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Bag-of-Feature-Graphs: A New Paradigm for Non-rigid Shape Retrieval

Bag-of-Feature-Graphs: A New Paradigm for Non-rigid Shape Retrieval. Tingbo HOU, Xiaohua HOU, Ming ZHONG and H ong QIN Department of Computer Science Stony Brook University (SUNY SB). Nonrigid Shape Retrieval. Shape Query. S hape D atabase. R etrieved S hapes. …. ….

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Bag-of-Feature-Graphs: A New Paradigm for Non-rigid Shape Retrieval

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  1. Bag-of-Feature-Graphs: A New Paradigm for Non-rigid Shape Retrieval Tingbo HOU, XiaohuaHOU, Ming ZHONGand Hong QIN Department of Computer Science Stony Brook University (SUNY SB) ICPR 2012

  2. Nonrigid Shape Retrieval Shape Query Shape Database Retrieved Shapes … … ICPR 2012

  3. Overview of BoFG Inspired by the ideas from Bag-of-Words (BoW) and Spatial-Sensitive Bag-of-Words (SS-BoW) Feature-driven Concise and fast to compute Spatially informative ICPR 2012

  4. Previous Works Relevant to This Project • Bag-of-Words • Y. Liu, H. Zha, and H. Qin. CVPR, 2006. • H. Tabia, M. Daoudi, J. P. Vandeborre, and O. Colot. 3DOR, 2010. • R. Toldo, U. Castellani, and A. Fusiello. VC, 2010. • G. Lavoué. 3DOR, 2011. • Shape Google (Spatially-Sensitive Bag-of-Words) • M. Ovsjanikov, A. M. Bronstein, L. J. Guibas and M. M. Bronstein. NORDIA, 2009. • (SI-HKS) M. M. Bronstein and I. Kokkinos. CVPR, 2010. • A. M. Bronstein, M. M. Bronstein, L. J. Guibas, and M. Ovsjanikov. ACM TOG, 2011. ICPR 2012

  5. Background (1) • Heat Kernel on surface • Amount of heat transferred from a point to in time • : -th eigenvalue and eigenfunction of the Laplace-Beltrami operator • Heat Kernel Signature (HKS): • HKS descriptor • A vector of HKS probed at different values of • Properties of Heat Kernel • Intrinsic (Invariant to rigid and isometric deformation) • Informative (locally and globally shape aware) • Stable ICPR 2012

  6. Background (2) • Geometric words • A representative HKS vector • Clustered in the HKS descriptor space by the k-means algorithm • Vocabulary • Similarity of point and word ICPR 2012

  7. Shape-Google Revisit (1) • Bag-of-Words • Word distribution of each point • BoW descriptor: vector • Measure the frequencies of words appearing on the shape ICPR 2012

  8. Shape-Google Revisit (2) • Spatially-Sensitive Bag-of-Words • SS-BOW descriptor: matrix • Measure the frequencies of word pairs ICPR 2012

  9. New Paradigm: Bag-of-Feature Graphs (1) Motivation: Reduce computation complexity Considering all points on shape -> only considering feature points Vector/matrix of word frequencies -> feature graphs associated with words ICPR 2012

  10. Formulation (1) … • Feature set: • Feature graph associated with the -th geometric word • represented as matrix • : Heat Kernel • Bag-of-Feature-Graphs representation of shape ICPR 2012

  11. Formulation (2) • BoFG descriptor • Multi-dimensional scaling (MDS): Choosing the 6 largest eigenvalues of each graph matrix denoted by • vector • Shape distance • Retrieval by approximate nearest neighbor (ANN) search ICPR 2012

  12. Nonrigid Shapes and Their BoFG Descriptors ICPR 2012

  13. : Number of vertices : Time complexity for computing HKS descriptor of a vertex Time Complexity of BoW, SS-BOW and BoFG ICPR 2012

  14. Experiments 1http://toca.cs.technion.ac.il/book/shrec.html • Test dataset: TOSCA1 • 12 classes of 148 non-rigid shapes • Each shape has 3K 30K vertices • Evaluated methods: BoW, FSS-BoW, SI-HKS, • Vocabulary • 48 words for BoW and SS-BoW (clustered from all shape points) • 4 words for BoFG (clustered only from feature points) • Feature numbers in BoFG: for each shape ICPR 2012

  15. ICPR 2012

  16. Experiments Time performance (in seconds) of three descriptors on two shapes with 3K and 30k vertices ICPR 2012

  17. Experiments (1) (2) (3) Precision-recall curves of evaluated methods, with categories of (1) null, (2) scale changes and (3) holes. ICPR 2012

  18. Partial shape retrieval Query shape is only a part of a complete model Online feature alignment is required to extract corresponding sub-graphs ICPR 2012

  19. Summary Bag-of-Feature-Graphs(BoFG) is a new paradigm for shape representation This representation is feature-driven, concise, and spatially-aware The key idea is to construct graphs of features associated with geometric words BoFG has much improved time-performance and competitive retrieval results in comparison with other state-of-the-art methods ICPR 2012

  20. Future Work Investigate graph comparison with heavy outliers Improve the performance on partial shape retrieval Acknowledgements: Research Grants from National Science Foundation ICPR 2012

  21. Thank You! Questions? ICPR 2012

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