estimation-quantization geometry coding using normal meshes sridhar lavu hyeokho choi richard...
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Estimation-Quantization Geometry Coding
using Normal Meshes
Sridhar LavuHyeokho Choi Richard Baraniuk
Rice University
3D Mesh Representation• Mesh representation
– 3D scan– Point clouds– Polygon mesh
Geometry0.0 0.0 0.01.0 0.0 0.01.0 1.0 0.00.0 1.0 0.00.5 0.5 1.0
Connectivity0 1 22 3 10 1 41 2 42 3 43 0 4• Goal
– Compression
• Problem – Massive data size– Michelangelo’s statue
of David: > billion triangles
Wavelet Coefficients• Normal wavelet coefficients• Tangential wavelet coefficients
• Goal – Model + Encode
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
Details
• Causal neighborhood– Estimate sigmai
2
• Quantized coefficients– Modified model– Generalized Gaussian density– Fixed shape at each scale– Estimate variance for each vertex
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
Error Metrics• Different surfaces
– Original mesh surface– Normal re-meshing– EQ algorithm coded mesh
• MSE
• Metro– “average distance between two
meshes”– Hausdorff distance
PSNR Plots• 0.5 – 1dB gain over
zero-tree coder [Guskov, Vidimce, Sweldens, Schroder], SIGGRAPH 2000
• Similar results with other data sets