Estimation-Quantization Geometry Coding using Normal Meshes

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
• 3D scan
• Point clouds
• Polygon mesh

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

• Problem
• Massive data size
• Michelangelos statue of David gt billion
  triangles

• 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 modelLopresto,
  Orchard, Ramchandran, DCC 1997
• ni N(0,sigmai2)
• sigmai2 local variance
• large ? rough region
• small ? smooth region

9
Details

• Causal neighborhood
• Estimate sigmai2
• Quantized coefficients
• 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
• 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