Isocharts StretchDriven Parameterization via Nonlinear Dimension Reduction Kun

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 l l Advantages n measures distortion properly for texturing apps 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”

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

Surface Spectral Analysis Geodesic Distance Distortion (GDD)

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

Surface Spectral Analysis 2. Perform eigenanalysis on DN to get embedding coords yi

Isomap → low stretch (take first two coords) [stretch, Sander 01], L 2 = 1. 04, 222 s Iso. Map, L 2 = 1. 04, 2 s [stretch, Sander 02], L 2 = 1. 03, 39 s Iso. Map+Optimization, L 2 = 1. 03, 6 s

Isomap → good charts (spectral clustering) Analysis Clustering

Results 19 charts, L 2=1. 03, running time 98 s, 97 k faces

Results 38 charts, L 2=1. 07, running time 287 s, 150 k faces

Results 23 charts, L 2=1. 06, running time 162 s, 112 k faces

Results 11 charts, L 2=1. 01, running time 4 s, 10 k faces

Remeshing Comparison Original model [Sander 03], 79. 5 d. B Iso-chart, 82. 9 d. B

Texture Synthesis Results