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postgraduate thesis: Studies on geometric shape reconstruction

TitleStudies on geometric shape reconstruction
Authors
Issue Date2015
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Zheng, W. [郑文妮]. (2015). Studies on geometric shape reconstruction. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5731099
AbstractThis thesis, on geometric shape modeling problems, contains two major chapters. In the first chapter, we propose a fast method for fitting planar Bspline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two alternating timeconsuming steps in every iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the LBFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to solve a linear system of equations or performing foot point projection in every iteration. As a result, the proposed method is much faster than existing methods. In the second chapter, we propose a new shape description method using a radial basis function built on the medial axis of the shape. By formulating our approach as a constrained L^1-minimization problem, our method produces sparse reconstruction result which uses much fewer basis functions than previous approaches. Besides the sparse representation capacity, our method also has advantages in two aspects: 1) Our method does not rely on normal information of input points. 2) Our method has stronger capacity in representing multi-scale shapes compared with existing methods. All these characteristics will be illustrated in the corresponding chapters and sections.
DegreeDoctor of Philosophy
SubjectComputer graphics
Geometry - Data processing
Dept/ProgramComputer Science
Persistent Identifierhttp://hdl.handle.net/10722/224647

 

DC FieldValueLanguage
dc.contributor.authorZheng, Wenni-
dc.contributor.author郑文妮-
dc.date.accessioned2016-04-11T23:15:17Z-
dc.date.available2016-04-11T23:15:17Z-
dc.date.issued2015-
dc.identifier.citationZheng, W. [郑文妮]. (2015). Studies on geometric shape reconstruction. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5731099-
dc.identifier.urihttp://hdl.handle.net/10722/224647-
dc.description.abstractThis thesis, on geometric shape modeling problems, contains two major chapters. In the first chapter, we propose a fast method for fitting planar Bspline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two alternating timeconsuming steps in every iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the LBFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to solve a linear system of equations or performing foot point projection in every iteration. As a result, the proposed method is much faster than existing methods. In the second chapter, we propose a new shape description method using a radial basis function built on the medial axis of the shape. By formulating our approach as a constrained L^1-minimization problem, our method produces sparse reconstruction result which uses much fewer basis functions than previous approaches. Besides the sparse representation capacity, our method also has advantages in two aspects: 1) Our method does not rely on normal information of input points. 2) Our method has stronger capacity in representing multi-scale shapes compared with existing methods. All these characteristics will be illustrated in the corresponding chapters and sections.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subject.lcshComputer graphics-
dc.subject.lcshGeometry - Data processing-
dc.titleStudies on geometric shape reconstruction-
dc.typePG_Thesis-
dc.identifier.hkulb5731099-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplineComputer Science-
dc.description.naturepublished_or_final_version-

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