Shape Compression using Shape Compression using Spherical Geometry Images Spherical Geometry Images Hugues Hoppe, Microsoft Research Hugues Hoppe, Microsoft Research Emil Praun, University of Utah Emil Praun, University of Utah
Shape Compression using Spherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah Hugues Hoppe, Microsoft Research Emil.
Mar 27, 2015
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Shape Compression usingShape Compression usingSpherical Geometry ImagesSpherical Geometry ImagesShape Compression usingShape Compression using
Spherical Geometry ImagesSpherical Geometry Images
Hugues Hoppe, Microsoft ResearchHugues Hoppe, Microsoft Research
Emil Praun, University of UtahEmil Praun, University of Utah
Hugues Hoppe, Microsoft ResearchHugues Hoppe, Microsoft Research
Emil Praun, University of UtahEmil Praun, University of Utah
Mesh representationMesh representation
semi-regularsemi-regularirregularirregular completely regularcompletely regular
What if What if imagesimages were represented with were represented with irregularirregular meshes?meshes?
DrawbacksDrawbacks:: storage of connectivitystorage of connectivity no random lookupno random lookup renderingrendering compositingcompositing filteringfiltering compressioncompression
demodemo
Simple 2D gridSimple 2D grid
AdvantagesAdvantages:: implicit connectivityimplicit connectivity 2D lookup2D lookup raster-scanraster-scan alpha blendingalpha blending DSPDSP JPEG 2000JPEG 2000
Representations for mediaRepresentations for mediaRepresentations for mediaRepresentations for media
Audio:Audio: uniform 1D griduniform 1D grid
Images:Images: uniform 2D griduniform 2D grid
Video:Video: uniform 3D griduniform 3D grid
Geometry: irregular meshGeometry: irregular mesh
Audio:Audio: uniform 1D griduniform 1D grid
Images:Images: uniform 2D griduniform 2D grid
Video:Video: uniform 3D griduniform 3D grid
Geometry: irregular meshGeometry: irregular mesh
historical artifact?historical artifact?
Geometry imageGeometry image
geometry imagegeometry image257 x 257; 12 bits/channel257 x 257; 12 bits/channel
3D geometry3D geometry2D grid sampling2D grid sampling
Geometry imageGeometry imageGeometry imageGeometry image
Geometry imageGeometry imageGeometry imageGeometry image
[[rr,,gg,,bb] = [] = [xx,,yy,,zz]]
renderrender
Advantages for hardware renderingAdvantages for hardware renderingAdvantages for hardware renderingAdvantages for hardware rendering
Regular sampling Regular sampling no vertex indices. no vertex indices. Regular sampling Regular sampling no vertex indices. no vertex indices.
Unified parametrization Unified parametrization no texture coordinates. no texture coordinates. Unified parametrization Unified parametrization no texture coordinates. no texture coordinates.
SequentialSequential traversal of source data traversal of source data SequentialSequential traversal of source data traversal of source data
Main questionsMain questionsMain questionsMain questions
cut?cut?
parametrize?parametrize?
