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Shape Analysis and Retrieval
Extended Gaussian Images Notes courtesy of Funk et al., SIGGRAPH 2004
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Extended Gaussian Image
Represent a model by a spherical function by binning surface normals Model Angular Bins EGI
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Subdividing the Sphere
20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces All bins have the same area
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Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces
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Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces
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Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces
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Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces
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Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces
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Angular Parameterization
4x4 Bins 8x8 Bins 16x16 Bins 32x32 Bins Different bins have different areas
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Angular Parameterization
Missing node where bins are small Different bins have different areas Smaller bins lose their votes
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Angular Parameterization
Normalize bins by bin area
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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
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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
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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
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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
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Retrieval Results Precision Recall
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