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

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Presentation on theme: "Iso-charts: Stretch-Driven Parameterization via Nonlinear Dimension Reduction Kun Zhou, John Snyder, Baining Guo, Harry Shum presented at SGP, June 2004."— Presentation transcript:

1 Iso-charts: Stretch-Driven Parameterization via 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 l Advantages n measures distortion properly for texturing apps l Disadvantages n requires nonlinear optimization (slow!) n provides no help in forming charts –resort to simple heuristics like planarity or compactness l Solution: apply Isomap (NDR technique) n stretch and Isomap related: both preserve lengths n eigenanalysis rather than nonlinear optimization n provides: –good initial guess for stretch optimization –good chartification heuristic via “spectral clustering” l Advantages n measures distortion properly for texturing apps l Disadvantages n requires nonlinear optimization (slow!) n provides no help in forming charts –resort to simple heuristics like planarity or compactness l Solution: apply Isomap (NDR technique) n stretch and Isomap related: both preserve lengths n eigenanalysis rather than nonlinear optimization n provides: –good initial guess for stretch optimization –good chartification heuristic via “spectral clustering”

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

5 Surface Spectral Analysis Geodesic Distance Distortion (GDD)

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

7 Surface Spectral Analysis 2. Perform eigenanalysis on D N to get embedding coords y i

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

9 Isomap → good charts (spectral clustering) Analysis Clustering

10 ResultsResults 19 charts, L 2 =1.03, running time 98s, 97k faces

11 ResultsResults 38 charts, L 2 =1.07, running time 287s, 150k faces

12 ResultsResults 23 charts, L 2 =1.06, running time 162s, 112k faces

13 ResultsResults 11 charts, L 2 =1.01, running time 4s, 10k faces

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

15 Texture Synthesis Results

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