Multimedia Tools and Applications

, Volume 76, Issue 15, pp 16189–16223 | Cite as

Projection matrix by orthogonal vanishing points



Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the intrinsic and extrinsic camera parameters. The proposed method reaches to a closed-form solution by considering only two feasible constraints of zero-skewness in the internal camera matrix and having two corresponding points between the world and the image. A nonlinear optimization procedure is proposed to enhance the computed camera parameters, especially when the measurement error of input parameters or the skew factor are not negligible. The proposed method has been run on real and synthetic data for more precise evaluations. The provided experimental results demonstrate the superiority of the proposed method.


Projection matrix Perspective transformation Camera calibration Vanishing points 



The authors would like to thank Mr. Yasin Zamani for providing the synthetic 3D-rendered dataset of soccer images. Special thanks to Mr. Mostafa Hadian, Mr. Afshin Bozorgpour, and Mrs. Sara Monji-azad for their valuable comments and suggestions to improve this work. We also would like to thank Prof. Mahmoud Reza Pishvaie for his guidance in solving some of the equations. This work has been partly supported by a grant from Iran National Science Foundation (INSF).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran

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