Construction approachesConstruction approachesConstruction approachesConstruction approaches
SphericalSphericalGeneral cutGeneral cut Multi-chartMulti-chart
[Gu et al. SIGGRAPH 2002][Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003][Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003][Sander et al. SGP 2003]
arbitrary surfacearbitrary surface genus-zero surfacegenus-zero surface
cut symmetriescut symmetries
>1 chart>1 chart
zipperingzippering
Construction approachesConstruction approachesConstruction approachesConstruction approaches
General cutGeneral cut
[Gu et al. SIGGRAPH 2002][Gu et al. SIGGRAPH 2002]
arbitrary surfacearbitrary surface
genus 6
Construction approachesConstruction approachesConstruction approachesConstruction approaches
SphericalSphericalGeneral cutGeneral cut Multi-chartMulti-chart
[Gu et al. SIGGRAPH 2002][Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003][Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003][Sander et al. SGP 2003]
arbitrary surfacearbitrary surface genus-zero surfacegenus-zero surface
cut symmetriescut symmetries
>1 chart>1 chart
zipperingzippering
piecewisepiecewise regular regular400x160
Construction approachesConstruction approachesConstruction approachesConstruction approaches
SphericalSphericalGeneral cutGeneral cut Multi-chartMulti-chart
[Gu et al. SIGGRAPH 2002][Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003][Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003][Sander et al. SGP 2003]
arbitrary surfacearbitrary surface genus-zero surfacegenus-zero surface
cut symmetriescut symmetries
>1 chart>1 chart
zipperingzippering
Spherical parameterization and remeshingSpherical parameterization and remeshingSpherical parameterization and remeshingSpherical parameterization and remeshing[Praun, Hoppe 2003][Praun, Hoppe 2003]
Spherical parameterization and remeshingSpherical parameterization and remeshingSpherical parameterization and remeshingSpherical parameterization and remeshing[Praun, Hoppe 2003][Praun, Hoppe 2003]
Spherical geometry imagesSpherical geometry imagesSpherical geometry imagesSpherical geometry images
StepsStepsStepsSteps
demodemodemodemo
image image IIdomain domain DDsphere sphere SSmesh mesh MM
Two challenges:Two challenges:
robustnessrobustness
good samplinggood sampling
Two challenges:Two challenges:
robustnessrobustness
good samplinggood sampling
Spherical parametrizationSpherical parametrizationSpherical parametrizationSpherical parametrization
sphere sphere SSmesh mesh MM
[Sander et al. 2001][Sander et al. 2001]
[Hormann et al. 1999][Hormann et al. 1999]
[Sander et al. 2002][Sander et al. 2002]
coarse-to-finecoarse-to-fine
stretch metricstretch metric
coarse-to-finecoarse-to-fine
stretch metricstretch metric
[Kent et al. 1992][Kent et al. 1992][Haker et al. 2000][Haker et al. 2000][Alexa 2002][Alexa 2002][Grimm 2002][Grimm 2002][Sheffer et al. 2003][Sheffer et al. 2003][Gotsman et al. 2003][Gotsman et al. 2003]
Coarse-to-fine algorithmCoarse-to-fine algorithmCoarse-to-fine algorithmCoarse-to-fine algorithm
Convert to progressive meshConvert to progressive mesh
Parametrize coarse-to-fineParametrize coarse-to-fine(maintain embedding & minimize stretch)(maintain embedding & minimize stretch)
Traditional conformal metricTraditional conformal metricTraditional conformal metricTraditional conformal metric
Preserve angles but “area compression”Preserve angles but “area compression” Bad for sampling using regular gridsBad for sampling using regular grids
Preserve angles but “area compression”Preserve angles but “area compression” Bad for sampling using regular gridsBad for sampling using regular grids
Stretch metricStretch metricStretch metricStretch metric [Sander et al. 2001][Sander et al. 2001]
[Sander et al. 2002][Sander et al. 2002]
Penalizes undersamplingPenalizes undersampling Better samples the surfaceBetter samples the surface
Applications of spherical remeshingApplications of spherical remeshingApplications of spherical remeshingApplications of spherical remeshing
Level-of-detail controlLevel-of-detail control
MorphingMorphing
Geometry amplificationGeometry amplification
Shape compressionShape compression
Level-of-detail controlLevel-of-detail control
MorphingMorphing
Geometry amplificationGeometry amplification
Shape compressionShape compression
Level-of-detail controlLevel-of-detail controlLevel-of-detail controlLevel-of-detail control
MorphingMorphingMorphingMorphing
Align meshes on the sphere.Align meshes on the sphere. Interpolate the resulting geometry images.Interpolate the resulting geometry images.
Align meshes on the sphere.Align meshes on the sphere. Interpolate the resulting geometry images.Interpolate the resulting geometry images.
