CASIA OpenIR  > 09年以前成果
A unified and complete framework of invariance for six points
Wu, YH; Hu, ZY; Li, H; Olver, PJ; Sommer, G
Source PublicationCOMPUTER ALGEBRA AND GEOMETRIC ALGEBRA WITH APPLICATIONS
2005
Volume3519Pages:403-417
SubtypeArticle
AbstractProjective geometric invariants play an important role in computer vision. To set up the invariant relationships between spatial points and their images from a single view, at least six pairs of spatial and image points are required. In this paper, we establish a unified and complete framework of the invariant relationships for six points. The framework covers the general case already developed in the literature and two novel cases. The two novel cases describe that six spatial points and the camera optical center lie on a quadric cone or a twisted cubic, called quadric cone case or twisted cubic case. For the general case and quadric cone case, camera parameters can be determined uniquely. For the twisted cubic case, camera parameters cannot be determined completely; this configuration of camera optical center and spatial points is called a critical configuration. The established unified framework may help to effectively identify the type of geometric information appearing in certain vision tasks, in particular critical geometric information. An obvious advantage using this framework to obtain geometric information is that no any explicit estimation on camera projective matrix and optical center is needed.
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
WOS KeywordPROJECTIVE RECONSTRUCTION ; GEOMETRIC APPROACH ; IMAGES
Indexed ByISTP ; SCI
Language英语
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000230362900028
Citation statistics
Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9077
Collection09年以前成果
AffiliationChinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Wu, YH,Hu, ZY,Li, H,et al. A unified and complete framework of invariance for six points[J]. COMPUTER ALGEBRA AND GEOMETRIC ALGEBRA WITH APPLICATIONS,2005,3519:403-417.
APA Wu, YH,Hu, ZY,Li, H,Olver, PJ,&Sommer, G.(2005).A unified and complete framework of invariance for six points.COMPUTER ALGEBRA AND GEOMETRIC ALGEBRA WITH APPLICATIONS,3519,403-417.
MLA Wu, YH,et al."A unified and complete framework of invariance for six points".COMPUTER ALGEBRA AND GEOMETRIC ALGEBRA WITH APPLICATIONS 3519(2005):403-417.
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