Sampson distance based joint estimation of multiple homographies with uncalibrated cameras
•Practitioners typically estimate multiple homographies separately.•Separate estimation does not enforce inter-homography constraints.•We jointly estimate homographies so that all constraints are satisfied.•Enforcing inter-homography constraints improves accuracy considerably.•Our cost function oper...
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| Vydané v: | Computer vision and image understanding Ročník 125; s. 200 - 213 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.08.2014
Elsevier |
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| ISSN: | 1077-3142, 1090-235X |
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| Abstract | •Practitioners typically estimate multiple homographies separately.•Separate estimation does not enforce inter-homography constraints.•We jointly estimate homographies so that all constraints are satisfied.•Enforcing inter-homography constraints improves accuracy considerably.•Our cost function operates directly on image points via the Sampson distance.
Two images of a scene consisting of multiple flat surfaces are related by a collection of homography matrices. Practitioners typically estimate these homographies separately thereby violating inherent inter-homography constraints that arise naturally out of the rigid geometry of the scene. We demonstrate that through a suitable choice of parametrisation multiple homographies can be jointly estimated in a manner so as to satisfy all inter-homography constraints. Unlike the cost functions used previously for solving this problem, our cost function does not correspond to fitting one set of homography matrices to another set of homography matrices. Instead, we utilise the Sampson distance for homography matrix estimation and operate directly on image data points. By using the Sampson distance and working directly on data points, we expedite the application of a vast amount of knowledge that already exists for Sampson-distance-based single homography or fundamental matrix estimation. The estimation framework reported in this paper establishes a new baseline for joint multiple homography estimation and at the same time raises intriguing new research questions. The work may be of interest to a broad range of researchers who require the estimation of homography matrices with uncalibrated cameras as part of their solution. |
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| AbstractList | •Practitioners typically estimate multiple homographies separately.•Separate estimation does not enforce inter-homography constraints.•We jointly estimate homographies so that all constraints are satisfied.•Enforcing inter-homography constraints improves accuracy considerably.•Our cost function operates directly on image points via the Sampson distance.
Two images of a scene consisting of multiple flat surfaces are related by a collection of homography matrices. Practitioners typically estimate these homographies separately thereby violating inherent inter-homography constraints that arise naturally out of the rigid geometry of the scene. We demonstrate that through a suitable choice of parametrisation multiple homographies can be jointly estimated in a manner so as to satisfy all inter-homography constraints. Unlike the cost functions used previously for solving this problem, our cost function does not correspond to fitting one set of homography matrices to another set of homography matrices. Instead, we utilise the Sampson distance for homography matrix estimation and operate directly on image data points. By using the Sampson distance and working directly on data points, we expedite the application of a vast amount of knowledge that already exists for Sampson-distance-based single homography or fundamental matrix estimation. The estimation framework reported in this paper establishes a new baseline for joint multiple homography estimation and at the same time raises intriguing new research questions. The work may be of interest to a broad range of researchers who require the estimation of homography matrices with uncalibrated cameras as part of their solution. Two images of a scene consisting of multiple flat surfaces are related by a collection of homography matrices. Practitioners typically estimate these homographies separately thereby violating inherent inter-homography constraints that arise naturally out of the rigid geometry of the scene. We demonstrate that through a suitable choice of parametrisation multiple homographies can be jointly estimated in a manner so as to satisfy all inter-homography constraints. Unlike the cost functions used previously for solving this problem, our cost function does not correspond to fitting one set of homography matrices to another set of homography matrices. Instead, we utilise the Sampson distance for homography matrix estimation and operate directly on image data points. By using the Sampson distance and working directly on data points, we expedite the application of a vast amount of knowledge that already exists for Sampson-distance-based single homography or fundamental matrix estimation. The estimation framework reported in this paper establishes a new baseline for joint multiple homography estimation and at the same time raises intriguing new research questions. The work may be of interest to a broad range of researchers who require the estimation of homography matrices with uncalibrated cameras as part of their solution. |
| Author | Chojnacki, Wojciech Szpak, Zygmunt L. van den Hengel, Anton Eriksson, Anders |
| Author_xml | – sequence: 1 givenname: Zygmunt L. surname: Szpak fullname: Szpak, Zygmunt L. email: zygmunt.szpak@adelaide.edu.au – sequence: 2 givenname: Wojciech surname: Chojnacki fullname: Chojnacki, Wojciech email: wojciech.chojnacki@adelaide.edu.au – sequence: 3 givenname: Anders surname: Eriksson fullname: Eriksson, Anders email: anders.eriksson@adelaide.edu.au – sequence: 4 givenname: Anton surname: van den Hengel fullname: van den Hengel, Anton email: anton.vandenhengel@adelaide.edu.au |
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| Cites_doi | 10.1007/s11785-012-0225-y 10.1007/s10851-007-0009-6 10.1109/TPAMI.2003.1227992 10.1109/ICCV.2011.6126485 10.1007/s11263-008-0167-z 10.5244/C.2.23 10.1007/3-540-61123-1_139 10.1109/34.601246 10.1109/34.982901 10.1109/ICCVW.2009.5457692 |
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| Keywords | Sampson distance Multiple homographies Latent variables Parameter estimation Maximum likelihood Image processing Epipolar geometry Image databank Latent variable model Modeling Multiple decision Multiple view Latent variable Image analysis Scene analysis Homograph Hidden variable theory Problem solving Cost function System identification Multiple choice |
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| SubjectTerms | Applied sciences Artificial intelligence Cameras Collection Computer science; control theory; systems Computer vision Cost function Data points Estimates Exact sciences and technology Fittings Latent variables Mathematics Maximum likelihood Multiple homographies Parameter estimation Parametric inference Pattern recognition. Digital image processing. Computational geometry Probability and statistics Sampson distance Sciences and techniques of general use Statistics |
| Title | Sampson distance based joint estimation of multiple homographies with uncalibrated cameras |
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