Calibration of central catadioptric cameras based on the projection properties between the right and oblique cones

Qingfeng Zhuo; Yue Zhao; Siwen Wang

doi:10.1364/AO.491337

Applied Optics
Vol. 62,
Issue 18,
pp. 4820-4830
(2023)
•https://doi.org/10.1364/AO.491337

Calibration of central catadioptric cameras based on the projection properties between the right and oblique cones

Qingfeng Zhuo, Yue Zhao, and Siwen Wang

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Qingfeng Zhuo, Yue Zhao, and Siwen Wang, "Calibration of central catadioptric cameras based on the projection properties between the right and oblique cones," Appl. Opt. 62, 4820-4830 (2023)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Related Topics
Table of Contents Category
- Imaging Systems, Image Processing, and Displays
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: March 22, 2023
- Revised Manuscript: May 5, 2023
- Manuscript Accepted: May 18, 2023
- Published: June 12, 2023

Abstract

Central catadioptric cameras with a single effective viewpoint can easily transform the original image into a perspective image. In this study, we proposed a calibration algorithm for central catadioptric cameras. A vanishing line was recovered by the images of two sphere images (or line images) and mirror contour based on the properties of right and oblique cones. Subsequently, the intrinsic parameters were solved by the image of circular points and the orthogonal vanishing points. Finally, the distortion coefficient was estimated based on the geometric properties of the right cone. The simulation and real-time experiments conducted proved the effectiveness and feasibility of the proposed algorithm.

Full Article | PDF Article

More Like This

Calibration of a paracatadioptric camera by projection imaging of a single sphere

Yuanzhen Li and Yue Zhao
Appl. Opt. 56(8) 2230-2240 (2017)

Calibrating a paracatadioptric camera by the property of the polar of a point at infinity with respect to a circle

Yue Zhao, Yuanzhen Li, and Bihui Zheng
Appl. Opt. 57(15) 4345-4352 (2018)

Calibration of camera intrinsic parameters based on the properties of the polar of circular points

Fengli Yang, Yue Zhao, and Xuechun Wang
Appl. Opt. 58(22) 5901-5909 (2019)

Previous Article Next Article

Data availability

The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (36)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

	Intrinsic Parameters
Methods	$f_{x}$	$f_{y}$	$s$	$u_{0}$	$v_{0}$
ICP	1077.3241	1472.2031	0.6657	650.3318	585.3312
OVP	1083.9102	1489.4563	0.7324	651.5634	585.9176
CPT	1079.6753	1483.6752	0.7057	653.3318	586.3475
Wu [13]	1081.3241	1486.6678	0.7298	645.5456	583.4578
GI	1092.6708	1477.3454	0.7463	643.7844	582.7845

Distortion	Methods
Coefficient	ICP	OVP	CPT	GI	DCT
$k_{1}$	0.2401	0.2408	–	–	–
$k_{2}$	0.1497	0.1512	–	–	–

	Methods
	ICP	OVP	ICP	GI	ICP
Parallel	0.7114	Parallel	0.7114	Parallel	0.7114
Orthogonal	89.5631	Orthogonal	89.5631	Orthogonal	89.5631

	Intrinsic Parameters
Methods	$f_{x}$	$f_{y}$	$s$	$u_{0}$	$v_{0}$
ICP	1077.3241	1472.2031	0.6657	650.3318	585.3312
OVP	1083.9102	1489.4563	0.7324	651.5634	585.9176
CPT	1079.6753	1483.6752	0.7057	653.3318	586.3475
Wu [13]	1081.3241	1486.6678	0.7298	645.5456	583.4578
GI	1092.6708	1477.3454	0.7463	643.7844	582.7845

Distortion	Methods
Coefficient	ICP	OVP	CPT	GI	DCT
$k_{1}$	0.2401	0.2408	–	–	–
$k_{2}$	0.1497	0.1512	–	–	–

Input: $n (n \geq 3)$ images containing two sphere images (or line images).
Output: Internal parameter matrix $K$ and radial distortion coefficients $k_{1}, k_{2}$ .
Step 1. Extract the pixel coordinates of the mirror contour and sphere images. Use the least square method [24] to fit the equations of the imaged mirror contour $c_{n 0}$ and sphere images (or line images) $c_{n 1}, c_{n 2}$ .
Step 2. Use Proposition 3 to get the vanishing line $l_{n \infty}$ on the plane where the mirror contour is located.
Step 3. Obtain the ICPs $m_{n +}, m_{n -}$ from Eq. (24) or the OVPs $v_{n i \infty}, v_{n i \infty}^{'}$ $(i = 1, 2)$ from Eqs. (27)–(30).
Step 4. Obtain the image of the absolute conic $ω$ from Eq. (26) or Eq. (31) to obtain the camera intrinsic parameters $K$ .
Step 5. Obtain and the radial distortion coefficients $k_{1}, k_{2}$ from Eq. (35).

Input: $n (n \geq 3)$ images containing two sphere images (or line images).
Output: Internal parameter matrix $K$ and radial distortion coefficients $k_{1}, k_{2}$ .
Step 1. Extract the pixel coordinates of the mirror contour and sphere images. Use the least square method [24] to fit the equations of the imaged mirror contour $c_{n 0}$ and sphere images (or line images) $c_{n 1}, c_{n 2}$ .
Step 2. Use Proposition 3 to get the vanishing line $l_{n \infty}$ on the plane where the mirror contour is located.
Step 3. Obtain the ICPs $m_{n +}, m_{n -}$ from Eq. (24) or the OVPs $v_{n i \infty}, v_{n i \infty}^{'}$ $(i = 1, 2)$ from Eqs. (27)–(30).
Step 4. Obtain the image of the absolute conic $ω$ from Eq. (26) or Eq. (31) to obtain the camera intrinsic parameters $K$ .
Step 5. Obtain and the radial distortion coefficients $k_{1}, k_{2}$ from Eq. (35).

Abstract

Data availability

Cited By

Figures (9)

Tables (5)

Equations (36)

Applied Optics