Rev. Fac. Ing. - Univ. Tarapacá, vol. 13 no. 1, 2005, pp. 57-67

COMPARACIÓN DE TÉCNICAS DE CALIBRACIÓN DE CÁMARAS DIGITALES

Diego Aracena Pizarro¹ Pedro Campos² Clésio Luis Tozzi³

1 Universidad de Tarapacá, Arica Chile, Académico Departamento de Computación e Informática, Facultad de Ingeniería, daracena@uta.cl

2 Universidad de Tarapacá, Arica Chile, Estudiante Magíster Ingeniería de Software, Facultad de Ingeniería, pcampos@uta.cl

3 Universidad Estatal de Campinas, São Paulo Brasil, Profesor Titular del Departamento de Ingeniería en Computación y Automatización, Facultad de Ingeniería Eléctrica y Computación, clesio@dca.fee.unicamp.br

RESUMEN

Este trabajo presenta una comparación de las técnicas de calibración propuestas por Tuceryan et al. [15], Trucco et al. [13] y Zhang [20], los cuales proponen maneras diferentes para determinar los parámetros a partir de puntos 3D conocidos y sus correspondientes en el plano imagen 2D. La correspondencia es extraída en forma manual, centrando la atención en la exactitud de los parámetros de cámara entregados (intrínsecos y extrínsecos). Los patrones pasivos utilizados consideran las técnicas de calibración con diferentes homografías, dependiendo de los planos existentes en el proceso. Zhang [20] propone una aproximación basada en patrones acomodados en una superficie planar 2D, donde la cámara o el patrón se desplaza sin conocer el movimiento. En cambio Tuceryan et al. [15] y Trucco et al. [13] se basan en un modelo conocido 3D y su correspondencia en el plano imagen 2D, diferenciándose en la consideración de los parámetros intrínsecos que deben ser determinados o de influencia en la matriz de cámara final.

Los algoritmos fueron implementados en Matlab 6.0, de acuerdo a la interpretación de los trabajos y técnicas de optimización extraídas desde la literatura citada.

Palabras clave: Visión computacional, calibración de cámara, homografía 3D-2D, matrices de proyección.

ABSTRACT

This work presents a comparison of the calibration techniques proposed by Tuceryan et al. [15], Trucco et al. [13] and Zhang [20], suggesting different ways to determine the parameters, starting from known 3D points and their corresponding points in the 2D image plane. The correspondence is manually extracted, being the obtained parameter accuracies (extrinsic and intrinsic) the most important. The passive patterns used consider the calibration techniques with different homographs, depending on the existing process planes. Zhang [20] proposes an approximation based on patterns located on a 2D planar surface, where the camera or the pattern are displaced without knowledge of the motion. Tuceryan et al. [15] and Trucco et al. [13] base their procedure in a known 3D model and its correspondence on a 2D image plane, the difference being in the consideration of the intrinsic parameters that must be determined or considered in the final camera matrix.

The algorithms were implemented using Matlab 6.0, according to the interpretation of the works and optimization techniques extracted from the cited literature.

Keywords: Computer vision, camera calibration, 3D-2D homograph, projection matrix.

REFERENCIAS

[1] D. Aracena, C. Tosí. "Algoritmo de Seguimiento para aplicaciones en Realidad Aumentada", X Encuentro Chileno de la Computación, Copiapó Chile, 2002.         [ Links ]

[2] A. Azarbayejani and A. Pentland. "Recursive estimation of motion, structure, and focal length", IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6):562-575, 1995.         [ Links ]

[3] Y. Bar-Shalom, X. Li. "Estimation and Tracking: principles, techniques and software", Artech House, Boston, 1993.         [ Links ]

[4] T. Broida, S. Chandrashekhar and R. Chellappa. "Recursive 3D Motion Estimation from a Monocular Image Sequence", IEEE Transactions on Aerospace and Electronic Systems Vo. 26, 4, July. Pp. 639-656, 1990.         [ Links ]

[5] F. Dornaika and R. Chung ; "An Algebraic Approach to Camera Self Calibration", Computer Vision and Image Understanding, Vol. 83, pp. 195-215, 2001.         [ Links ]

[6] O. Faugeras. "Tridimensional Computer Vision: A Geometric Viewpoint" Artificial Intece. MIT Press, 1993.         [ Links ]

[7] R.M. Haralick, C. Lee, K. Ottenberg and N. Nolle. "Re-view and analisys of solutions of the three point perspective pose estimation problem" International Journal of Computer Vision, Vol. 13, 3, pp. 331-356, 1994.         [ Links ]

[8] R.I. Hartley. "In Defence of the 8-point Algorithm", in Proceeding of the IEEE International Conference on Computer Vision, 1995.         [ Links ]

[9] R.I. Hartley. "Kruppa’s Equations Derived from Fundamental Matrix", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, (2), pp. 133-135, Feb, 1997.         [ Links ]

[10] P. McLauchlan and D. Murray. "A Unifying Framework for Structure and Motion recovery From Image Sequence", In Proc. 5th Int’l Conf. On Computer Vision, Boston, pp. 314-320, June, 1995.         [ Links ]

[11] L. Shapiro and G. Stockman. "Computer Vision" updated in March, 2000, http://george.ee.washington.edu/courses.html         [ Links ]

[12] Z. Sun y C. Rayburn. "Camera Calibration"; UNR & Ford Motor Company, 2001.         [ Links ]

[13] E. Trucco and A. Verri. "Introductory to techniques for 3-D computer vision"; Prentice Hall. 1998.         [ Links ]

[14] R. Tsai. "A Versatile Camera Calibration Technique for Hogh-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses", IEEE Journal of Robotics and Automation, Vol. RA-3,4,pp. 323-344. August, 1987.         [ Links ]

[15] M. Tuceryan, D. Greer, R. Whitaker, D. Breen, C. Crapton and K. Ahlers. "Calibration Requirements and Procedures for a Monitor-Based Augmented Reality System", IEEE Trans. On Visualization and Computer Graphics, Vol. 1, 3, Sep. Pag 255-273, 1995.         [ Links ]

[16] J. Weng, T. Huang and N. Ahuja. "Motion and Structure from two Perspective Views: Algorithms, Error Analysis and Error Estimation", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, (5), pp. 451-476, 1989.         [ Links ]

[17] J. Weng, P. Cohen and Herniou. "Camera Calibration with Distortion Models Accuracy Evaluation". IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, (10), pp. 965-980, 1992.         [ Links ]

[18] X. Zhang and N. Navab. "Tracking and Pose Estimation for Computer Assisted Localization in Industrial Environments", Fifth IEEE Workshop on Applications of Computer Vision, pp. 214-221, December 04-06. 2000.         [ Links ]

[19] Z. Zhang, R. Deriche, O. Faugeras, Q. Luong. "A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry", INRIA Research Report 2273, May. 1996.         [ Links ]

[20] A. Zhang. "A Flexible New Technique for Camera Calibration"; 1999 http://research.microsoft.com/~zhang.        [ Links ]

Recibido el 28 de marzo de 2005, aceptado el 25 de abril de 2005