Shape Analysis and Retrieval Extended Gaussian Images Notes

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 All bins have the same area 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

Hierarchical Search 20 Faces Icosahedron 80 Faces 320 Faces 1280 Faces

Angular Parameterization 4 x 4 Bins 8 x 8 Bins 16 x 16 Bins Different bins have different areas 32 x 32 Bins

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 – 2 D array of information – Can be defined for most models Point Clouds Polygon Soups Closed Meshes Shape Spectrum Genus-0 Meshes

Extended Gaussian Image • Properties: – Invertible for convex shapes – 2 D array of information – Can be defined for most models • Limitations: – Too much information is lost – Normals are sensitive to noise 3 D Model EGI

Extended Gaussian Image • Properties: – Invertible for convex shapes – 2 D 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/

Precision Retrieval Results Recall