Geometry of single axis motions using conic fitting
Previous algorithms for recovering 3D geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two-view fundamental matrices and three-view trifocal tensors. We propose three new methods that are based on fitting a conic l...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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IEEE
2003
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| _version_ | 1824459140127260672 |
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| author | Jiang, G Tsui, H-T Quan, L Zisserman, A |
| author_facet | Jiang, G Tsui, H-T Quan, L Zisserman, A |
| author_sort | Jiang, G |
| collection | OXFORD |
| description | Previous algorithms for recovering 3D geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two-view fundamental matrices and three-view trifocal tensors. We propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views. The main advantage is that determining only five parameters of a conic from one corresponding point over at least five views is simpler and more robust than determining a fundamental matrix from two views or a trifocal tensor from three views. It is shown that the geometry of single axis motion can be recovered either by computing one conic locus and one fundamental matrix or by computing at least two conic loci. A maximum likelihood solution based on this parametrization of the single axis motion is also described for optimal estimation using three or more loci. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new methods. |
| first_indexed | 2025-02-19T04:37:03Z |
| format | Journal article |
| id | oxford-uuid:de9f2d34-8538-4945-8ebd-153ab12cccfb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-02-19T04:37:03Z |
| publishDate | 2003 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:de9f2d34-8538-4945-8ebd-153ab12cccfb2025-02-05T12:47:10ZGeometry of single axis motions using conic fittingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:de9f2d34-8538-4945-8ebd-153ab12cccfbEnglishSymplectic ElementsIEEE2003Jiang, GTsui, H-TQuan, LZisserman, APrevious algorithms for recovering 3D geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two-view fundamental matrices and three-view trifocal tensors. We propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views. The main advantage is that determining only five parameters of a conic from one corresponding point over at least five views is simpler and more robust than determining a fundamental matrix from two views or a trifocal tensor from three views. It is shown that the geometry of single axis motion can be recovered either by computing one conic locus and one fundamental matrix or by computing at least two conic loci. A maximum likelihood solution based on this parametrization of the single axis motion is also described for optimal estimation using three or more loci. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new methods. |
| spellingShingle | Jiang, G Tsui, H-T Quan, L Zisserman, A Geometry of single axis motions using conic fitting |
| title | Geometry of single axis motions using conic fitting |
| title_full | Geometry of single axis motions using conic fitting |
| title_fullStr | Geometry of single axis motions using conic fitting |
| title_full_unstemmed | Geometry of single axis motions using conic fitting |
| title_short | Geometry of single axis motions using conic fitting |
| title_sort | geometry of single axis motions using conic fitting |
| work_keys_str_mv | AT jiangg geometryofsingleaxismotionsusingconicfitting AT tsuiht geometryofsingleaxismotionsusingconicfitting AT quanl geometryofsingleaxismotionsusingconicfitting AT zissermana geometryofsingleaxismotionsusingconicfitting |