{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hamiltonian-operator-for-spectral-shape","title":"Hamiltonian operator for spectral shape analysis","arxiv_id":"1611.01990","date":"2016-11-07","proceeding":null,"authors":["Yoni Choukroun","Alon Shtern","Alex Bronstein","Ron Kimmel"],"abstract":"Many shape analysis methods treat the geometry of an object as a metric space\nthat can be captured by the Laplace-Beltrami operator. In this paper, we\npropose to adapt the classical Hamiltonian operator from quantum mechanics to\nthe field of shape analysis. To this end we study the addition of a potential\nfunction to the Laplacian as a generator for dual spaces in which shape\nprocessing is performed. We present a general optimization approach for solving\nvariational problems involving the basis defined by the Hamiltonian using\nperturbation theory for its eigenvectors. The suggested operator is shown to\nproduce better functional spaces to operate with, as demonstrated on different\nshape analysis tasks.","url_abs":"http://arxiv.org/abs/1611.01990v2","url_pdf":"http://arxiv.org/pdf/1611.01990v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hamiltonian-operator-for-spectral-shape","repo_url":"https://github.com/dominikpenk/mesh-signatures","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}