{"id":{"repo_id":"bradford","oai_identifier":"oai:bradscholars.brad.ac.uk:10454/14425"},"canonical_url":"https://search.dev.ndltd.org/etd/bradford/oai:bradscholars.brad.ac.uk:10454/14425","repository":{"repo_id":"bradford","name":"University of Bradford","base_url":"https://bradscholars.brad.ac.uk/oai/request"},"display":{"title":"Modelling facial action units using partial differential equations.","abstract":"This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions.","abstract_html":"This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions.","abstract_has_math":false,"creators":["Ismail, Nur B.B."],"institution":"University of Bradford","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ugail, Hassan","Gonzalez Castro, Gabriela"],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-24T01:15:21Z","subjects":["Geometric modelling; 3D face modelling; Partial differential equations; PDE method; Action units; Facial expressions"],"languages":["en"],"rights":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10454/14425","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ugail, Hassan","Gonzalez Castro, Gabriela"]},{"key":"dc:creator","label":"Author","values":["Ismail, Nur B.B."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-01-09T16:14:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-01-09T16:14:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Centre of Visual Computing, Faculty of Engineering and Informatics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Bradford"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geometric modelling; 3D face modelling; Partial differential equations; PDE method; Action units; Facial expressions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10454/14425"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. In particular, a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to suitable boundary conditions is utilized, where the chosen boundary curves are based on muscles movement defined by Facial Action Coding System (FACS). This study involved three stages: modelling faces, manipulating faces and application to simple facial animation. In the first stage, PDE method is used in modelling and generating a smooth 3D face. The PDE formulation using small sets of parameters contributes to the efficiency of human face representation. In the manipulation stage, a generic PDE face of neutral expression is manipulated to a face with expression using PDE descriptors that uniquely represents an action unit. A combination of the PDE descriptor results in a generic PDE face having an expression, which successfully modelled four basic expressions: happy, sad, fear and disgust. An example of application is given using simple animation technique called blendshapes. This technique uses generic PDE face in animating basic expressions."]},{"key":"dc:title","label":"Title","values":["Modelling facial action units using partial differential equations."]}]}],"canonical_facts":{"dc:contributor.advisor":["Ugail, Hassan","Gonzalez Castro, Gabriela"],"dc:creator":["Ismail, Nur B.B."],"dc:date.accessioned":["2018-01-09T16:14:30Z"],"dc:date.available":["2018-01-09T16:14:30Z"],"dc:date.issued":["2015"],"dc:description.abstract":["This thesis discusses a novel method for modelling facial action units. It presents facial action units model based on boundary value problems for accurate representation of human facial expression in three-dimensions. 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This technique uses generic PDE face in animating basic expressions."],"dc:identifier.uri":["http://hdl.handle.net/10454/14425"],"dc:language.iso":["en"],"dc:publisher.department":["Centre of Visual Computing, Faculty of Engineering and Informatics"],"dc:publisher.institution":["University of Bradford"],"dc:rights":["<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png\" /></a><br />The University of Bradford theses are licenced under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/3.0/\">Creative Commons Licence</a>."],"dc:subject":["Geometric modelling; 3D face modelling; Partial differential equations; PDE method; Action units; Facial expressions"],"dc:title":["Modelling facial action units using partial differential equations."],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:15:21Z"}