Geometry amplificationGeometry amplificationGeometry amplificationGeometry amplification
257x257257x257scalar displacements
simulation
33x3333x3365x6565x65
129x129129x129
257x257257x257
GPUGPU
CPUCPU
floating-pointfloating-pointgeometry imagegeometry image ++
[Losasso et al. SGP 2003][Losasso et al. SGP 2003]
demodemo
““smooth geometry images”smooth geometry images”
Shape compressionShape compressionShape compressionShape compression
(Genus-zero shapes)(Genus-zero shapes)
Spherical image topologySpherical image topology
Infinite 2D tilingInfinite 2D tiling
Wavelets on regular 2D gridWavelets on regular 2D grid
(Genus-zero shapes)(Genus-zero shapes)
Spherical image topologySpherical image topology
Infinite 2D tilingInfinite 2D tiling
Wavelets on regular 2D gridWavelets on regular 2D grid
Spherical image topologySpherical image topologySpherical image topologySpherical image topology
Spherical image topologySpherical image topologySpherical image topologySpherical image topology
Spherical image topologySpherical image topologySpherical image topologySpherical image topology
Infinite 2D tilingInfinite 2D tilingInfinite 2D tilingInfinite 2D tiling
Wavelets on regular 2D gridWavelets on regular 2D gridWavelets on regular 2D gridWavelets on regular 2D grid
spherical waveletsspherical wavelets image waveletsimage wavelets[Schröder[Schröder & Sweldens 1995] & Sweldens 1995] [Davis [Davis 1995] [Antonini et al 1992]1995] [Antonini et al 1992]
Test modelsTest modelsTest modelsTest models
Compression resultsCompression resultsCompression resultsCompression results
Compression resultsCompression resultsCompression resultsCompression results
45
50
55
60
65
70
75
80
85
90
100 1000 10000 100000File Size (bytes)
PSNR
Spherical wavelets
Image wavelets
Globally smooth [2003]
Normal mesh [2002]
PGC [2000]
TG [1998]
Compression resultsCompression resultsCompression resultsCompression results
45
50
55
60
65
70
75
80
85
90
100 1000 10000 100000File Size (bytes)
PSNR
Spherical wavelets
Image wavelets
Normal mesh [2002]
Compression resultsCompression resultsCompression resultsCompression results
45
50
55
60
65
70
75
80
85
90
100 1000 10000 100000File Size (bytes)
PSNR
Spherical wavelets
Image wavelets
Globally smooth [2003]
Normal mesh [2002]
PGC [2000]
TG [1998]
Compression resultsCompression resultsCompression resultsCompression results
45
50
55
60
65
70
75
80
85
90
100 1000 10000 100000File Size (bytes)
PSNR
Spherical wavelets
Image wavelets
Globally smooth [2003]
Normal mesh [2002]
PGC [2000]
TG [1998]
SummarySummarySummarySummary
Geometry imageGeometry image Simplicity of 2D gridSimplicity of 2D grid
ApplicationsApplications RenderingRendering LODLOD MorphingMorphing Geometry amplificationGeometry amplification Shape compressionShape compression
Geometry imageGeometry image Simplicity of 2D gridSimplicity of 2D grid
ApplicationsApplications RenderingRendering LODLOD MorphingMorphing Geometry amplificationGeometry amplification Shape compressionShape compression
Future workFuture workFuture workFuture work
Visual error metricsVisual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003] [Touma & Gotsman 1998] [Sorkine et al 2003]
Attenuation of rippling artifactsAttenuation of rippling artifacts
Surface boundariesSurface boundaries
Animated meshesAnimated meshes “geometry videos” [Briceño et al 2003] “geometry videos” [Briceño et al 2003]
Visual error metricsVisual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003] [Touma & Gotsman 1998] [Sorkine et al 2003]
Attenuation of rippling artifactsAttenuation of rippling artifacts
Surface boundariesSurface boundaries
Animated meshesAnimated meshes “geometry videos” [Briceño et al 2003] “geometry videos” [Briceño et al 2003]
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