--- _id: '3313' abstract: - lang: eng text: Interpreting an image as a function on a compact sub- set of the Euclidean plane, we get its scale-space by diffu- sion, spreading the image over the entire plane. This gener- ates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian ker- nel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods. article_number: '6126271' author: - first_name: Chao full_name: Chen, Chao id: 3E92416E-F248-11E8-B48F-1D18A9856A87 last_name: Chen - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: 'Chen C, Edelsbrunner H. Diffusion runs low on persistence fast. In: Proceedings of the IEEE International Conference on Computer Vision. IEEE; 2011. doi:10.1109/ICCV.2011.6126271' apa: 'Chen, C., & Edelsbrunner, H. (2011). Diffusion runs low on persistence fast. In Proceedings of the IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE. https://doi.org/10.1109/ICCV.2011.6126271' chicago: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” In Proceedings of the IEEE International Conference on Computer Vision. IEEE, 2011. https://doi.org/10.1109/ICCV.2011.6126271. ieee: C. Chen and H. Edelsbrunner, “Diffusion runs low on persistence fast,” in Proceedings of the IEEE International Conference on Computer Vision, Barcelona, Spain, 2011. ista: 'Chen C, Edelsbrunner H. 2011. Diffusion runs low on persistence fast. Proceedings of the IEEE International Conference on Computer Vision. ICCV: International Conference on Computer Vision, 6126271.' mla: Chen, Chao, and Herbert Edelsbrunner. “Diffusion Runs Low on Persistence Fast.” Proceedings of the IEEE International Conference on Computer Vision, 6126271, IEEE, 2011, doi:10.1109/ICCV.2011.6126271. short: C. Chen, H. Edelsbrunner, in:, Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2011. conference: end_date: 2011-11-13 location: Barcelona, Spain name: 'ICCV: International Conference on Computer Vision' start_date: 2011-11-06 date_created: 2018-12-11T12:02:37Z date_published: 2011-11-06T00:00:00Z date_updated: 2021-01-12T07:42:35Z day: '06' ddc: - '000' department: - _id: HeEd doi: 10.1109/ICCV.2011.6126271 file: - access_level: open_access checksum: 6984684081ba123808b344f9f2e64a8f content_type: application/pdf creator: system date_created: 2018-12-12T10:17:28Z date_updated: 2020-07-14T12:46:07Z file_id: '5282' file_name: IST-2016-540-v1+1_2011-P-08-RunEmpty.pdf file_size: 614050 relation: main_file file_date_updated: 2020-07-14T12:46:07Z has_accepted_license: '1' language: - iso: eng month: '11' oa: 1 oa_version: Submitted Version publication: Proceedings of the IEEE International Conference on Computer Vision publication_status: published publisher: IEEE publist_id: '3327' pubrep_id: '540' quality_controlled: '1' scopus_import: 1 status: public title: Diffusion runs low on persistence fast type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2011' ...