10 cameramodels

# 10 cameramodels - Camera Models Acknowledgements Marc...

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Spring 2006 Camera Models Camera Models Acknowledgements Marc Pollefeys for some of the slides Hartley and Zisserman: book figures from the web Matthew Turk: for some of the slides Thursday, February 18, 2010

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Camera Models 2 Camera model Camera calibration Single view geom. Single view geometry A camera is a mapping between the 3D world and a 2D image. Thursday, February 18, 2010
Camera Models 3 Pinhole camera geometry A general projective camera P maps world points X to image points x according to x = P X. Center of projection is assumed to be at the origin of the Euclidean coordinate system. Center of projection == camera center == optical center Image plane is at z = f . Thursday, February 18, 2010

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Camera Models 4 Terminology The line from the camera center perpendicular to the image plane is called the principal axis or principal ray of the camera. The point where the principal axis meets the image plane is called the principal point . The plane through the camera center parallel to the image plane is called the principal plane of the camera. Thursday, February 18, 2010
X Y Z 1 fX fY Z = f 0 f 0 1 0 X Y Z 1 Camera Models 5 Central projection in homogeneous coordinates Thursday, February 18, 2010

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X Y Z 1 fX fY Z = f 0 f 0 1 0 X Y Z 1 Camera Models 5 Central projection in homogeneous coordinates Thursday, February 18, 2010
We use x for the image point represented by the homogeneous 3-vector. We use P for the 3 × 4 homogeneous camera projection matrix. x = P X Camera Models notation 6 We use X for the world point represented by the homogeneous 4-vector ( X, Y, Z, 1) T . We can then write: This assumes that the origin of coordinates in the image plane is at the principal point. Thursday, February 18, 2010

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fX fY Z = f 0 f 0 1 0 X Y Z 1 Camera Models 7 Camera projection matrix P P: principal point Principal plane fX fY Z = f f 1 1 0 1 0 1 0 X Y Z 1 Thursday, February 18, 2010
fX fY Z = f 0 f 0 1 0 X Y Z 1 Camera Models 7 Camera projection matrix P P: principal point Principal plane fX fY Z = f f 1 1 0 1 0 1 0 X Y Z 1 Thursday, February 18, 2010

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X Y Z 1 fX + Zp x fY + Zp y Z = f p x 0 f p y 0 1 0 X Y Z 1 Camera Models 8 Pinhole point offset Image (x,y) and camera (x_cam, y_cam) coordinate systems. Thursday, February 18, 2010
X Y Z 1 fX + Zp x fY + Zp y Z = f p x 0 f p y 0 1 0 X Y Z 1 Camera Models 8 principal point Pinhole point offset Image (x,y) and camera (x_cam, y_cam) coordinate systems.

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