Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks
In this paper, we propose a generalization of convolutional neural networks (CNN) to non‐Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the lo...
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| Published in: | Computer graphics forum Vol. 34; no. 5; pp. 13 - 23 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
Blackwell Publishing Ltd
01.08.2015
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| ISSN: | 0167-7055, 1467-8659 |
| Online Access: | Get full text |
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| Abstract | In this paper, we propose a generalization of convolutional neural networks (CNN) to non‐Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the local behavior of some dense intrinsic descriptor, roughly acting as an analogy to patches in images. The resulting local frequency representations are then passed through a bank of filters whose coefficient are determined by a learning procedure minimizing a task‐specific cost. Our approach generalizes several previous methods such as HKS, WKS, spectral CNN, and GPS embeddings. Experimental results show that the proposed approach allows learning class‐specific shape descriptors significantly outperforming recent state‐of‐the‐art methods on standard benchmarks. |
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| AbstractList | In this paper, we propose a generalization of convolutional neural networks (CNN) to non‐Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform to manifolds) that is used to extract the local behavior of some dense intrinsic descriptor, roughly acting as an analogy to patches in images. The resulting local frequency representations are then passed through a bank of filters whose coefficient are determined by a learning procedure minimizing a task‐specific cost. Our approach generalizes several previous methods such as HKS, WKS, spectral CNN, and GPS embeddings. Experimental results show that the proposed approach allows learning class‐specific shape descriptors significantly outperforming recent state‐of‐the‐art methods on standard benchmarks. |
| Author | Bronstein, M. M. Vandergheynst, P. Boscaini, D. Masci, J. Melzi, S. Castellani, U. |
| Author_xml | – sequence: 1 givenname: D. surname: Boscaini fullname: Boscaini, D. organization: Institute of Computational Science, Faculty of Informatics, University of Lugano (USI), Switzerland – sequence: 2 givenname: J. surname: Masci fullname: Masci, J. organization: Institute of Computational Science, Faculty of Informatics, University of Lugano (USI), Switzerland – sequence: 3 givenname: S. surname: Melzi fullname: Melzi, S. organization: Department of Informatics, University of Verona, Italy – sequence: 4 givenname: M. M. surname: Bronstein fullname: Bronstein, M. M. organization: Institute of Computational Science, Faculty of Informatics, University of Lugano (USI), Switzerland – sequence: 5 givenname: U. surname: Castellani fullname: Castellani, U. organization: Department of Informatics, University of Verona, Italy – sequence: 6 givenname: P. surname: Vandergheynst fullname: Vandergheynst, P. organization: Department of Electrical Engineering, EPFL, Lausanne, Switzerland |
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| Copyright | 2015 The Author(s) Computer Graphics Forum © 2015 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2015 The Eurographics Association and John Wiley & Sons Ltd. |
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| References_xml | – reference: Elad A., Kimmel R.: On bending invariant signatures for surfaces. PAMI 25, 10 (2003), 1285-1295. 1 – reference: Coifman R.R., Lafon S.: Diffusion maps. Applied and Computational Harmonic Analysis 21, 1 (2006), 5-30. 1, 3, 4 – reference: Lian Z., et al.: A comparison of methods for non-rigid 3D shape retrieval. Pattern Recognition 46, 1 (2013), 449-461. 1 – reference: Reuter M., Wolter F.-E., Peinecke N.: Laplace-beltrami spectra as 'shape-dna' of surfaces and solids. Computer-Aided Design 38, 4 (2006), 342-366. 1 – reference: Litman R., Bronstein A., Bronstein M., Castellani U.: Supervised learning of bag-of-features shape descriptors using sparse coding. CGF 33, 5 (2014), 127-136. 1, 2 – reference: Sun J., Ovsjanikov M., Guibas L.J.: A concise and provably informative multi-scale signature based on heat diffusion. CGF 28, 5 (2009), 1383-1392. 1, 3, 7 – reference: Kim V.G., Lipman Y., Funkhouser T.: Blended intrinsic maps. TOG 30, 4 (2011), 1-12. 8 – reference: Osada R., Funkhouser T., Chazelle B., Dobkin D.: Shape distributions. TOG 21, 4 (2002), 807-832. 1 – reference: Anguelov D., et al.: SCAPE: Shape completion and animation of people. TOG 24, 3 (2005), 408-416. 7 – reference: Sipiran I., Bustos B.: Harris 3D: a robust extension of the harris operator for interest point detection on 3D meshes. Visual Computer 27, 11 (2011), 963-976. 1 – reference: Neumann T., Varanasi K., Theobalt C., Magnor M., Wacker M.: Compressed manifold modes for mesh processing. In Computer Graphics Forum (2014), vol. 33, pp. 35-44. 4 – reference: Lowe D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60, 2 (2004), 91-110. 1 – reference: Kalogerakis E., Hertzmann A., Singh K.: Learning 3D mesh segmentation and labeling. TOG 29, 3 (2010). 1 – reference: Pauly M., Keiser R., Gross M.: Multi-scale feature extraction on point-sampled surfaces. 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| Snippet | In this paper, we propose a generalization of convolutional neural networks (CNN) to non‐Euclidean domains for the analysis of deformable shapes. Our... In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our... |
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| SubjectTerms | Analysis Categories and Subject Descriptors (according to ACM CCS) Computational Geometry and Object Modeling [I.3.5] Computer graphics Cost engineering Deformation Feature Measurement [I.4.7] Formability Fourier transforms Learning Learning [I.2.6] Networks Neural networks Spectra State of the art Studies Topological manifolds |
| Title | Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks |
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