{"alternative_title":["ISTA Thesis"],"title":"The hole system of triangulated shapes","status":"public","related_material":{"record":[{"relation":"part_of_dissertation","id":"6608","status":"public"}]},"publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2020-02-06T14:56:53Z","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"abstract":[{"lang":"eng","text":"Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.\r\n\r\nFor the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries."}],"publication_status":"published","date_published":"2020-02-10T00:00:00Z","supervisor":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"}],"month":"02","article_processing_charge":"No","date_updated":"2023-09-07T13:15:30Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","type":"dissertation","file":[{"creator":"koelsboe","access_level":"open_access","file_name":"thesis_ist-final_noack.pdf","content_type":"application/pdf","checksum":"1df9f8c530b443c0e63a3f2e4fde412e","relation":"main_file","date_created":"2020-02-06T14:43:54Z","file_size":76195184,"file_id":"7461","date_updated":"2020-07-14T12:47:58Z"},{"file_id":"7462","file_size":122103715,"date_created":"2020-02-06T14:52:45Z","description":"latex source files, figures","date_updated":"2020-07-14T12:47:58Z","content_type":"application/x-zip-compressed","file_name":"latex-files.zip","creator":"koelsboe","access_level":"closed","relation":"source_file","checksum":"7a52383c812b0be64d3826546509e5a4"}],"degree_awarded":"PhD","day":"10","ddc":["514"],"keyword":["shape reconstruction","hole manipulation","ordered complexes","Alpha complex","Wrap complex","computational topology","Bregman geometry"],"file_date_updated":"2020-07-14T12:47:58Z","year":"2020","_id":"7460","language":[{"iso":"eng"}],"citation":{"ieee":"K. Ölsböck, “The hole system of triangulated shapes,” Institute of Science and Technology Austria, 2020.","mla":"Ölsböck, Katharina. <i>The Hole System of Triangulated Shapes</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7460\">10.15479/AT:ISTA:7460</a>.","short":"K. Ölsböck, The Hole System of Triangulated Shapes, Institute of Science and Technology Austria, 2020.","ama":"Ölsböck K. The hole system of triangulated shapes. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7460\">10.15479/AT:ISTA:7460</a>","chicago":"Ölsböck, Katharina. “The Hole System of Triangulated Shapes.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7460\">https://doi.org/10.15479/AT:ISTA:7460</a>.","ista":"Ölsböck K. 2020. The hole system of triangulated shapes. Institute of Science and Technology Austria.","apa":"Ölsböck, K. (2020). <i>The hole system of triangulated shapes</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7460\">https://doi.org/10.15479/AT:ISTA:7460</a>"},"publication_identifier":{"issn":["2663-337X"]},"author":[{"id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina","first_name":"Katharina","last_name":"Ölsböck","orcid":"0000-0002-4672-8297"}],"has_accepted_license":"1","doi":"10.15479/AT:ISTA:7460","page":"155"}