Shape Compression using Spherical Geometry Images
Hugues Hoppe, Microsoft Research Emil Praun, University of Utah
Mesh representation
irregular semi-regular completely regular
What if images were represented with irregular meshes?
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:
Images: Video:
uniform 1D grid
uniform 2D grid uniform 3D grid
Geometry: irregular mesh
historical artifact?
Geometry image
2D grid sampling 3D geometry
geometry image
257 x 257; 12 bits/channel
Geometry image
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]
Spherical geometry images
Steps
mesh M
sphere S
domain D
image I
demo
Spherical parametrization
[Kent et al. 1992] [Haker et al. 2000] [Alexa 2002] [Grimm 2002] [Sheffer et al. 2003] [Gotsman et al. 2003]
mesh M
sphere S
Two challenges:
robustness
coarse-to-fine
[Hormann et al. 1999] [Sander et al. 2001]
good sampling stretch metric
[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
Stretch metric
[Sander et al. 2001] [Sander et al. 2002]
Penalizes undersampling Better samples the surface
Applications of spherical remeshing
Level-of-detail control
Morphing
Geometry amplification Shape compression
Level-of-detail control
Morphing
Align meshes on the sphere. Interpolate the resulting geometry images.
Geometry amplification
simulation
[Losasso et al. SGP 2003]
“smooth geometry images”
CPU
GPU
33x33
65x65
129x129 257x257
floating-point geometry image
+
257x257
scalar displacements
demo
Shape compression
(Genus-zero shapes)
Spherical image topology Infinite 2D tiling
Wavelets on regular 2D grid
Spherical image topology
Spherical image topology
Spherical image topology
Infinite 2D tiling
Wavelets on regular 2D grid
spherical wavelets
[Schröder & Sweldens 1995]
image wavelets
[Davis 1995] [Antonini et al 1992]
Test models
Compression results
Compression results
90
PSNR
85 80 75 70 65 Spherical wavelets 60 55 50 45 100 1000 10000 100000 Image wavelets Globally smooth [2003] Normal mesh [2002] PGC [2000] TG [1998]
File Size (bytes)
Compression results
90
PSNR
85 80 75 70 65 60 Spherical wavelets 55 Image wavelets 50 45 100 1000 10000 100000 Normal mesh [2002]
File Size (bytes)
Compression results
90
PSNR
85 80 75 70 65 Spherical wavelets 60 55 50 45 100 1000 10000 100000 Image wavelets Globally smooth [2003] Normal mesh [2002] PGC [2000] TG [1998]
File Size (bytes)
Compression results
90
PSNR
85 80 75 70 65 Spherical wavelets 60 55 50 45 100 1000 10000 100000 Image wavelets Globally smooth [2003] Normal mesh [2002] PGC [2000] TG [1998]
File Size (bytes)
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]