{"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/a-geometric-framework-for-stochastic-shape","title":"A Geometric Framework for Stochastic Shape Analysis","arxiv_id":"1703.09971","date":"2017-03-29","proceeding":null,"authors":["Alexis Arnaudon","Darryl D. Holm","Stefan Sommer"],"abstract":"We introduce a stochastic model of diffeomorphisms, whose action on a variety\nof data types descends to stochastic evolution of shapes, images and landmarks.\nThe stochasticity is introduced in the vector field which transports the data\nin the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework for\nshape analysis and image registration. The stochasticity thereby models errors\nor uncertainties of the flow in following the prescribed deformation velocity.\nThe approach is illustrated in the example of finite dimensional landmark\nmanifolds, whose stochastic evolution is studied both via the Fokker-Planck\nequation and by numerical simulations. We derive two approaches for inferring\nparameters of the stochastic model from landmark configurations observed at\ndiscrete time points. The first of the two approaches matches moments of the\nFokker-Planck equation to sample moments of the data, while the second approach\nemploys an Expectation-Maximisation based algorithm using a Monte Carlo bridge\nsampling scheme to optimise the data likelihood. We derive and numerically test\nthe ability of the two approaches to infer the spatial correlation length of\nthe underlying noise.","url_abs":"http://arxiv.org/abs/1703.09971v3","url_pdf":"http://arxiv.org/pdf/1703.09971v3.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":"a-geometric-framework-for-stochastic-shape","repo_url":"https://bitbucket.org/stefansommer/stochlandyn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"image-registration","task_name":"Image Registration"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}