{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/90683"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/90683","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Curve characterization with high-order tensor singular value decomposition","abstract":"Made available in DSpace on 2016-07-07T19:58:19Z (GMT). No. of bitstreams: 2 CAI-THESIS-2016.pdf: 2599852 bytes, checksum: c5150b52d2e0c26a7abcb48c71c76bf3 (MD5) LICENSE.txt: 4206 bytes, checksum: cd03b4878a87f39bc09a17838bd5b8de (MD5) Previous issue date: 2016-04-28","abstract_html":"Made available in DSpace on 2016-07-07T19:58:19Z (GMT). No. of bitstreams: 2 CAI-THESIS-2016.pdf: 2599852 bytes, checksum: c5150b52d2e0c26a7abcb48c71c76bf3 (MD5) LICENSE.txt: 4206 bytes, checksum: cd03b4878a87f39bc09a17838bd5b8de (MD5) Previous issue date: 2016-04-28","abstract_has_math":false,"creators":["Cai, Muyun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Tortorelli, Daniel A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T19:58:19Z","date_published":"2016-07-07T19:58:19Z","updated_at":"2026-07-22T22:26:34Z","subjects":["curve characterization","Mikowski valuation"],"languages":["en"],"rights":["Copyright 2016 Muyun Cai"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/90683","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tortorelli, Daniel A."]},{"key":"dc:creator","label":"Author","values":["Cai, Muyun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-07-07T19:58:19Z","2016-04-28","2016-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["curve characterization","Mikowski valuation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Muyun Cai"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/90683"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Made available in DSpace on 2016-07-07T19:58:19Z (GMT). No. of bitstreams: 2 CAI-THESIS-2016.pdf: 2599852 bytes, checksum: c5150b52d2e0c26a7abcb48c71c76bf3 (MD5) LICENSE.txt: 4206 bytes, checksum: cd03b4878a87f39bc09a17838bd5b8de (MD5) Previous issue date: 2016-04-28","Oil has been found on what was once the banks of ancient rivers. As a consequence, there is an interest in identifying the locations of ancient rivers, which in turn motivates the need for criteria to identify river locations. To that end, we develop geometric descriptors to quantify river geometries and to observe their statistics. The river geometries are represented by curves which define their center lines. Curve descriptors are defined via Minkowski valuations and high-order singular value decomposition. The advantage of this method is that a large number of descriptors can be readily generated. The statistic study is conducted on a few groups of curves and a collection of rivers in Texas. To create the descriptors, high order Minkowski valuation tensors are generated based on the curves' position vectors, normal vectors and curvatures. Next, these tensors are decomposed via high-order singular-value decomposition into scalar descriptors derived from the eigenvalues of the tensors. Correlation amongst the descriptors are subsequently obtained and the independent ones are identified. At last, two sets of statistical analysis are conducted. The first analysis provides insights to the physics of the descriptors. Groups of curves are generated in this analysis, wherein specific geometric features are varied, and the change in the curve descriptors is observed. Thus we infer correlations between geometric features and descriptors. The second analysis evaluates a descriptors-based criterion to identify river-like curves. In this analysis, the descriptors of 1722 10-mile Texas river segments are obtained and a joint density probability function amongst the independent descriptors is created. The probability function is subsequently used as a criterion to identify river-like curves among randomly generated ones.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms","The student, Muyun Cai, accepted the attached license on 2016-04-27 at 15:00.","The student, Muyun Cai, submitted this Thesis for approval on 2016-04-27 at 15:07.","This Thesis was approved for publication on 2016-04-28 at 10:37.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9555 on 2016-07-07 at 13:33:44"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Curve characterization with high-order tensor singular value decomposition"]}]}],"canonical_facts":{"dc:contributor":["Tortorelli, Daniel A."],"dc:creator":["Cai, Muyun"],"dc:date":["2016-07-07T19:58:19Z","2016-04-28","2016-05"],"dc:description":["Made available in DSpace on 2016-07-07T19:58:19Z (GMT). No. of bitstreams: 2 CAI-THESIS-2016.pdf: 2599852 bytes, checksum: c5150b52d2e0c26a7abcb48c71c76bf3 (MD5) LICENSE.txt: 4206 bytes, checksum: cd03b4878a87f39bc09a17838bd5b8de (MD5) Previous issue date: 2016-04-28","Oil has been found on what was once the banks of ancient rivers. As a consequence, there is an interest in identifying the locations of ancient rivers, which in turn motivates the need for criteria to identify river locations. To that end, we develop geometric descriptors to quantify river geometries and to observe their statistics. The river geometries are represented by curves which define their center lines. Curve descriptors are defined via Minkowski valuations and high-order singular value decomposition. The advantage of this method is that a large number of descriptors can be readily generated. The statistic study is conducted on a few groups of curves and a collection of rivers in Texas. To create the descriptors, high order Minkowski valuation tensors are generated based on the curves' position vectors, normal vectors and curvatures. Next, these tensors are decomposed via high-order singular-value decomposition into scalar descriptors derived from the eigenvalues of the tensors. Correlation amongst the descriptors are subsequently obtained and the independent ones are identified. At last, two sets of statistical analysis are conducted. The first analysis provides insights to the physics of the descriptors. Groups of curves are generated in this analysis, wherein specific geometric features are varied, and the change in the curve descriptors is observed. Thus we infer correlations between geometric features and descriptors. The second analysis evaluates a descriptors-based criterion to identify river-like curves. In this analysis, the descriptors of 1722 10-mile Texas river segments are obtained and a joint density probability function amongst the independent descriptors is created. The probability function is subsequently used as a criterion to identify river-like curves among randomly generated ones.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms","The student, Muyun Cai, accepted the attached license on 2016-04-27 at 15:00.","The student, Muyun Cai, submitted this Thesis for approval on 2016-04-27 at 15:07.","This Thesis was approved for publication on 2016-04-28 at 10:37.","DSpace SAF Submission Ingestion Package generated from Vireo submission #9555 on 2016-07-07 at 13:33:44"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/90683"],"dc:language":["en"],"dc:rights":["Copyright 2016 Muyun Cai"],"dc:subject":["curve characterization","Mikowski valuation"],"dc:title":["Curve characterization with high-order tensor singular value decomposition"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:34Z"}