Isocharts: StretchDriven Parameterization via Nonlinear Dimension Reduction

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Iso-charts Stretch-Driven Parameterizationvia
Nonlinear Dimension Reduction

• Kun Zhou, John Snyder, Baining Guo, Harry Shum

presented at SGP, June 2004
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Goals of Mesh Parameterization
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Stretch-Driven Parameterization

• Advantages
• measures distortion properly for texturing apps
• Disadvantages
• requires nonlinear optimization (slow!)
• provides no help in forming charts
• resort to simple heuristics like planarity or
  compactness
• Solution apply Isomap (NDR technique)
• stretch and Isomap related both preserve lengths
• eigenanalysis rather than nonlinear optimization
• provides
• good initial guess for stretch optimization
• good chartification heuristic via spectral
  clustering

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IsoMap
Tenenbaum et al, 2000
Data points in high dimensional space
Data points in low dimensional space
Neighborhood graph
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Surface Spectral Analysis
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Surface Spectral Analysis
1. Construct matrix of squared geodesic distances
DN
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Surface Spectral Analysis
2. Perform eigenanalysis on DN to get embedding
coords yi
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Isomap ? low stretch (take first two coords)
stretch, Sander01, L2 1.04, 222s
stretch, Sander02, L2 1.03, 39s
IsoMap, L2 1.04, 2s
IsoMapOptimization, L2 1.03, 6s
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Isomap ? good charts (spectral clustering)
Analysis
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Results
19 charts, L21.03, running time 98s, 97k faces
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Results
38 charts, L21.07, running time 287s, 150k faces
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Results
23 charts, L21.06, running time 162s, 112k faces
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Results
11 charts, L21.01, running time 4s, 10k faces
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Remeshing Comparison
Sander03, 79.5dB
Iso-chart, 82.9dB
Original model
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Texture Synthesis Results