Persistent Heat Signature for Pose-oblivious Matching of Incomplete Models
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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)
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Problem• Query and match partial, incomplete and
pose-altered models
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Previous Work
• [CTS03]; [OBBG09]; [KFR04]; [BCG08]; [L06]; [RSWN09] …
• No unified approach for pose-invariant matching of partial, incomplete models
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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
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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
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HKS as Shape Descriptor
• Possible solutions:
‒ Choose the maxima values for some t• Too many for small t
• Sensitive to incompleteness of shape for large t
Need to choose a concise subset of HKS values
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Persistent HKS
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Persistence[Edelsbrunner et al 02]
• Tracks topological changes in sub-level sets
• Pairs point that created a component with one that destroyed it
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Persistent Maxima with Region Merging
• Apply Persistence to HKS
‒ To obtain persistent maxima
• Region-merging algorithm
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Persistent Maxima with Region Merging
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Persistent Maxima with Region Merging
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Persistent Maxima
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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
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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
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Scalability
• Expensive to compute the eigenvalues and eigenvectors for large matrices
• Use an HKS-aware sub-sampling method
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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
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Results
• 300 Database Models (22 Classes)
‒ 198 Complete
‒ 102 Incomplete
• 50 Query Models
‒ 18 Complete
‒ 32 Incomplete
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Results
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Comparison
# queries ours EVD LFD32 Incomplete 91 62 5918 Complete 83 100 39
Total 88 76 52
• 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
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Comparison
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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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