1. Shape Compression usingSpherical Geometry Images Hugues Hoppe, Microsoft Research Emil Praun, University of Utah

2. Mesh representation irregular semi-regular completely regular

3. What if images were represented with irregularmeshes? Drawbacks: • storage of connectivity • no random lookup • rendering • compositing • filtering • compression demo

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

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

6. Geometry image 3D geometry 2D grid sampling geometry image257 x 257; 12 bits/channel

7. Geometry image

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

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

10. Main questions cut? parametrize?

11. 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

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

13. 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

14. 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

15. Spherical parameterization and remeshing [Praun, Hoppe 2003]

16. Spherical parameterization and remeshing [Praun, Hoppe 2003]

17. Spherical geometry images

18. Steps mesh M sphere S domain D image I demo

19. 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]

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

21. Traditional conformal metric • Preserve angles but “area compression” • Bad for sampling using regular grids

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

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

24. Level-of-detail control

25. Morphing • Align meshes on the sphere. • Interpolate the resulting geometry images.

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

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

28. Spherical image topology

29. Spherical image topology

30. Spherical image topology

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

35. Compression results

36. Compression results

37. Compression results

38. Compression results

39. Summary • Geometry image • Simplicity of 2D grid • Applications • Rendering • LOD • Morphing • Geometry amplification • Shape compression

40. 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]