1. Estimation-Quantization Geometry Coding using Normal Meshes
Sridhar Lavu
Hyeokho Choi Richard Baraniuk
Rice University

2. 3D Surfaces Applications Video games Animations 3D Object modeling
e-commerce

3. 3D Mesh Representation Mesh representation Problem Goal 3D scan
Point clouds
Polygon mesh
Problem
Massive data size
Michelangelo’s statue of David: > billion triangles
Connectivity
0 1 2
2 3 1
0 1 4
1 2 4
2 3 4
3 0 4
Geometry
Goal
Compression

4. Multiscale Representation
Regular or semi-regular meshes
Connectivity  Base mesh connectivity

5. Wavelet Transform Prediction residuals Wavelet transform
3D coefficients (x,y,z)

6. Normal Meshes Normal mesh representation
3D (x,y,z)  1D normal coefficient

7. Wavelet Coefficients Normal wavelet coefficients
Tangential wavelet coefficients
Goal
Model + Encode

8. Wavelet Coefficient Model
Statistical model for normal mesh wavelet coefficients
Expectation-Quantization model [Lopresto, Orchard, Ramchandran], DCC 1997
ni ~ N(0,sigmai2)
sigmai2 = local variance
large  rough region
small  smooth region

9. Details Causal neighborhood Quantized coefficients Estimate sigmai2
Modified model
Generalized Gaussian density
Fixed shape at each scale
Estimate variance for each vertex

10. Vertex Scanning Order
Each scale
Each base triangle

11. Vertex Neighborhood

12. Estimate-Quantization Steps
Estimate step
Shape parameter
Variance parameter
R-D optimized quantize step
Rate = - log probability
Distortion = MSE of coefficient
Pick a lambda R-D operating point
Entropy code
Arithmetic coder

13. Summary

14. Error Metrics Different surfaces MSE Metro Original mesh surface
Normal re-meshing
EQ algorithm coded mesh
MSE
Metro
“average distance between two meshes”
Hausdorff distance

15. PSNR Plots
0.5 – 1dB gain over zero-tree coder [Guskov, Vidimce, Sweldens, Schroder], SIGGRAPH 2000
Similar results with other data sets

16. Conclusions
0.5 – 1dB gain
Over state-of-the-art mesh zerotree coder
3D surfaces much easier to compress than 2D images
Very smooth (continuous)
Worst case: sharp crease
Future research
More appropriate distortion metrics in normal mesh wavelet domain