L4(CamMod)

L4(CamMod) - Camera Models Acknowledgements Used...

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1 Camera Models Acknowledgements Used slides/content with permission from Marc Pollefeys for the slides Hartley and Zisserman: book figures from the web Matthew Turk: for the slides Spring 2006 Camera Models 2 Camera model Camera calibration Single view geom. Single view geometry
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2 Spring 2006 Camera Models 3 Pinhole camera geometry • A general projective camera P maps world points X to image points x according to x = P X. Spring 2006 Camera Models 4 T T Z fY Z fX Z Y X ) / , / ( ) , , ( ± ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ · · · ¸ ¹ º º º » ¼ = ± ± ± ² ³ ´ ´ ´ µ ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ 1 0 1 0 0 1 Z Y X f f Z fY fX Z Y X ± Central projection in homogeneous coordinates
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3 Spring 2006 Camera Models 5 ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ · · · ¸ ¹ º º º » ¼ = ± ± ± ² ³ ´ ´ ´ µ 1 0 1 0 0 Z Y X f f Z fY fX ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ · · · ¸ ¹ º º º » ¼ · · · ¸ ¹ º º º » ¼ = ± ± ± ² ³ ´ ´ ´ µ 1 0 1 0 1 0 1 1 Z Y X f f Z fY fX PX x = [] 0 | I ) 1 , , ( diag P f f = Camera projection matrix P P: principal point Principal plane Spring 2006 Camera Models 6 T y x T p Z fY p Z fX Z Y X ) / , / ( ) , , ( + + ± principal point T y x p p ) , ( ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ · · · ¸ ¹ º º º » ¼ = ± ± ± ² ³ ´ ´ ´ µ + + ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ 1 0 1 0 0 1 Z Y X p f p f Z Zp fY Zp fX Z Y X y x x x ± Pinhole point offset Image (x,y) and camera (x_cam, y_cam) coordinate systems.
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4 Spring 2006 Camera Models 7 ± ± ± ± ± ² ³ ´ ´ ´ ´ ´ µ · · · ¸ ¹ º º º
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L4(CamMod) - Camera Models Acknowledgements Used...

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