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

• 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

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

# 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

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