光学

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1 Fundamentals of Projector-Camera Systems and Their Calibration Methods Takayuki OKATANI To make the images projected by projector s appear as desired, it is e ective and sometimes an only choice to capture the projected images using a camera and control the images of the projectors by analyzing the captured images. To perform this, it is necessary to be able to calibrate the system consisting of projectors and camera s, called the projector-camera system. A projector is similar to a camera geometrically as well as photometrically. Thus, methods of multi-view, projective geometry developed in the field of computer vision, which were originally targeted at cameras, can be utilized for projector-camera systems. This paper explains how to do this, in an unified and exhaustive manner, by categorizing problems in terms of purposes of the system, surface shapes of the projection target etc. Key words: projector-camera, calibration, multi-view geometry a 1 b 1 c 1 d

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5 6 b x, y u, v u u x, y, v v x, y 4 u x, y, v x, y 3. 2 R, t H c H p H pc H c H 1 p H cp H 1 pc 1 H cp H p H c 10 H p X, Y x, y x, y, 1 H p X, Y, 1 4 H cp H p H c 6 X, Y x c, y c H c H p H cp H c H p H c 6 a H c H c c K K 2.2 x x E K x E Kx 0 E t R R, t

6 1 1 F F R, t 1 1 y 3. 3 K 3 7 H c 4 H 1 c 3 7 f x 0, y n 2 n n 2 x y n

7 7 Brugel x y Q AR SIFT 8 OpenCV 2 1 SIFT SIFT RANSAC RANdom SAmple Consensus R. Hartley and A. Zisserman: Multi-View Geometry in Computer Vision Cambridge University Press, B. K. P. Horn: Robot Vision MIT Press, Cambridge, T. Okatani and K. Deguchi: Easy calibration of a multi-projector display system, Int. J. Comput. Vision, D. Abe, T. Okatani and K. Deguchi: Flexible online calibration for a mobile projector-camera system, Proc. ACCV 2010, Lect. Notes Comput. Sci., T. Okatani and K. Deguchi: Autocalibration of a projectorcamera system, IEEE Trans. Pattern Anal. Machine Intell., Z. Zhang: A flexible new technique for camera calibration, IEEE Trans. Pattern Anal. Machine Intell., David G. Lowe: Distinctive image features from scale-invariant keypoints, Int. J. Comput. Vision, M. Ashdown, T. Okabe, I. Sato and Y. Sato: Robust contentdependent photometric projector compensation, Proc. IEEE Int. Workshop on Projector-Camera Systems 2006 pp D Features framework

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