[{"conference":{"name":"SSVM: Scale Space and Variational Methods in Computer Vision","end_date":"2011-06-02","start_date":"2011-05-29","location":"Ein-Gedi, Israel"},"date_created":"2024-10-15T11:20:54Z","quality_controlled":"1","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349","9783642247859"],"isbn":["9783642247842"]},"language":[{"iso":"eng"}],"author":[{"full_name":"Aflalo, Yonathan","last_name":"Aflalo","first_name":"Yonathan"},{"orcid":"0000-0001-9699-8730","full_name":"Bronstein, Alexander","first_name":"Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","last_name":"Bronstein"},{"last_name":"Bronstein","full_name":"Bronstein, Michael M.","first_name":"Michael M."},{"last_name":"Kimmel","full_name":"Kimmel, Ron","first_name":"Ron"}],"title":"Deformable shape retrieval by learning diffusion kernels","date_published":"2012-01-09T00:00:00Z","citation":{"chicago":"Aflalo, Yonathan, Alex M. Bronstein, Michael M. Bronstein, and Ron Kimmel. “Deformable Shape Retrieval by Learning Diffusion Kernels.” In <i>3rd International Conference on Scale Space and Variational Methods in Computer Vision</i>, 6667:689–700. Springer Nature, 2012. <a href=\"https://doi.org/10.1007/978-3-642-24785-9_58\">https://doi.org/10.1007/978-3-642-24785-9_58</a>.","ama":"Aflalo Y, Bronstein AM, Bronstein MM, Kimmel R. Deformable shape retrieval by learning diffusion kernels. In: <i>3rd International Conference on Scale Space and Variational Methods in Computer Vision</i>. Vol 6667. Springer Nature; 2012:689-700. doi:<a href=\"https://doi.org/10.1007/978-3-642-24785-9_58\">10.1007/978-3-642-24785-9_58</a>","apa":"Aflalo, Y., Bronstein, A. M., Bronstein, M. M., &#38; Kimmel, R. (2012). Deformable shape retrieval by learning diffusion kernels. In <i>3rd International Conference on Scale Space and Variational Methods in Computer Vision</i> (Vol. 6667, pp. 689–700). Ein-Gedi, Israel: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-642-24785-9_58\">https://doi.org/10.1007/978-3-642-24785-9_58</a>","mla":"Aflalo, Yonathan, et al. “Deformable Shape Retrieval by Learning Diffusion Kernels.” <i>3rd International Conference on Scale Space and Variational Methods in Computer Vision</i>, vol. 6667, Springer Nature, 2012, pp. 689–700, doi:<a href=\"https://doi.org/10.1007/978-3-642-24785-9_58\">10.1007/978-3-642-24785-9_58</a>.","ieee":"Y. Aflalo, A. M. Bronstein, M. M. Bronstein, and R. Kimmel, “Deformable shape retrieval by learning diffusion kernels,” in <i>3rd International Conference on Scale Space and Variational Methods in Computer Vision</i>, Ein-Gedi, Israel, 2012, vol. 6667, pp. 689–700.","ista":"Aflalo Y, Bronstein AM, Bronstein MM, Kimmel R. 2012. Deformable shape retrieval by learning diffusion kernels. 3rd International Conference on Scale Space and Variational Methods in Computer Vision. SSVM: Scale Space and Variational Methods in Computer Vision, LNCS, vol. 6667, 689–700.","short":"Y. Aflalo, A.M. Bronstein, M.M. Bronstein, R. Kimmel, in:, 3rd International Conference on Scale Space and Variational Methods in Computer Vision, Springer Nature, 2012, pp. 689–700."},"article_processing_charge":"No","volume":6667,"month":"01","intvolume":"      6667","date_updated":"2025-01-16T12:42:32Z","status":"public","type":"conference","extern":"1","publication_status":"published","publisher":"Springer Nature","alternative_title":["LNCS"],"doi":"10.1007/978-3-642-24785-9_58","oa_version":"None","year":"2012","_id":"18345","page":"689-700","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"09","abstract":[{"lang":"eng","text":"In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal denoising. Here, we adopt similar concepts to construct optimal diffusion geometric shape descriptors. The analogy of Fourier basis are the eigenfunctions of the Laplace-Beltrami operator, in which many geometric constructions such as diffusion metrics, can be represented. By designing a filter of the Laplace-Beltrami eigenvalues, it is theoretically possible to achieve invariance to different shape transformations, like scaling. Given a set of shape classes with different transformations, we learn the optimal filter by minimizing the ratio between knowingly similar and knowingly dissimilar diffusion distances it induces. The output of the proposed framework is a filter that is optimally tuned to handle transformations that characterize the training set."}],"publication":"3rd International Conference on Scale Space and Variational Methods in Computer Vision"}]