Iso-charts: Stretch-Driven Iso-charts: Stretch-Driven Parameterization Parameterization via Nonlinear Dimension Reduction via Nonlinear Dimension Reduction Kun Zhou, John Snyder, Baining Guo, Harry Shum Kun Zhou, John Snyder, Baining Guo, Harry Shum presented at SGP, June 2004 presented at SGP, June 2004
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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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Kun Zhou, John Snyder, Baining Guo, Harry ShumKun Zhou, John Snyder, Baining Guo, Harry ShumKun Zhou, John Snyder, Baining Guo, Harry ShumKun Zhou, John Snyder, Baining Guo, Harry Shum
presented at SGP, June 2004presented at SGP, June 2004
Goals of Mesh ParameterizationGoals of Mesh ParameterizationGoals of Mesh ParameterizationGoals of Mesh Parameterization
measures distortion properly for texturing appsmeasures distortion properly for texturing apps
DisadvantagesDisadvantages requires nonlinear optimization (slow!)requires nonlinear optimization (slow!) provides no help in forming chartsprovides no help in forming charts
– resort to simple heuristics like planarity or compactnessresort to simple heuristics like planarity or compactness
Solution: apply Solution: apply IsomapIsomap (NDR technique) (NDR technique) stretch and Isomap related: both preserve lengthsstretch and Isomap related: both preserve lengths eigenanalysis rather than nonlinear optimizationeigenanalysis rather than nonlinear optimization provides:provides:
– good initial guess for stretch optimizationgood initial guess for stretch optimization
– good chartification heuristic via “spectral clustering”good chartification heuristic via “spectral clustering”
AdvantagesAdvantages measures distortion properly for texturing appsmeasures distortion properly for texturing apps
DisadvantagesDisadvantages requires nonlinear optimization (slow!)requires nonlinear optimization (slow!) provides no help in forming chartsprovides no help in forming charts
– resort to simple heuristics like planarity or compactnessresort to simple heuristics like planarity or compactness
Solution: apply Solution: apply IsomapIsomap (NDR technique) (NDR technique) stretch and Isomap related: both preserve lengthsstretch and Isomap related: both preserve lengths eigenanalysis rather than nonlinear optimizationeigenanalysis rather than nonlinear optimization provides:provides:
– good initial guess for stretch optimizationgood initial guess for stretch optimization
– good chartification heuristic via “spectral clustering”good chartification heuristic via “spectral clustering”
2. Perform eigenanalysis on 2. Perform eigenanalysis on DDNN to getto get embedding coords embedding coords yyii
Tnn
T
T
N
v
v
v
yyy
22
11
21
|||
|||
12d
Nd2
Nd1
1x
2x
Nx
Isomap → low stretch (take first two coords)Isomap → low stretch (take first two coords)Isomap → low stretch (take first two coords)Isomap → low stretch (take first two coords)