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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 • [CTS03]; [OBBG09]; [KFR04]; [BCG08]; [L06]; [RSWN09] … • No unified approach for pose-invariant matching of partial, incomplete models 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 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 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 Persistent HKS Persistence [Edelsbrunner et al 02] • Tracks topological changes in sub-level sets • Pairs point that created a component with one that destroyed it Persistent Maxima with Region Merging • Apply Persistence to HKS ‒ To obtain persistent maxima • Region-merging algorithm Persistent Maxima with Region Merging Persistent Maxima with Region Merging Persistent Maxima 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 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 Scalability • Expensive to compute the eigenvalues and eigenvectors for large matrices • Use an HKS-aware sub-sampling method 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 Results • 300 Database Models (22 Classes) ‒ 198 Complete ‒ 102 Incomplete • 50 Query Models ‒ 18 Complete ‒ 32 Incomplete Results 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 # queries 32 Incomplete 18 Complete Total ours 91 83 88 EVD 62 100 76 LFD 59 39 52 Comparison 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