Bi-tangent line based approach for multi-camera calibration using spheres

Jian Yu; Feipeng Da

doi:10.1364/JOSAA.35.000221

Bi-tangent line based approach for multi-camera calibration using spheres

Jian Yu and Feipeng Da

Journal of the Optical Society of America A
Vol. 35,
Issue 2,
pp. 221-229
(2018)
•https://doi.org/10.1364/JOSAA.35.000221

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Jian Yu and Feipeng Da, "Bi-tangent line based approach for multi-camera calibration using spheres," J. Opt. Soc. Am. A 35, 221-229 (2018)

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Related Topics
Table of Contents Category
- Machine Vision
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Machine vision (150.0150)
- Calibration (150.1488)
- Industrial optical metrology (150.3045)
- Vision (330.7310)

About this Article
History
- Original Manuscript: August 22, 2017
- Revised Manuscript: December 2, 2017
- Manuscript Accepted: December 12, 2017
- Published: January 9, 2018

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Abstract

This paper presents a novel approach for multi-camera calibration using spheres. We determine the projection of sphere centers first through bi-tangent lines of projection conics, which provides another solution for camera parameters on the basis of the relationship between the images of spheres and the image of the absolute conic in dual space. All parameters are refined by an optimization with the purpose of minimizing the reprojection error, which is divided into two independent parts associated with the corresponding shape parameters of the conics. Experimental results from the synthetic and real data show the feasibility and the accuracy achieved by our approach.

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	$f_{u}$ (% error)	$f_{v}$ (% error)	$s$ (% error)	$u_{0}$ (% error)	$v_{0}$ (% error)
Ground Truth	1000	980	2	400	300
SDP	984.093(1.59)	964.595(1.57)	1.739(13.05)	395.764(1.06)	300.884(0.29)
Ort	984.022(1.60)	964.446(1.59)	1.725(13.77)	395.774(1.06)	300.853(0.28)
Ours	984.364(1.56)	964.855(1.55)	1.721(13.95)	395.779(1.06)	300.871(0.29)

	Sphere1	Sphere2	Sphere3	Dist(Ave)
Ground Truth	[60,60,500]′	[80,−60,480]′	[−100,−50,530]′	NaN
SDP	[62.42,59.87,494.95]′	[82.66,−60.81,475.66]′	[−98.41,−50.78,524.96]′	5.36
Ort	[62.48,59.90,494.88]′	[82.57,−60.81,475.62]′	[−98.41,−50.77,524.90]′	5.41
Ours	[62.48,59.89,495.07]′	[82.56,−60.81,475.80]′	[−98.42,−50.78,525.10]′	5.24

	Chessboard	SDP	Ort	Ours
$f_{u}$	2490.86	2545.38	2546.89	2533.08
$f_{v}$	2492.07	2541.01	2543.36	2528.67
$s$	0.49	1.26	1.14	1.13
$u_{0}$	712.57	697.88	697.87	698.92
$v_{0}$	490.59	500.31	500.59	495.51
$k_{1}$	−0.133	—	—	−0.059
$k_{2}$	0.070	—	—	0.022
$p_{1}$	$- 2.8 e - 3$	—	—	$2.183 e - 7$
$p_{2}$	$- 2.713 e - 4$	—	—	$- 1.975 e - 7$

	$f_{u}$ (% error)	$f_{v}$ (% error)	$s$ (% error)	$u_{0}$ (% error)	$v_{0}$ (% error)
Ground Truth	1000	980	2	400	300
SDP	984.093(1.59)	964.595(1.57)	1.739(13.05)	395.764(1.06)	300.884(0.29)
Ort	984.022(1.60)	964.446(1.59)	1.725(13.77)	395.774(1.06)	300.853(0.28)
Ours	984.364(1.56)	964.855(1.55)	1.721(13.95)	395.779(1.06)	300.871(0.29)

	Sphere1	Sphere2	Sphere3	Dist(Ave)
Ground Truth	[60,60,500]′	[80,−60,480]′	[−100,−50,530]′	NaN
SDP	[62.42,59.87,494.95]′	[82.66,−60.81,475.66]′	[−98.41,−50.78,524.96]′	5.36
Ort	[62.48,59.90,494.88]′	[82.57,−60.81,475.62]′	[−98.41,−50.77,524.90]′	5.41
Ours	[62.48,59.89,495.07]′	[82.56,−60.81,475.80]′	[−98.42,−50.78,525.10]′	5.24

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