Shape Compression using Spherical Geometry Images Hugues Hoppe

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

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

Mesh representation irregular semi-regular completely regular

Mesh representation irregular semi-regular completely regular

What if images were represented with irregular meshes? Drawbacks: l storage of connectivity l

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 demo

Simple 2 D grid Advantages: l implicit connectivity l 2 D lookup l raster-scan

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

Representations for media l Audio: uniform 1 D grid l Images: uniform 2 D

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

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

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

Geometry image

Geometry image

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

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

Advantages for hardware rendering l Regular sampling no vertex indices. l Sequential traversal of

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

Main questions cut? parametrize?

Main questions cut? parametrize?

Construction approaches General cut Spherical Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe.

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 >1 chart cut symmetries zippering

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

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.

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 >1 chart cut symmetries zippering 400 x 160 piecewise regular

Construction approaches General cut Spherical Multi-chart [Gu et al. SIGGRAPH 2002] [Praun & Hoppe.

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 >1 chart cut symmetries zippering

Spherical parameterization and remeshing [Praun, Hoppe 2003]

Spherical parameterization and remeshing [Praun, Hoppe 2003]

Spherical parameterization and remeshing [Praun, Hoppe 2003]

Spherical parameterization and remeshing [Praun, Hoppe 2003]

Spherical geometry images

Spherical geometry images

Steps mesh M sphere S domain D demo image I

Steps mesh M sphere S domain D demo image I

Spherical parametrization [Kent et al. 1992] [Haker et al. 2000] [Alexa 2002] [Grimm 2002]

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

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

Traditional conformal metric l l Preserve angles but “area compression” Bad for sampling using

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

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

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

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

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

Level-of-detail control

Level-of-detail control

Morphing l l Align meshes on the sphere. Interpolate the resulting geometry images.

Morphing l l Align meshes on the sphere. Interpolate the resulting geometry images.

Geometry amplification simulation [Losasso et al. SGP 2003] “smooth geometry images” CPU GPU 33

Geometry amplification simulation [Losasso et al. SGP 2003] “smooth geometry images” CPU GPU 33 x 33 65 x 65 floating-point geometry image 129 x 129 257 x 257 + 257 x 257 scalar displacements demo

Shape compression (Genus-zero shapes) l Spherical image topology l Infinite 2 D tiling l

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

Spherical image topology

Spherical image topology

Spherical image topology

Spherical image topology

Spherical image topology

Spherical image topology

Infinite 2 D tiling

Infinite 2 D tiling

Wavelets on regular 2 D grid spherical wavelets image wavelets [Schröder & Sweldens 1995]

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

Test models

Test models

Compression results

Compression results

Compression results

Compression results

Compression results

Compression results

Compression results

Compression results

Compression results

Compression results

Summary l Geometry image n l Simplicity of 2 D grid Applications n n

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

Future work l Visual error metrics [Touma & Gotsman 1998] [Sorkine et al 2003]

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]