{"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/elastic-functional-coding-of-riemannian","title":"Elastic Functional Coding of Riemannian Trajectories","arxiv_id":"1603.02200","date":"2016-03-07","proceeding":null,"authors":["Rushil Anirudh","Pavan Turaga","Jingyong Su","Anuj Srivastava"],"abstract":"Visual observations of dynamic phenomena, such as human actions, are often\nrepresented as sequences of smoothly-varying features . In cases where the\nfeature spaces can be structured as Riemannian manifolds, the corresponding\nrepresentations become trajectories on manifolds. Analysis of these\ntrajectories is challenging due to non-linearity of underlying spaces and\nhigh-dimensionality of trajectories. In vision problems, given the nature of\nphysical systems involved, these phenomena are better characterized on a\nlow-dimensional manifold compared to the space of Riemannian trajectories. For\ninstance, if one does not impose physical constraints of the human body, in\ndata involving human action analysis, the resulting representation space will\nhave highly redundant features. Learning an effective, low-dimensional\nembedding for action representations will have a huge impact in the areas of\nsearch and retrieval, visualization, learning, and recognition. The difficulty\nlies in inherent non-linearity of the domain and temporal variability of\nactions that can distort any traditional metric between trajectories. To\novercome these issues, we use the framework based on transported square-root\nvelocity fields (TSRVF); this framework has several desirable properties,\nincluding a rate-invariant metric and vector space representations. We propose\nto learn an embedding such that each action trajectory is mapped to a single\npoint in a low-dimensional Euclidean space, and the trajectories that differ\nonly in temporal rates map to the same point. We utilize the TSRVF\nrepresentation, and accompanying statistical summaries of Riemannian\ntrajectories, to extend existing coding methods such as PCA, KSVD and Label\nConsistent KSVD to Riemannian trajectories or more generally to Riemannian\nfunctions.","url_abs":"http://arxiv.org/abs/1603.02200v1","url_pdf":"http://arxiv.org/pdf/1603.02200v1.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":"elastic-functional-coding-of-riemannian","repo_url":"https://github.com/rushilanirudh/tsrvf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"action-analysis","task_name":"Action Analysis"},{"task_slug":"retrieval","task_name":"Retrieval"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}