDragon 1.6MRaptor 2M

Ti i g

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

ConnectivityEntropycoding

ExperimentalResults

Discussion

TimingStreaming compressed meshes can be done in Real-Time?

Vertex ThroughputTo evaluate how fast a mesh can be compressed we canthink in terms of vertex throughput , that is how much of vertices can be trasferred in a second

Vertex throuput is measured in vertices per second [vps]

Measusements

Model Vertices Time [ms] Throughput [vps]

Raptor 1,000,080 4,132 (2,582) 242,013 (387,327)Dragon 655,980 5,851 (1,982) 112,114 (330,968)Eros 476,596 3,940 (1,462) 120,963 (325,989)

Table: Compression (Uncompression) timing parameters

Network Throughput

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Network ThroughputBandwidth requirements

Streaming ThroughputFor streaming non-compressed meshes the bottleneck isalways the available bandwith.

Streaming compressed meshes is instead usually limited byencoder speed.

Measurements

Model Size [Kb] Time [ms] Throughput [Mbps]Raptor 1,787 4,132 3.4Dragon 1,117 5,581 1.6Eros 603 3,940 1.2

Discussion

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

DiscussionFuture work

Improving throughputOur research aims at speeding up the compression process

by using parallel processing techniques (OpenMP,GPGPU).References:

J. Rountree, Novel Technologies for the Manipulation of Meshes on the CPU and GPU

M. Sattler, Simple and efficient compression of animationsequences

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3D GeometryCompression

Paolo SimoneGasparello

Concepts

Geometry

Connectivity

Entropycoding

ExperimentalResults

Discussion

Thank you

Questions?

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