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Shape Analysis and Retrieval
Extended Gaussian Images
Notes courtesy of Funk et al., SIGGRAPH 2004
Extended Gaussian Image
• Represent a model by a spherical function by binning surface normals
Model Angular Bins EGI
Subdividing the Sphere
20 FacesIcosahedron
80 Faces 320 Faces 1280 Faces
All bins have the same area
Hierarchical Search
80 Faces 320 Faces 1280 Faces20 FacesIcosahedron
Hierarchical Search
80 Faces 320 Faces 1280 Faces20 FacesIcosahedron
Hierarchical Search
80 Faces 320 Faces 1280 Faces20 FacesIcosahedron
Hierarchical Search
80 Faces 320 Faces 1280 Faces20 FacesIcosahedron
Hierarchical Search
80 Faces 320 Faces 1280 Faces20 FacesIcosahedron
Angular Parameterization
Different bins have different areas
4x4 Bins 8x8 Bins 16x16 Bins 32x32 Bins
Angular Parameterization
Different bins have different areas• Smaller bins lose their votes
Missing node where bins are small
Angular Parameterization
Normalize bins by bin area
Extended Gaussian Image
• Properties:– Invertible for convex shapes
– 2D array of information
– Can be defined for most models
Point Clouds
Polygon Soups
Closed Meshes
Genus-0 Meshes
Shape Spectrum
Extended Gaussian Image
• Properties:– Invertible for convex shapes
– 2D array of information
– Can be defined for most models
• Limitations:– Too much information is lost– Normals are sensitive to noise
3D Model EGI
Extended Gaussian Image
• Properties:– Invertible for convex shapes
– 2D array of information
– Can be defined for most models
• Limitations:– Too much information is lost– Normals are sensitive to noise
Initial Model Noisy Model
Retrieval Results
Princeton Shape Benchmark:(~900 models, ~90 classes)
14 biplanes 50 human bipeds 7 dogs 17 fish
16 swords 6 skulls 15 desk chairs 13 electric guitars
http://www.shape.cs.princeton.edu/benchmark/
Retrieval Results
Recall
Precision
0%
50%
100%
0% 50% 100%
Extended Gaussian Image (2D)D2 (1D)Random
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