The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Integral Invariants for Shape Matching
Abstract
For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.
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Cites
Shape matching and object recognition using shape contexts
Belongie, S., Malik, J., & Puzicha, J. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.993558 · Cited by 6,306
Mumford, D., Fogarty, J., & Kirwan, F. (1994) · Springer Grundlehren · doi:10.1007/978-3-642-57916-5 · Cited by 2,564
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Kumar, N., Belhumeur, P. N., Biswas, A., Jacobs, D. W., Kress, W. J., Lopez, I. C., & Soares, J. V. B. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-33709-3_36 · Cited by 802
The wave kernel signature: A quantum mechanical approach to shape analysis
Aubry, M., Schlickewei, U., & Cremers, D. (2011) · 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops) · doi:10.1109/iccvw.2011.6130444 · Cited by 731
Self-citationGeodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721
Gromov‐Hausdorff Stable Signatures for Shapes using Persistence
Chazal, F., Cohen‐Steiner, D., Guibas, L. J., Mémoli, F., & Oudot, S. Y. (2009) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2009.01516.x · Cited by 225
Metadata
- Authors
- Manay, S., Cremers, D., Hong, B.-W., Yezzi, A. J., & Soatto, S.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2006-10
- Volume
- 28
- Issue
- 10
- Pages
- 1602-1618
- ISSN
- 0162-8828 (ISSN-L)
- 2160-9292
- OpenAlex
- W2143357187
- Cited by
- 234
- References
- 2
- FWCI
- 15.29
- Type
- journal article
- Language
- en
- Open access
- closed
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- Manay, S., Cremers, D., Hong, B.-W., Yezzi, A. J., & Soatto, S. (2006). Integral Invariants for Shape Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/tpami.2006.208
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