A Camera Calibration Method Using Parallelogramatic Grid Points

Akira TAKAHASHI; Ikuo ISHII; Hideo MAKINO; Makoto NAKASHIZUKA

A Camera Calibration Method Using Parallelogramatic Grid Points

Akira TAKAHASHI, Ikuo ISHII, Hideo MAKINO, Makoto NAKASHIZUKA

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In this paper, we propose a camera calibration method that estimates both intrinsic parameters (perspective and distortion) and extrinsic parameters (rotational and translational). All camera parameters can be determined from one or more images of planar pattern consists of parallelogramatic grid points. As far as the pattern can be visible, the relative relations between camera and patterns are arbitrary. So, we have only to prepare a pattern, and take one or more images changing the relative relation between camera and the pattern, arbitrarily; neither solid object of ground truth nor precise z-stage are required. Moreover, constraint conditions that are imposed on rotational parameters are explicitly satisfied; no intermediate parameter that connected several actual camera parameters are used. Taking account of the conflicting fact that the amount of distortion is small in the neighborhood of the image center, and that small image has poor clues of 3-D information, we adopt iterative procedure. The best parameters are searched changing the size and number of parallelograms selected from grid points. The procedure of the iteration is as follows: The perspective parameters are estimated from the shape of parallelogram by nonlinear optimizations. The rotational parameters are calculated from the shape of parallelogram. The translational parameters are estimated from the size of parallelogram by least squares method. Then, the distortion parameters are estimated using all grid points by least squares method. The computer simulation demonstrates the efficiency of the proposed method. And the results of the implementation using real images are also shown.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.11 pp.1579-1587

Publication Date: 1996/11/25

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Type of Manuscript: PAPER

Category: Image Processing,Computer Graphics and Pattern Recognition

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Akira TAKAHASHI, Ikuo ISHII, Hideo MAKINO, Makoto NAKASHIZUKA, "A Camera Calibration Method Using Parallelogramatic Grid Points" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 11, pp. 1579-1587, November 1996, doi: .
Abstract: In this paper, we propose a camera calibration method that estimates both intrinsic parameters (perspective and distortion) and extrinsic parameters (rotational and translational). All camera parameters can be determined from one or more images of planar pattern consists of parallelogramatic grid points. As far as the pattern can be visible, the relative relations between camera and patterns are arbitrary. So, we have only to prepare a pattern, and take one or more images changing the relative relation between camera and the pattern, arbitrarily; neither solid object of ground truth nor precise z-stage are required. Moreover, constraint conditions that are imposed on rotational parameters are explicitly satisfied; no intermediate parameter that connected several actual camera parameters are used. Taking account of the conflicting fact that the amount of distortion is small in the neighborhood of the image center, and that small image has poor clues of 3-D information, we adopt iterative procedure. The best parameters are searched changing the size and number of parallelograms selected from grid points. The procedure of the iteration is as follows: The perspective parameters are estimated from the shape of parallelogram by nonlinear optimizations. The rotational parameters are calculated from the shape of parallelogram. The translational parameters are estimated from the size of parallelogram by least squares method. Then, the distortion parameters are estimated using all grid points by least squares method. The computer simulation demonstrates the efficiency of the proposed method. And the results of the implementation using real images are also shown.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e79-d_11_1579/_p

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@ARTICLE{e79-d_11_1579,
author={Akira TAKAHASHI, Ikuo ISHII, Hideo MAKINO, Makoto NAKASHIZUKA, },
journal={IEICE TRANSACTIONS on Information},
title={A Camera Calibration Method Using Parallelogramatic Grid Points},
year={1996},
volume={E79-D},
number={11},
pages={1579-1587},
abstract={In this paper, we propose a camera calibration method that estimates both intrinsic parameters (perspective and distortion) and extrinsic parameters (rotational and translational). All camera parameters can be determined from one or more images of planar pattern consists of parallelogramatic grid points. As far as the pattern can be visible, the relative relations between camera and patterns are arbitrary. So, we have only to prepare a pattern, and take one or more images changing the relative relation between camera and the pattern, arbitrarily; neither solid object of ground truth nor precise z-stage are required. Moreover, constraint conditions that are imposed on rotational parameters are explicitly satisfied; no intermediate parameter that connected several actual camera parameters are used. Taking account of the conflicting fact that the amount of distortion is small in the neighborhood of the image center, and that small image has poor clues of 3-D information, we adopt iterative procedure. The best parameters are searched changing the size and number of parallelograms selected from grid points. The procedure of the iteration is as follows: The perspective parameters are estimated from the shape of parallelogram by nonlinear optimizations. The rotational parameters are calculated from the shape of parallelogram. The translational parameters are estimated from the size of parallelogram by least squares method. Then, the distortion parameters are estimated using all grid points by least squares method. The computer simulation demonstrates the efficiency of the proposed method. And the results of the implementation using real images are also shown.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - A Camera Calibration Method Using Parallelogramatic Grid Points
T2 - IEICE TRANSACTIONS on Information
SP - 1579
EP - 1587
AU - Akira TAKAHASHI
AU - Ikuo ISHII
AU - Hideo MAKINO
AU - Makoto NAKASHIZUKA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 11
JA - IEICE TRANSACTIONS on Information
Y1 - November 1996
AB - In this paper, we propose a camera calibration method that estimates both intrinsic parameters (perspective and distortion) and extrinsic parameters (rotational and translational). All camera parameters can be determined from one or more images of planar pattern consists of parallelogramatic grid points. As far as the pattern can be visible, the relative relations between camera and patterns are arbitrary. So, we have only to prepare a pattern, and take one or more images changing the relative relation between camera and the pattern, arbitrarily; neither solid object of ground truth nor precise z-stage are required. Moreover, constraint conditions that are imposed on rotational parameters are explicitly satisfied; no intermediate parameter that connected several actual camera parameters are used. Taking account of the conflicting fact that the amount of distortion is small in the neighborhood of the image center, and that small image has poor clues of 3-D information, we adopt iterative procedure. The best parameters are searched changing the size and number of parallelograms selected from grid points. The procedure of the iteration is as follows: The perspective parameters are estimated from the shape of parallelogram by nonlinear optimizations. The rotational parameters are calculated from the shape of parallelogram. The translational parameters are estimated from the size of parallelogram by least squares method. Then, the distortion parameters are estimated using all grid points by least squares method. The computer simulation demonstrates the efficiency of the proposed method. And the results of the implementation using real images are also shown.
ER -