Les capteurs catadioptriques et mon travail sur le calibrage/Catadioptric sensor, my work on calibration
Presentation
Catadioptric sensors are a combination of a
mirror and a video camera. A special and very interesting configuration is the one that uses a revolution
profile mirror as it provides 360 field of view at a classical video frame rate. This configuration is
well adapted for mobile robots and video security systems. For this kind of applications,
the increased fov is a major improvement. Catadioptric sensors are not the only way to get a panoramic fov. You can
get panoramic images with fisheye lens or rotating sensors...
Unlike devices based on rotating camera, with a revolution mirror, the increased field of view is not at the expense of acquisition speed. Indeed the speed of acquisition is that of the conventional camera. However, the field of view has been expanded but not the size of the image sensor, the resolution of this type of sensor is then reduced.
Calibration Process
The calibration procees is not easy. Intrinsics parameters must be estimated as well as mirror parameters, especially the distance between the mirror and the camera. Without this distance, this kind of sensors can't be used properly.
The main idea of the calibration proces we propose is quite simple: the mirror can be use as a calibration pattern. The mirror is always visible in the image and is never partially hidden. The dimension is well known.
In order to perform this calibration process we adapt the two plans method[GrThKa88]. This method is simple: two calibration plans are selected in space, the two homographies (H1 and H2) are computed. The homographies project image plan onto each calibration plan. By the use of this homographies, a set of points on the image is projected onto each calibration plan. Each point of the image gives a couple of points in space and each couple of points defines a line in space. All lines converge towards the focal point of the camera.
To adapt this method to our sensor, we select the upper and the lower boundaries of the mirror. We compute homographies. By the use of homographies we project a set of points in space. For each point in the image, we get a couple of points in space. Each couple of points defines a line and all lines converge towards the focal point of the camera. All lines are expressed in the mirror coordinate space, the focal point of the camera is expressed in this coordinate space. The relative placement mirror/camera can be deducted.
It is also possible, by the use of all lines, to estimate intrinsics parameters of the camera[GrThKa88].
Comparaison of existing methods
This table compares most of existing methods :
| Method | Sensor | Estimated param. | >Missing param. | >Constraints |
|---|---|---|---|---|
| Direct circle-based self-calibration | only paracatadioptric | parabol param. and image center | skew and aspect ratio | none |
| Self-calibration method | only paracatadioptric | parabol param. and image center, skew and aspect ratio | none | tracking (moving camera and static environnement) |
| Mi\v{c}u\v{s}\'ik and Pajdla | only paracatadioptric and hyperbolic | parabol param. and image center, skew and aspect ratio | none | tracking (moving camera and static environnement) |
| Geyer and Daniilidis | only paracatadioptric | parabol param. and image center, skew and aspect ratio | none | many sets of parallele lines in space |
| Geyer and Daniilidis | only paracatadioptric | parabol param. and image center, skew and aspect ratio | none | at least 3 lines in space |
| Xianghua Ying et Zhanyi Hu | only SVP sensors | the focal lenght, image center, skew and aspect ratio | none | at least 3 lines or 3 spheres in space |
| Cyril Cauchois | only conic mirror | intrinsic (with distorsion !) and extrinsic | none | calibration pattern mounted on the sensor |
| Carnegie Mellon University | all types of mirror | relative placement of the mirror in respect to the camera | intrinsic | precisly located patterns all arround the sensor |
| Our method | All type unless a telecentric lens is used | intrinsic param. and relative position of the mirror in respect to the camera | none | none (only two plans of the mirror must be known) |
This table shows that our method is less constraining than the majority of the existing methods. Our method can also be adapted to a many diffenrent kind of sensors and does not relied on the shape of the mirror.
Conclusion
We propose a simple and efficient calibration method for catadioptric panoramic sensors. This method can be apply on many different kind of sensors. As the calibration process does not requiered human intervention, it can be performed whenever needed (periodically, after a special event...). The main issue is the extraction of calibration patterns. The precision of the calibration process depends on this step...
Bibliography and links
More details can be found in:- "Calibration of Panoramic Catadioptric Sensors Made Easier", J. Fabrizio, J.-P. Tarel, et R. Benosman, IEEE European Conference Computer Vision, Workshop on Omnidirectional Vision (ECCV 02), page 45-52, Copenhague, 02 Juin 2002.
- "Localisation d'obstacles coopératifs par systèmes de vision classiques et panoramiques", J. Fabrizio - PhD thesis - Université Pierre et Marie Curie - Paris VI - December 15, 2004
- "Localisation d'obstacles coopératifs par systèmes de vision classiques et panoramiques", J. Fabrizio - PhD thesis - Université Pierre et Marie Curie - Paris VI - December 15, 2004
[GrThKa88] K. Gremban, C. H. Thorpe, and T. Kanade. "Geometric camera calibration using systems of linear equations.", Proceedings of IEEE Conference on Robotics and Automation (ICRA '88), Vol. 1, April, 1988, pp. 562 - 567.
Calibration methods:
Sing Bing Kang. "Catadioptric self-calibration.", In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, volume 1, pages 201-207, 2000.
Branislav Micusk and Tomas Pajdla. "Para-catadioptric camera auto-calibration from epipolar geometry.", Proceedings of the Asian Conference on Computer Vision, January 2004.
Christopher Geyer and Kostas Daniilidis. "Catadioptric camera calibration.", In Proceedings of the 7th International Conference on Computer Vision, Kerkyra, pages 398-404, 1999.
Christopher Geyer and Kostas Daniilidis. "Paracatadioptric camera calibration.", IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5):687-695, 2002.
Xianghua Ying and Zhanyi Hu. "Catadioptric camera calibrage using geometric invariants.", In Proceedings of the 9th International Conference on Computer Vision, Nice, 2003.
Cyril Cauchois. "Modelisation et Calibration du Capteur Omnidirectionnel SYCLOP : Application a la Localisation Absolue en Milieu Structure.", PhD thesis, 2001.
D. Strelow, J. Mishler, D. Koes, and S. Singh. "Precise omnidirectional camera calibration.", In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 689-694, 2001.