{"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/isospectralization-or-how-to-hear-shape-style","title":"Isospectralization, or how to hear shape, style, and correspondence","arxiv_id":"1811.11465","date":"2018-11-28","proceeding":"CVPR 2019 6","authors":["Luca Cosmo","Mikhail Panine","Arianna Rampini","Maks Ovsjanikov","Michael M. Bronstein","Emanuele Rodolà"],"abstract":"The question whether one can recover the shape of a geometric object from its\nLaplacian spectrum ('hear the shape of the drum') is a classical problem in\nspectral geometry with a broad range of implications and applications. While\ntheoretically the answer to this question is negative (there exist examples of\niso-spectral but non-isometric manifolds), little is known about the practical\npossibility of using the spectrum for shape reconstruction and optimization. In\nthis paper, we introduce a numerical procedure called isospectralization,\nconsisting of deforming one shape to make its Laplacian spectrum match that of\nanother. We implement the isospectralization procedure using modern\ndifferentiable programming techniques and exemplify its applications in some of\nthe classical and notoriously hard problems in geometry processing, computer\nvision, and graphics such as shape reconstruction, pose and style transfer, and\ndense deformable correspondence.","url_abs":"http://arxiv.org/abs/1811.11465v2","url_pdf":"http://arxiv.org/pdf/1811.11465v2.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":"isospectralization-or-how-to-hear-shape-style","repo_url":"https://github.com/lcosmo/isospectralization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"style-transfer","task_name":"Style Transfer"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1811.11465","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1811.11465"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/lcosmo/isospectralization","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"listed":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"79aab67527ff4367","entry":"totuple","repo":"lcosmo/isospectralization","repo_kind":"listed","path":"code_for_2D/shape_library.py","file_url":"https://github.com/lcosmo/isospectralization/blob/HEAD/code_for_2D/shape_library.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"79aab67527ff4367"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}