• Infrared and Laser Engineering
  • Vol. 50, Issue 11, 20210071 (2021)
Wenyi Chen1、2, Jie Xu1、*, and Hui Yang1
Author Affiliations
  • 1Industry School of Modern Post, Xi’an University of Posts and Telecommunications, Xi’an 710061, China
  • 2Collaborative Innovation Center for Modern Post, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
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    DOI: 10.3788/IRLA20210071 Cite this Article
    Wenyi Chen, Jie Xu, Hui Yang. Camera calibration method based on double neural network[J]. Infrared and Laser Engineering, 2021, 50(11): 20210071 Copy Citation Text show less

    Abstract

    In computer vision, camera calibration as the premise of camera measurement technology, is an essential part. Aiming at the problem that the training accuracy of camera calibration method based on neural network is not high enough, a camera calibration method based on double neural network was proposed. Starting from the imaging model, it was deduced that the camera coordinate ${Z_{\text{c}}}$ was a function of the world coordinate and the pixel coordinate. On the basis of considering ${Z_{\text{c}}}$, the imaging model was simplified into two function relations, and two neural networks were used for calibration, which not only differentiated the task amount of single neural network, but also fully followed the imaging model. The experimental results show that compared with other calibration methods based on neural network, this method improves the accuracy of camera calibration. And the average calibration error is 0.1786 ${\rm{mm}}$ in the calibration range of $400\;{\rm{mm}} \times 300\;{\rm{mm}}$, which verifies the feasibility and effectiveness of proposed method.
    $ {Z_{\rm{c}}}\left[ {\begin{array}{*{20}{c}} u \\ v \\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {f/{\rm d}x} \\ 0 \\ 0 \end{array}}&{\begin{array}{*{20}{c}} 0 \\ {f/{\rm d}y} \\ 0 \end{array}}&{\begin{array}{*{20}{c}} {{u_{\rm{o}}}} \\ {{v_{\rm{o}}}} \\ 1 \end{array}}&{\begin{array}{*{20}{c}} 0 \\ 0 \\ 0 \end{array}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} \boldsymbol{R}&\boldsymbol{T} \\ {{\boldsymbol{O}^{\rm T}}}&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{X_{\rm{w}}}} \\ {{Y_{\rm{w}}}} \\ {{Z_{\rm{w}}}} \\ 1 \end{array}} \right] $(1)

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    $ \left[ \begin{gathered} {X_{\rm{c}}} \\ {Y_{\rm{c}}} \\ {Z_{\rm{c}}} \\ \end{gathered} \right] = \boldsymbol{R}\left[ \begin{gathered} {X_{\rm{w}}} \\ {Y_{\rm{w}}} \\ {Z_{\rm{w}}} \\ \end{gathered} \right] + \boldsymbol{T} $(2)

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    $ {Z_{\rm{c}}}\left[ {\begin{array}{*{20}{c}} u \\ v \\ 1 \end{array}} \right] = \boldsymbol{K}\left(\boldsymbol{R}\left[ \begin{gathered} {X_{\rm{w}}} \\ {Y_{\rm{w}}} \\ {Z_{\rm{w}}} \\ \end{gathered} \right] + \boldsymbol{T}\right) $(3)

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    $ \left[ \begin{gathered} {X_{\rm{w}}} \\ {Y_{\rm{w}}} \\ {Z_{\rm{w}}} \\ \end{gathered} \right] = {\boldsymbol{R}^{ - 1}}\left({\boldsymbol{K}^{ - 1}}{Z_{\rm{c}}}\left[ \begin{gathered} u \\ v \\ 1 \\ \end{gathered} \right] - \boldsymbol{T}\right) $(4)

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    $ \boldsymbol{A} = {\boldsymbol{R}^{ - 1}}{\boldsymbol{K}^{ - 1}}\left[ \begin{gathered} u \\ v \\ 1 \\ \end{gathered} \right],\;\;B = {\boldsymbol{R}^{ - 1}}\boldsymbol T $(5)

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    $ {Z_{\rm{w}}} = {Z_{\rm{c}}}\boldsymbol{A}(3,1) - \boldsymbol{B}(3,1) $(6)

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    $ {Z_{\rm{c}}} = \frac{{{Z_{\rm{w}}} + \boldsymbol{B}(3,1)}}{{\boldsymbol{A}(3,1)}} $(7)

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    $ {Z_{\rm{c}}} = f(u,v,{Z_{\rm{w}}}) $(8)

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    $ {X_{\rm{w}}} = {Z_{\rm{c}}}\boldsymbol{A}(1,1) - \boldsymbol{B}(1,1) = {f_1}(u,v,{Z_{\rm{w}}}) $(9)

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    $ {Y_{\rm{w}}} = {Z_{\rm{c}}}\boldsymbol{A}(2,1) - \boldsymbol{B}(2,1) = {f_2}(u,v,{Z_{\rm{w}}}) $(10)

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    $ {f_{{xz}}}(u,v) \to ({X_{\rm{w}}},{Z_{\rm{w}}}) $(11)

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    $ {f_{{yz}}}(u,v) \to ({Y_{\rm{w}}},{Z_{\rm{w}}}) $(12)

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    $ fitness = \sum\limits_{i = 1}^M {\sum\limits_{k = 1}^K {{{({d_{ik}} - {y_{ik}})}^2}} } $(13)

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    $ E = \frac{{\sqrt {{{({X_{\rm{w}}} - {X_{\rm{w}}}')}^2} + {{({Y_{\rm{w}}} - {Y_{\rm{w}}}')}^2} + {{({Z_{\rm{w}}} - {Z_{\rm{w}}}')}^2}} }}{n} $(14)

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    Wenyi Chen, Jie Xu, Hui Yang. Camera calibration method based on double neural network[J]. Infrared and Laser Engineering, 2021, 50(11): 20210071
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