A six point solution for structure and motion
The paper has two main contributions: The first is a set of methods for computing structure and motion for m ≥ 3 views of 6 points. It is shown that a geometric image error can be minimized over all views by a simple three parameter numerical optimization. Then, that an algebraic image error can be...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Springer
2003
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| _version_ | 1817931379488325632 |
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| author | Schaffalitzky, F Zisserman, A Hartley, RI Torr, PHS |
| author_facet | Schaffalitzky, F Zisserman, A Hartley, RI Torr, PHS |
| author_sort | Schaffalitzky, F |
| collection | OXFORD |
| description | The paper has two main contributions: The first is a set of methods for computing structure and motion for m ≥ 3 views of 6 points. It is shown that a geometric image error can be minimized over all views by a simple three parameter numerical optimization. Then, that an algebraic image error can be minimized over all views by computing the solution to a cubic in one variable. Finally, a minor point, is that this “quasi-linear" linear solution enables a more concise algorithm, than any given previously, for the reconstruction of 6 points in 3 views. The second contribution is an m view n ≥ 6 point robust reconstruction algorithm which uses the 6 point method as a search engine. This extends the successful RANSAC based algorithms for 2-views and 3-views to m views. The algorithm can cope with missing data and mismatched data and may be used as an efficient initializer for bundle adjustment. The new algorithms are evaluated on synthetic and real image sequences, and compared to optimal estimation results (bundle adjustment). |
| first_indexed | 2024-12-09T03:21:05Z |
| format | Conference item |
| id | oxford-uuid:314485fb-2e66-4f2d-9feb-948a57552a68 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:21:05Z |
| publishDate | 2003 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:314485fb-2e66-4f2d-9feb-948a57552a682024-11-12T15:47:04ZA six point solution for structure and motionConference itemhttp://purl.org/coar/resource_type/c_5794uuid:314485fb-2e66-4f2d-9feb-948a57552a68EnglishSymplectic ElementsSpringer2003Schaffalitzky, FZisserman, AHartley, RITorr, PHSThe paper has two main contributions: The first is a set of methods for computing structure and motion for m ≥ 3 views of 6 points. It is shown that a geometric image error can be minimized over all views by a simple three parameter numerical optimization. Then, that an algebraic image error can be minimized over all views by computing the solution to a cubic in one variable. Finally, a minor point, is that this “quasi-linear" linear solution enables a more concise algorithm, than any given previously, for the reconstruction of 6 points in 3 views. The second contribution is an m view n ≥ 6 point robust reconstruction algorithm which uses the 6 point method as a search engine. This extends the successful RANSAC based algorithms for 2-views and 3-views to m views. The algorithm can cope with missing data and mismatched data and may be used as an efficient initializer for bundle adjustment. The new algorithms are evaluated on synthetic and real image sequences, and compared to optimal estimation results (bundle adjustment). |
| spellingShingle | Schaffalitzky, F Zisserman, A Hartley, RI Torr, PHS A six point solution for structure and motion |
| title | A six point solution for structure and motion |
| title_full | A six point solution for structure and motion |
| title_fullStr | A six point solution for structure and motion |
| title_full_unstemmed | A six point solution for structure and motion |
| title_short | A six point solution for structure and motion |
| title_sort | six point solution for structure and motion |
| work_keys_str_mv | AT schaffalitzkyf asixpointsolutionforstructureandmotion AT zissermana asixpointsolutionforstructureandmotion AT hartleyri asixpointsolutionforstructureandmotion AT torrphs asixpointsolutionforstructureandmotion AT schaffalitzkyf sixpointsolutionforstructureandmotion AT zissermana sixpointsolutionforstructureandmotion AT hartleyri sixpointsolutionforstructureandmotion AT torrphs sixpointsolutionforstructureandmotion |