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Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction

Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction. Kun Zhou, John Snyder, Baining Guo, Harry Shum. presented at SGP, June 2004. Goals of Mesh Parameterization. Large Charts. Low Distortion. Stretch-Driven Parameterization. Advantages

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Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction

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  1. Iso-charts: Stretch-Driven Parameterizationvia Nonlinear Dimension Reduction Kun Zhou, John Snyder, Baining Guo, Harry Shum presented at SGP, June 2004

  2. Goals of Mesh Parameterization Large Charts Low Distortion

  3. 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”

  4. IsoMap [Tenenbaum et al, 2000] Data points in high dimensional space Neighborhood graph Data points in low dimensional space

  5. Surface Spectral Analysis Geodesic Distance Distortion (GDD)

  6. Surface Spectral Analysis 1. Construct matrix of squared geodesic distances DN

  7. Surface Spectral Analysis 2. Perform eigenanalysis on DNto get embedding coords yi

  8. Isomap → low stretch (take first two coords) [stretch, Sander01], L2= 1.04, 222s [stretch, Sander02], L2= 1.03, 39s IsoMap, L2= 1.04, 2s IsoMap+Optimization, L2= 1.03, 6s

  9. Isomap → good charts (spectral clustering) Clustering Analysis

  10. Results 19 charts, L2=1.03, running time 98s, 97k faces

  11. Results 38 charts, L2=1.07, running time 287s, 150k faces

  12. Results 23 charts, L2=1.06, running time 162s, 112k faces

  13. Results 11 charts, L2=1.01, running time 4s, 10k faces

  14. Remeshing Comparison [Sander03], 79.5dB Iso-chart, 82.9dB Original model

  15. Texture Synthesis Results

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