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Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models

Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models. Tamal K. Dey, Kuiyu Li, Chuanjiang Luo, Pawas Ranjan, Issam Safa, Yusu Wang [ The Ohio State University ] (SGP 2010). Problem. Query and match partial, incomplete and pose-altered models. Previous Work.

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Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models

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  1. Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models Tamal K. Dey, Kuiyu Li, Chuanjiang Luo, Pawas Ranjan, Issam Safa, Yusu Wang [The Ohio State University] (SGP 2010)

  2. Problem • Query and match partial, incomplete and pose-altered models

  3. Previous Work • [CTS03]; [OBBG09]; [KFR04]; [BCG08]; [L06]; [RSWN09] … • No unified approach for pose-invariant matching of partial, incomplete models

  4. Descriptor based Matching • Represent shape with descriptor • Compare descriptors • Local vs Global descriptors Need a multi-scale descriptor to capture both local and global features

  5. HKS [Sun-Ovsjanikov-Guibas 09] • Signifies the amount of heat left at a point x ϵ M at time t, if unit heat were placed at x when t=0 • Isometry invariant • Stable against noise, small topological changes • Local changes at small t for incomplete models

  6. HKS as Shape Descriptor Need to choose a concise subset of HKS values • Possible solutions: • Choose the maxima values for some t • Too many for small t • Sensitive to incompleteness of shape for large t

  7. Persistent HKS

  8. Persistence[Edelsbrunner et al 02] • Tracks topological changes in sub-level sets • Pairs point that created a component with one that destroyed it

  9. Persistent Maxima with Region Merging • Apply Persistence to HKS • To obtain persistent maxima • Region-merging algorithm

  10. Persistent Maxima with Region Merging

  11. Persistent Maxima with Region Merging

  12. Persistent Maxima

  13. Feature Vector • Assign a multi-scale feature vector to each persistent maximum • HKS function values at multiple time scales • A shape is represented by 15 feature vectors in 15D space

  14. The Algorithm • Compute the HKS function on input mesh for small t • Find persistent maxima • Compute HKS values for multiple t at the persistent maxima

  15. Scalability • Expensive to compute the eigenvalues and eigenvectors for large matrices • Use an HKS-aware sub-sampling method

  16. Scoring & Matching • Pre-compute feature vectors for database • Given a query • Compute feature vectors of query • Compare with feature vectors in database • Score is based on L1-norm of feature vectors

  17. Results • 300 Database Models (22 Classes) • 198 Complete • 102 Incomplete • 50 Query Models • 18 Complete • 32 Incomplete

  18. Results

  19. Comparison • Eigen-Value Descriptor [JZ07] • Light Field Distribution [CTSO03] • Top-k Hit Rate • Query hit if model of same class present in top-k results returned

  20. Comparison

  21. Conclusion • Combine techniques from spectral theory and computational topology • Fast database-style shape retrieval • Unified method for pose-oblivious, incomplete shape matching • Handling non-manifold meshes • Matching feature-less shapes

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