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Article: Design and analysis of optimization methods for subdivision surface fitting

TitleDesign and analysis of optimization methods for subdivision surface fitting
Authors
KeywordsFitting
Optimization
Squared distance
Subdivision surface
Issue Date2007
PublisherI E E E. The Journal's web site is located at http://www.computer.org/tvcg
Citation
Ieee Transactions On Visualization And Computer Graphics, 2007, v. 13 n. 5, p. 878-890 How to Cite?
AbstractWe present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically motivated optimization schemes and reveal their intrinsic relations with standard methods for constrained nonlinear optimization. A commonly used method in graphics, called point distance minimization, is shown to use a variant of the gradient descent step and thus has only linear convergence. The second method, called tangent distance minimization, which is well known in computer vision, is shown to use the Gauss-Newton step and, thus, demonstrates near-quadratic convergence for zero residual problems but may not converge otherwise. Finally, we show that an optimization scheme called squared distance minimization, recently proposed by Pottmann et al., can be derived from the Newton method. Hence, with proper regularization, tangent distance minimization and squared distance minimization are more efficient than point distance minimization, We also investigate the effects of two step-size control methods - Levenberg-Marquardt regularization and the Armijo rule - on the convergence stability and efficiency of the above optimization schemes. © 2007 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/57247
ISSN
2015 Impact Factor: 1.4
2015 SCImago Journal Rankings: 0.917
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorCheng, KSDen_HK
dc.contributor.authorWang, Wen_HK
dc.contributor.authorQin, Hen_HK
dc.contributor.authorWong, KYKen_HK
dc.contributor.authorYang, Hen_HK
dc.contributor.authorLiu, Yen_HK
dc.date.accessioned2010-04-12T01:30:47Z-
dc.date.available2010-04-12T01:30:47Z-
dc.date.issued2007en_HK
dc.identifier.citationIeee Transactions On Visualization And Computer Graphics, 2007, v. 13 n. 5, p. 878-890en_HK
dc.identifier.issn1077-2626en_HK
dc.identifier.urihttp://hdl.handle.net/10722/57247-
dc.description.abstractWe present a complete framework for computing a subdivision surface to approximate unorganized point sample data, which is a separable nonlinear least squares problem. We study the convergence and stability of three geometrically motivated optimization schemes and reveal their intrinsic relations with standard methods for constrained nonlinear optimization. A commonly used method in graphics, called point distance minimization, is shown to use a variant of the gradient descent step and thus has only linear convergence. The second method, called tangent distance minimization, which is well known in computer vision, is shown to use the Gauss-Newton step and, thus, demonstrates near-quadratic convergence for zero residual problems but may not converge otherwise. Finally, we show that an optimization scheme called squared distance minimization, recently proposed by Pottmann et al., can be derived from the Newton method. Hence, with proper regularization, tangent distance minimization and squared distance minimization are more efficient than point distance minimization, We also investigate the effects of two step-size control methods - Levenberg-Marquardt regularization and the Armijo rule - on the convergence stability and efficiency of the above optimization schemes. © 2007 IEEE.en_HK
dc.languageengen_HK
dc.publisherI E E E. The Journal's web site is located at http://www.computer.org/tvcgen_HK
dc.relation.ispartofIEEE Transactions on Visualization and Computer Graphicsen_HK
dc.rights©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectFittingen_HK
dc.subjectOptimizationen_HK
dc.subjectSquared distanceen_HK
dc.subjectSubdivision surfaceen_HK
dc.titleDesign and analysis of optimization methods for subdivision surface fittingen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1077-2626&volume=13&issue=5&spage=878&epage=890&date=2007&atitle=Design+and+analysis+of+optimization+methods+for+subdivision+surface+fittingen_HK
dc.identifier.emailWang, W:wenping@cs.hku.hken_HK
dc.identifier.emailWong, KYK:kykwong@cs.hku.hken_HK
dc.identifier.authorityWang, W=rp00186en_HK
dc.identifier.authorityWong, KYK=rp01393en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/TVCG.2007.1064en_HK
dc.identifier.pmid17622673en_HK
dc.identifier.scopuseid_2-s2.0-34548540231en_HK
dc.identifier.hkuros139283-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-34548540231&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume13en_HK
dc.identifier.issue5en_HK
dc.identifier.spage878en_HK
dc.identifier.epage890en_HK
dc.identifier.isiWOS:000247893800003-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridCheng, KSD=21733550700en_HK
dc.identifier.scopusauthoridWang, W=35147101600en_HK
dc.identifier.scopusauthoridQin, H=34974717300en_HK
dc.identifier.scopusauthoridWong, KYK=24402187900en_HK
dc.identifier.scopusauthoridYang, H=15137870100en_HK
dc.identifier.scopusauthoridLiu, Y=27172089200en_HK

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