Suboptimal Solutions to the Algebraic-Error Line Triangulation

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	Suboptimal Solutions to the Algebraic-Error Line Triangulation
	Zhang, Qiang 1,2; Wu, Yan 1; Wang, Fan 1; Dong, Qiulei3 ; Jiao, Licheng 2
刊名	JOURNAL OF MATHEMATICAL IMAGING AND VISION
	2014-07-01
卷号	49 期号:3 页码:611-632
关键词	Line triangulation Multiple views Algebraic error Plucker line coordinates Suboptimal solutions
英文摘要	Line triangulation, a foundational problem in computer vision, is to estimate the 3D line position from a set of measured image lines with known camera projection matrices. Aiming to improve the triangulation's efficiency, in this work, two algorithms are proposed to find suboptimal solutions under the algebraic-error optimality criterion of the Plucker line coordinates. In these proposed algorithms, the algebraic-error optimality criterion is reformulated by the transformation of the Klein constraint. By relaxing the quadratic unit norm constraint to six linear constraints, six new single-quadric-constraint optimality criteria are constructed in the new formulation, whose optimal solutions can be obtained by solving polynomial equations. Moreover, we prove that the minimum algebraic error of either the first three or the last three of the six new criteria is not more than v 3 times of that of the original algebraic-error optimality criterion. Thus, with three new criteria and all the six criteria, suboptimal solutions under the algebraic error minimization and the geometric error minimization are obtained. Experimental results show the effectiveness of our proposed algorithms.
WOS标题词	Science & Technology ; Technology ; Physical Sciences
类目[WOS]	Computer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied
研究领域[WOS]	Computer Science ; Mathematics
关键词[WOS]	GEOMETRIC RECONSTRUCTION ; OPTIMIZATION ; MOTION ; CORRESPONDENCES
收录类别	SCI
语种	英语
WOS记录号	WOS:000339822700006
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/2986]
专题	自动化研究所_模式识别国家重点实验室_机器人视觉团队
作者单位	1.Xidian Univ, Sch Elect Engn, Xian 710071, Peoples R China 2.Xidian Univ, Minist Educ, Key Lab Intelligent Percept & Image Understanding, Xian 710071, Peoples R China 3.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Qiang,Wu, Yan,Wang, Fan,et al. Suboptimal Solutions to the Algebraic-Error Line Triangulation[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION,2014,49(3):611-632.
APA	Zhang, Qiang,Wu, Yan,Wang, Fan,Dong, Qiulei,&Jiao, Licheng.(2014).Suboptimal Solutions to the Algebraic-Error Line Triangulation.JOURNAL OF MATHEMATICAL IMAGING AND VISION,49(3),611-632.
MLA	Zhang, Qiang,et al."Suboptimal Solutions to the Algebraic-Error Line Triangulation".JOURNAL OF MATHEMATICAL IMAGING AND VISION 49.3(2014):611-632.