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Explore using irregular meshes for geometry image representation, advantages over regular grids, construction approaches, and applications of spherical wavelets in shape compression.
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Shape Compression usingSpherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah
Mesh representation irregular semi-regular completely regular
What if images were represented with irregularmeshes? Drawbacks: • storage of connectivity • no random lookup • rendering • compositing • filtering • compression demo
Simple 2D grid Advantages: • implicit connectivity • 2D lookup • raster-scan • alpha blending • DSP • JPEG 2000
Representations for media • Audio: uniform 1D grid • Images: uniform 2D grid • Video: uniform 3D grid • Geometry: irregular mesh historical artifact?
Geometry image 3D geometry 2D grid sampling geometry image257 x 257; 12 bits/channel
Geometry image render [r,g,b] = [x,y,z]
Advantages for hardware rendering • Regular sampling no vertex indices. • Sequential traversal of source data • Unified parametrization no texture coordinates.
Main questions cut? parametrize?
Construction approaches General cut Spherical Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries >1 chart zippering
Construction approaches General cut [Gu et al. SIGGRAPH 2002] arbitrary surface genus 6
Construction approaches General cut Spherical Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries >1 chart zippering 400x160 piecewise regular
Construction approaches General cut Spherical Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries >1 chart zippering
Spherical parameterization and remeshing [Praun, Hoppe 2003]
Spherical parameterization and remeshing [Praun, Hoppe 2003]
Steps mesh M sphere S domain D image I demo
sphere S mesh M Spherical parametrization • Two challenges: • robustness • good sampling [Kent et al. 1992] [Haker et al. 2000] [Alexa 2002] [Grimm 2002] [Sheffer et al. 2003] [Gotsman et al. 2003] coarse-to-fine stretch metric [Hormann et al. 1999] [Sander et al. 2001] [Sander et al. 2002]
Coarse-to-fine algorithm Convert to progressive mesh Parametrize coarse-to-fine (maintain embedding & minimize stretch)
Traditional conformal metric • Preserve angles but “area compression” • Bad for sampling using regular grids
[Sander et al. 2001] Stretch metric [Sander et al. 2002] • Penalizes undersampling • Better samples the surface
Applications of spherical remeshing • Level-of-detail control • Morphing • Geometry amplification • Shape compression
Morphing • Align meshes on the sphere. • Interpolate the resulting geometry images.
Geometry amplification [Losasso et al. SGP 2003] “smooth geometry images” simulation CPU GPU 33x33 65x65 129x129 floating-pointgeometry image 257x257 + 257x257 scalar displacements demo
Shape compression (Genus-zero shapes) • Spherical image topology • Infinite 2D tiling • Wavelets on regular 2D grid
Wavelets on regular 2D grid spherical wavelets image wavelets [Schröder & Sweldens 1995] [Davis 1995] [Antonini et al 1992]
Summary • Geometry image • Simplicity of 2D grid • Applications • Rendering • LOD • Morphing • Geometry amplification • Shape compression
Future work • Visual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003] • Attenuation of rippling artifacts • Surface boundaries • Animated meshes “geometry videos” [Briceño et al 2003]