Elsevier

Pattern Recognition

Volume 38, Issue 1, January 2005, Pages 143-150
Pattern Recognition

Initialization method for self-calibration using 2-views

https://doi.org/10.1016/j.patcog.2004.05.005Get rights and content

Abstract

Recently, 3D structure recovery through self-calibration of camera has been actively researched. Traditional calibration algorithm requires known 3D coordinates of the control points while self-calibration only requires the corresponding points of images, thus it has more flexibility in real application. In general, self-calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera. Thus, it requires initial value for the nonlinear minimization. Traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change. In this paper, we propose new initialization method using the minimum 2 images. Proposed method is based on the assumption that the least violation of the camera's intrinsic parameter gives more stable initial value. Synthetic and real experiment shows this result.

Introduction

Recently, 3D structure recovery through self-calibration of camera has been actively researched. Traditional calibration algorithm requires known 3D coordinates of the control points while self-calibration only requires the corresponding points of images, thus it has more flexibility in real application. In general, self-calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera. Thus, it requires initial value for the nonlinear minimization. Traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change.

Faugeras et al. [1] proposed a self-calibration algorithm that uses the Kruppa equation. It enforces that the planes through two camera centers that are tangent to the absolute conic should also be tangent to both of its images. Hartley [2] proposed another method based on the minimization of the difference between the internal camera parameters for the different views. Polleyfeys et al. [3] proposed a stratified approach that first recovers the affine geometry using the modulus constraint and then recover the Euclidean geometry through the absolute conic. Heyden and Åström [4], Triggs [5] and Pollefeys and Van Gool [6] use explicit constraints that relate the absolute conic to its images. These formulations are especially interesting since they can easily be extended to deal with the varying internal camera parameters.

Recently self-calibration algorithms that can deal with the varying camera's intrinsic parameters were proposed. Heyden and Åström [7] proposed a self-calibration algorithm that uses explicit constraints from the assumption of the intrinsic parameters of the camera. They proved that self-calibration is possible under varying cameras with the assumptions that the aspect ratio is known and there is no skew. They solved the problem using the bundle adjustment that requires simultaneous minimization on the all reconstructed points and cameras. Moreover, the initialization problem was not properly presented. Bougnoux [8] proposed a practical self-calibration algorithm that used the constraints derived from Heyden and Åström [7]. He proposed the linear initialization step in the nonlinear minimization. He used the bundle adjustment in the projective reconstruction step. Similarly, Pollefeys et al. [9] proposed a versatile self-calibration method that can deal with a number of types of constraints about the camera. They showed a specialized version for the case where the focal length varies, possibly also the principal point. Fusiello [18] presents a review paper about uncalibrated Euclidean reconstruction, where he points out the importance of the initialization method for autocalibration techniques to be able to be used in the real-world application.

In this paper, we propose new initialization method for the self-calibration algorithm by using the minimal two images, which result in the more stable initial values for the nonlinear minimization. This results in the solving of the simultaneous equations of the second-order, and gives two solutions that have opposite direction in projective space. Proposed method is based on the assumption that the least violation of the camera's intrinsic parameter gives more stable initial value. Synthetic and real experiments show this result. Finally, we can have more robust self-calibration algorithm based on the proposed initialization method.

Section snippets

Self-calibration algorithm

In this section, we review the self-calibration algorithm that appears in [8]. The process of projection of a point in 3D to the image plane can be represented as the following sequential steps:Peuc=AP0T=αuγu00αvv0001100001000010Rt03T1,where T represents the transformation of coordinate systems from world to the camera-centered system, P0 is the perspective projection and A consists of the intrinsic parameters of camera.

We use the following assumptions about the intrinsic parameters of camera:γ=

New initialization method

We need initial values to run the nonlinear minimization. The cost function of Eq. (8) has many local minima. Thus, it is important to have good initial values close to the true ones to guarantee the convergence. The initial value proposed by Bougnoux [8] often does not guarantee convergence. This is due to the fact that least-squares solution under the assumption that intrinsic parameters are constant under the varying cameras makes the initial values even worse. We propose new initialization

Experimental results

Synthetic and real experiments using additional constraint about the position of the principal point can be found in [12]. Here we present experimental results related to the proposed initialization method. Fig. 2 represents calibration box and control points used in the experiments, and they are acquired by a color CCD camera (Sony EVI-300). Calibration box size is 150mm×150mm×150mm. Tsai [17], Bougnoux [8] and proposed algorithm is compared. Table 1 shows the estimated initial f and q=(q1,q2,q

Conclusion

As pointed out in review paper [18] about uncalibrated Euclidean reconstruction, sensitivity to noise and initialization are two important issues for self-calibration techniques to be used in the real-world application. This paper addresses the initialization method of the self-calibration. New initialization method for the self-calibration using the minimum 2 views is presented. Proposed method is based on the assumption least violation about the camera gives more accurate initial values for

Summary

Recently, 3D structure recovery through self-calibration of camera has been actively researched. Traditional calibration algorithm requires known 3D coordinates of the control points while self-calibration only requires the corresponding points of images, thus it has more flexibility in real application. In general, self-calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera. Thus, it requires initial value for the

Acknowledgements

This research is supported by Tongmyong University of IT's research Financial Aid. Authors are graceful for its financial support.

About the Author—JONG-EUN, HA: He received a B.S. and a M.E. degree in Mechanical Engineering from Seoul National University, Seoul, Korea, in 1992 and 1994, respectively, and the Ph.D. Degree in Robotics and Computer Vision Lab. at KAIST in 2000. During 2000.02–2002.08, he worked at Samsung Corning where he developed machine vision system. Since 2002, he has been full-time lecturer at the department of multimedia engineering in Tongmyong University of Information Technology. His current

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There are more references available in the full text version of this article.

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About the Author—JONG-EUN, HA: He received a B.S. and a M.E. degree in Mechanical Engineering from Seoul National University, Seoul, Korea, in 1992 and 1994, respectively, and the Ph.D. Degree in Robotics and Computer Vision Lab. at KAIST in 2000. During 2000.02–2002.08, he worked at Samsung Corning where he developed machine vision system. Since 2002, he has been full-time lecturer at the department of multimedia engineering in Tongmyong University of Information Technology. His current research interests are robust self-calibration, mark-free motion capture, and object detection and recognition.

About the Author—DONG-JOONG, KANG: He received a B.S. degree in Precision Engineering from Pusan National University, Pusan, Korea, in 1988 and an M.E. degree in Mechanical Engineering from KAIST (Korea Advanced Institute of Science and Technology), Seoul, Korea, in 1990. He also received a Ph.D. degree in Automation and Design Engineering at KAIST, in 1998. In 1997–1999, he was a research engineer at SAIT (Samsung Advanced Institute of Technology). Since 2000, he has been an assistant professor in Tongmyong University of Information Technology. His current interests include visual inspection, robotics and automation, optimization theory in computer vision, and HCI (Human–Computer Interface) application of vision algorithms. He is a member of the IEEE and ICASE.

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