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 Faces Icosahedron 80 Faces 320 Faces 1280 Faces All bins have the same area

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Angular Parameterization 4x4 Bins 8x8 Bins 16x16 Bins 32x32 Bins Different bins have different areas

Angular Parameterization Missing node where bins are small Different bins have different areas Smaller bins lose their votes

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 Precision Recall