Title: 3D Geometry Coding using Mixture Models and the Estimation Quantization Algorithm
13D Geometry Coding usingMixture Models andthe
Estimation Quantization Algorithm
- Sridhar Lavu
- Masters Defense
- Electrical Computer Engineering
DSP Group
Rice University
September 2002
23D Surfaces
- Video games
- Animations - Bugs Life, Toy Story 2
- 3D object modeling - CAD
- e-commerce
33D Surfaces
- Geometry, color, texture
- 3D scanning
- Polygon meshes
- Problem - large data sets
- Geometry compression
100,000 triangles
4Contribution
- 3D geometry coder
- Multilevel representation
- Normal meshes
- EQ algorithm
- Estimation-Quantization (EQ)
- Local context information
- RD optimization
5Related Work
- Zerotree coder for the wavelet coefficients of
normal meshes - RD optimization based quantization algorithm for
the wavelet coefficients of meshes
6Outline
- 3D surface data
- Multilevel representation
- Normal meshes
- Wavelet transform
- EQ algorithm
- Error metrics
- Results
73D geometry data
- Geometry
- Polygon meshes
- Geometry connectivity
Geometry 0.0 0.0 0.0 1.0 0.0 0.0 1.0 1.0 0.0 0.0
1.0 0.0 0.5 0.5 1.0
Connectivity 0 1 2 2 3 1 0 1 4 1 2 4 2 3 4 3 0 4
8Multilevel Representations
Original
Coarse
Multilevel triangular meshes
Original ? Normal meshes
9Normal meshes
- Multilevel representation
- Base mesh
- Successively refine the mesh
- Subdivision
10Subdivision
- Linear subdivision
- Butterfly subdivision
- Loop subdivision
11Butterfly Subdivision
12Normal Meshes
- Predict b and n
- Find intersection
- Store offset
- 1 number per vertex
13Wavelet Transforms
- Irregular data
- Lifting scheme predict and update
- Subdivision predict step
- Wavelet transforms
- Butterfly wavelet transform
- Loop wavelet transform
14Wavelet Transforms and Normal Meshes
Wavelet coefficients
Non-normal vertices
15Related Work - Zerotree
Zerotrees
Mesh zerotree coding
Mesh zerotree
Zerotree coding
EQ coding
16Review
- Multilevel representations for meshes
- Normal meshes
- Wavelet transforms
- Subdivision
- Lifting
- Related work - ZT based algorithm
- Contribution EQ based algorithm
173D EQ Coder
- Local context information
- Model for wavelet coefficients
- Generalized Gaussian distribution
- EQ Algorithm
- Estimate Step
- Quantize Step
- RD Optimization
18Wavelet Coefficient Model
- Generalized Gaussian distribution
19Wavelet Coefficient Model
- Generalized Gaussian (GGD)
- ? Shape Fixed at each level
- ? Variance Local neighborhood
- ? Mean Zero
20EQ Algorithm
- Scan the vertices
- Estimate, quantize, encode
- Estimate step - variance
- Local neighborhood
- Causal neighborhood
- Quantized neighbors
- Quantize step
- Deadzone quantizer
- RD optimization
21EQ Algorithm (cont.)
- RD optimization
- Rate -log(probability)
- Distortion MSE of coefficients
- Entropy coding
- Arithmetic coder
22Normal vs. Tangential
- Smooth surfaces
- Global error contribution
- Normal Higher
- Tangential Lower
- Precision
- Normal Higher Lower l
- Tangential Lower Higher l
- Most tangential components are zero
- Single quantizer per level
23Neighborhood
24Ordering - Base Triangles
25Ordering - Vertices
26Summary of EQ Algorithm
- Pick l
- Determine ordering
- Ordering of base triangles
- Ordering inside each base triangle
- Local causal neighborhood
- Estimate s
- Quantize using RD optimization
- Normal vs. tangential
27Performance Measure
- Error metrics
- MSE ?
- Hausdorff distance
- Min, max, mean, mean squared
28Results
- Metric - PSNR
- Bits-per-vertex (bpv)
- Reconstructed mesh vs. original mesh
- Metro and MeshDev software tools
29Results - EQ vs. ZT
30Results EQ vs. ZT(Lifted Butterfly)
31Results - EQ vs. ZT(Loop Wavelets)
32Results (Bounds)
- Upper bound
- Complete context
- Lower bound
- No context
33Summary
- Multilevel representations
- Normal meshes
- Wavelet transforms
- GGD model
- Local context based coder
- EQ vs. ZT
34Conclusion Future Work
- Conclusions
- GGD model EQ algorithm
- 0.5 1 dB gain
- Future work
- Vertex based error for RD optimization
- New algorithms
- Space-Frequency quantization (SFQ)
35(No Transcript)
36Scaling Coefficients andConnectivity
- Scaling coefficients
- Vertices of base mesh
- Uniform quantization
- Connectivity
- Semi-regular connectivity
- Base mesh connectivity
- TG Coder (lossless)
37Lifting (Predict, Update)
Forward
Inverse
38Lifting - Haar
39Loop Wavelet Transform
40Causal Neighborhoods
41EQ Unpredictable sets
- Empty causal neighborhood
- Zero s estimate
- Classify as unpredictable (U) set
- Model U set as zero-mean GGD
- Use a single s and n for U set
42EQ Threshold step
- Iteration of E and Q steps
- First iteration
- Threshold coefficients
- Partition U and P sets
- Estimate s and n
- Use estimates in next iteration
43Normal Predictable Set
44Normal Unpredictable Set
45Tangential Set
46Hausdorff Distance
47Mesh Zerotree Coding
48Results Venus PSNR
49Results Rabbit PSNR