A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX
Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective t...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2016-06-01
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| Series: | ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| Online Access: | http://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-3/75/2016/isprs-annals-III-3-75-2016.pdf |
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| author | I. Kalisperakis G. Karras E. Petsa |
| author_facet | I. Kalisperakis G. Karras E. Petsa |
| author_sort | I. Kalisperakis |
| collection | DOAJ |
| description | Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two
bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the
image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical
coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer
Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In
this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of
epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these
constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the
fundamental matrix and the principal point position of a stereopair. |
| first_indexed | 2024-12-20T12:36:17Z |
| format | Article |
| id | doaj.art-9e63366f1b0d47bd883060fa0ad5c559 |
| institution | Directory Open Access Journal |
| issn | 2194-9042 2194-9050 |
| language | English |
| last_indexed | 2024-12-20T12:36:17Z |
| publishDate | 2016-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| spelling | doaj.art-9e63366f1b0d47bd883060fa0ad5c5592022-12-21T19:40:36ZengCopernicus PublicationsISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences2194-90422194-90502016-06-01III-3758210.5194/isprs-annals-III-3-75-2016A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIXI. Kalisperakis0G. Karras1E. Petsa2Laboratory of Photogrammetry, Department of Civil Engineering and Surveying & Geoinformatics Engineering, Technological Educational Institute of Athens, 12210 Athens, GreeceLaboratory of Photogrammetry, Department of Surveying, National Technical University of Athens, 15780 Athens, GreeceLaboratory of Photogrammetry, Department of Civil Engineering and Surveying & Geoinformatics Engineering, Technological Educational Institute of Athens, 12210 Athens, GreeceEpipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.http://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-3/75/2016/isprs-annals-III-3-75-2016.pdf |
| spellingShingle | I. Kalisperakis G. Karras E. Petsa A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| title | A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX |
| title_full | A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX |
| title_fullStr | A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX |
| title_full_unstemmed | A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX |
| title_short | A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX |
| title_sort | euclidean formulation of interior orientation costraints imposed by the fundamental matrix |
| url | http://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-3/75/2016/isprs-annals-III-3-75-2016.pdf |
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