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Shape Analysis and Retrieval

Shape Analysis and Retrieval. Shape Histograms Ankerst et al. 1999. Notes courtesy of Funk et al. , SIGGRAPH 2004. Shape Histograms. Shape descriptor stores a histogram of how much surface resides at different bins in space. Model. Shape Histogram (Sectors + Shells).

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Shape Analysis and Retrieval

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  1. Shape Analysis and Retrieval Shape Histograms Ankerst et al. 1999 Notes courtesy of Funk et al., SIGGRAPH 2004

  2. Shape Histograms • Shape descriptor stores a histogram of how much surface resides at different bins in space Model Shape Histogram (Sectors + Shells)

  3. Boundary Voxel Representation • Represent a model as the (anti-aliased) rasterization of its surface into a regular grid: • A voxel has value 1 (or area of intersection) if it intersects the boundary • A voxel has value 0 if it doesn’t intersect Model Voxel Grid

  4. Boundary Voxel Representation • Properties: • Invertible • 3D array of information • Can be defined for any model Point Clouds Polygon Soups Closed Meshes Genus-0 Meshes Shape Spectrum

  5. Retrieval Results

  6. Histogram Representations • Challenge: • Histogram comparisons measure overlap, not proximity.

  7. Histogram Representations • Solution: • Quadratic distance form:

  8. Histogram Representations • Solution: • Quadratic distance form: M is a symmetric matrix and can be expressed as:O is a rotation and D is diagonal with positive entries. Taking the square root:

  9. Histogram Representations • Solution: • Quadratic distance form factors: If v=(v1,…,vn), we have: That is, M1/2(v) is just the convolution of v with some filter.

  10. Convolving with a Gaussian • The value at a point is obtained by summing Gaussians distributed over the surface of the model. • Distributes the surface into adjacent bins • Blurs the model, loses high frequency information Surface Gaussian Gaussian convolved surface

  11. Gaussian EDT • The value at a point is obtained by summing the Gaussian of the closest point on the model surface. • Distributes the surface into adjacent bins • Maintains high-frequency information max Gaussian EDT Surface Gaussian [Kazhdan et al., 2003]

  12. Gaussian EDT • Properties: • Invertible • 3D array of information • Can be defined for any model • Difference measures proximity between surfaces Point Clouds Polygon Soups Closed Meshes Genus-0 Meshes Shape Spectrum

  13. Retrieval Results

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