A General Imaging Model Based Method for Scheimpflug Camera Calibration

Fig. 5. Schematic of calibration principle of general imaging model[42]. (a) Camera as black box, with one pixel and its camera ray; (b) pixel sees a point on a calibration object, whose coordinates are identified in a frame associated with the object; (c) same as (b) for another position of the calibration object; (d) if the object's motion is known, the two points on the calibration object can be placed in the same coordinate frame here the same one as in (c) the camera ray is then determined by joini

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Fig. 6. Schematic of general non-parametric imaging model

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Fig. 7. Reconstructed results and error distribution of planar calibration plate. (a) Reconstructed results of calibration plate; (b) error distribution of reconstructed control points

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Fig. 8. Two-dimensional electric rotary table

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Fig. 9. Three-dimensional electric translation table

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Table 1. Results of relative pose of calibration plate calibrated by different calibration models

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Table 1. Results of relative pose of calibration plate calibrated by different calibration models

Calibration model	( $\begin{matrix} R_{1}^{1} \end{matrix}$ , $\begin{matrix} R_{2}^{1} \end{matrix}$ , $\begin{matrix} R_{3}^{1} \end{matrix}$ )	( $\begin{matrix} T_{1}^{1} \end{matrix}$ , $\begin{matrix} T_{2}^{1} \end{matrix}$ , $\begin{matrix} T_{3}^{1} \end{matrix}$ ) /mm	( $\begin{matrix} R_{1}^{2} \end{matrix}$ , $\begin{matrix} R_{2}^{2} \end{matrix}$ , $\begin{matrix} R_{3}^{2} \end{matrix}$ )	( $\begin{matrix} T_{1}^{2} \end{matrix}$ , $\begin{matrix} T_{2}^{2} \end{matrix}$ , $\begin{matrix} T_{3}^{2} \end{matrix}$ ) /mm
Ref.[16] method	(1.5067,1.5080,-0.8159)	(-54.7739,-45.2021,442.8741)	(1.9628,0.7965,-0.3941)	(-66.5666,-26.0286,400.8027)
Ref.[2] method	(1.5392,1.4766,-0.8186)	(-53.7829,-48.3303,441.7981)	(1.9208,0.7914,-0.4100)	(-67.8423,-25.1659,399.2397)
Ref.[27] method	(1.4928,1.4434,-0.9046)	(-52.5684,-44.1141,441.0225)	(1.8824,0.7641,-0.4607)	(-65.8903,-25.5468,397.2328)
Proposed method	(1.5123,1.4682,-0.8481)	(-53.3728,-46.9573,441.6816)	(1.9031,0.7725,-0.4432)	(-66.7914,-25.6247,398.4627)

Table 2. Deviation of calibration results using general non-parametric imaging model and classical parametric models
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Table 2. Deviation of calibration results using general non-parametric imaging model and classical parametric models
Item Ref.[16] Ref.[2] Ref.[27]
Rotation 0.0548 0.0435 0.0500
Translation / mm 1.3653 1.3116 1.2975

Table 3. Pose estimation accuracy of Scheimpflug camera using different imaging models

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Table 3. Pose estimation accuracy of Scheimpflug camera using different imaging models

Experiment time	Item	Ref.[16] method	Ref.[2] method	Ref.[27] method	Proposed method
1^st	RMSE of rotation /(°)RMSE of translation /mm	0.03871.4659	0.04091.5109	0.04001.4905	0.04171.5305
2^nd	RMSE of rotation /(°)RMSE of translation /mm	0.04121.5562	0.04281.6042	0.04241.5732	0.04321.6655

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Cong Sun, Haibo Liu, Shengyi Chen, Yang Shang. A General Imaging Model Based Method for Scheimpflug Camera Calibration[J]. Acta Optica Sinica, 2018, 38(8): 0815009

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Paper Information

Category: Machine Vision

Received: Dec. 13, 2017

Accepted: Jan. 29, 2018

Published Online: Sep. 6, 2018

The Author Email:

DOI:10.3788/AOS201838.0815009

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Results of relative pose of calibration plate calibrated by different calibration models

Table 1. Results of relative pose of calibration plate calibrated by different calibration models

Table 2. Deviation of calibration results using general non-parametric imaging model and classical parametric models

Table 2. Deviation of calibration results using general non-parametric imaging model and classical parametric models

Table 3. Pose estimation accuracy of Scheimpflug camera using different imaging models

Table 3. Pose estimation accuracy of Scheimpflug camera using different imaging models