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Shape Compression using Spherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah Hugues Hoppe, Microsoft Research Emil.

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Presentation on theme: "Shape Compression using Spherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah Hugues Hoppe, Microsoft Research Emil."— Presentation transcript:

1 Shape Compression using Spherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah Hugues Hoppe, Microsoft Research Emil Praun, University of Utah

2 Mesh representation semi-regularirregular completely regular

3 What if images were represented with irregular meshes? Drawbacks: l storage of connectivity l no random lookup l rendering l compositing l filtering l compression Drawbacks: l storage of connectivity l no random lookup l rendering l compositing l filtering l compression demo

4 Simple 2D grid Advantages: l implicit connectivity l 2D lookup l raster-scan l alpha blending l DSP l JPEG 2000

5 Representations for media l Audio:uniform 1D grid l Images:uniform 2D grid l Video:uniform 3D grid l Geometry: irregular mesh l Audio:uniform 1D grid l Images:uniform 2D grid l Video:uniform 3D grid l Geometry: irregular mesh historical artifact?

6 Geometry image geometry image 257 x 257; 12 bits/channel 3D geometry 2D grid sampling

7 Geometry image

8 [r,g,b] = [x,y,z] render

9 Advantages for hardware rendering l Regular sampling no vertex indices. l Unified parametrization no texture coordinates. l Sequential traversal of source data

10 Main questions cut? parametrize?

11 Construction approaches Spherical General cut Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries cut symmetries >1 chart zippering zippering

12 Construction approaches General cut [Gu et al. SIGGRAPH 2002] arbitrary surface genus 6

13 Construction approaches Spherical General cut Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries cut symmetries >1 chart zippering zippering piecewise regular 400x160

14 Construction approaches Spherical General cut Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe. SIGGRAPH 2003] [Sander et al. SGP 2003] arbitrary surface genus-zero surface cut symmetries cut symmetries >1 chart zippering zippering

15 Spherical parameterization and remeshing [Praun, Hoppe 2003]

16 Spherical parameterization and remeshing [Praun, Hoppe 2003]

17 Spherical geometry images

18 StepsSteps demo image I domain D sphere S mesh M

19 l Two challenges: n robustness n good sampling l Two challenges: n robustness n good sampling Spherical parametrization sphere S mesh M [Sander et al. 2001] [Hormann et al. 1999] [Sander et al. 2002] coarse-to-fine coarse-to-fine stretch metric stretch metric coarse-to-fine coarse-to-fine stretch metric stretch metric [Kent et al. 1992] [Haker et al. 2000] [Alexa 2002] [Grimm 2002] [Sheffer et al. 2003] [Gotsman et al. 2003]

20 Coarse-to-fine algorithm Convert to progressive mesh Parametrize coarse-to-fine (maintain embedding & minimize stretch)

21 Traditional conformal metric l Preserve angles but area compression l Bad for sampling using regular grids l Preserve angles but area compression l Bad for sampling using regular grids

22 Stretch metric [Sander et al. 2001] [Sander et al. 2002] l Penalizes undersampling l Better samples the surface

23 Applications of spherical remeshing l Level-of-detail control l Morphing l Geometry amplification l Shape compression l Level-of-detail control l Morphing l Geometry amplification l Shape compression

24 Level-of-detail control

25 MorphingMorphing l Align meshes on the sphere. l Interpolate the resulting geometry images. l Align meshes on the sphere. l Interpolate the resulting geometry images.

26 Geometry amplification 257x257 scalar displacements simulation 33x33 65x65 129x129 257x257 GPU CPU floating-point geometry image + [Losasso et al. SGP 2003] demo smooth geometry images

27 Shape compression (Genus-zero shapes) l Spherical image topology l Infinite 2D tiling l Wavelets on regular 2D grid (Genus-zero shapes) l Spherical image topology l Infinite 2D tiling l Wavelets on regular 2D grid

28 Spherical image topology

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31 Infinite 2D tiling

32 Wavelets on regular 2D grid spherical wavelets image wavelets [Schröder & Sweldens 1995] [Davis 1995] [Antonini et al 1992]

33 Test models

34 Compression results

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39 SummarySummary l Geometry image n Simplicity of 2D grid l Applications n Rendering n LOD n Morphing n Geometry amplification n Shape compression l Geometry image n Simplicity of 2D grid l Applications n Rendering n LOD n Morphing n Geometry amplification n Shape compression

40 Future work l Visual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003] l Attenuation of rippling artifacts l Surface boundaries l Animated meshes geometry videos [Briceño et al 2003] l Visual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003] l Attenuation of rippling artifacts l Surface boundaries l Animated meshes geometry videos [Briceño et al 2003]


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