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# lec5 - Announcements HW1 has been posted See links on web...

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1 CSE152, Spring 2011 Intro Computer Vision Introduction to Computer Vision CSE 152 Lecture 5 CSE152, Spring 2011 Intro Computer Vision Announcements HW1 has been posted See links on web page for reading CSE152, Spring 2011 Intro Computer Vision Coordinate Changes: Rigid Transformations both translation and rotatoin CSE152, Spring 2011 Intro Computer Vision Rotation About ( k x , k y , k z ), a unit vector on an arbitrary axis (Rodrigues Formula) x' y' z' 1 = x y z 1 k x k x (1-c)+c k y k x (1-c)+k z s k z k x (1-c)-k y s 0 0 0 0 1 k x k y (1-c)-k z s k y k y (1-c)+c k z k y (1-c)-k x s 0 k x k z (1-c)+k y s k y k z (1-c)-k x s k z k z (1-c)+c 0 where c = cos θ & s = sin θ Rotate( k , θ ) x y z θ k CSE152, Spring 2011 Intro Computer Vision Camera parameters • Issue – camera may not be at the origin, looking down the z-axis extrinsic parameters (Rigid Transformation) – one unit in camera coordinates may not be the same as one unit in world coordinates intrinsic parameters - focal length, principal point, aspect ratio, angle between axes, etc. U V W Λি Νয় Μ৏ Μ৏ Μ৏ Ξ৯ Πਏ Ο৿ Ο৿ Ο৿ = Transformation representing intrinsic parameters Λি Νয় Μ৏ Μ৏ Μ৏ Ξ৯ Πਏ Ο৿ Ο৿ Ο৿ 1 0 0 0 0 1 0 0 0 0 1 0 Λি Νয় Μ৏ Μ৏ Μ৏ Ξ৯ Πਏ Ο৿ Ο৿ Ο৿ Transformation representing extrinsic parameters Λি Νয় Μ৏ Μ৏ Μ৏ Ξ৯ Πਏ Ο৿ Ο৿ Ο৿ X Y Z T Λি Νয় Μ৏ Μ৏ Μ৏ Μ৏ Ξ৯ Πਏ Ο৿ Ο৿ Ο৿ Ο৿ 3 x 3 4 x 4 CSE152, Spring 2011 Intro Computer Vision , estimate intrinsic and extrinsic camera parameters • See Text book for how to do it. Camera Calibration

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2 CSE152, Spring 2011 Intro Computer Vision Limits for pinhole cameras CSE152, Spring 2011 Intro Computer Vision Thin Lens: Image of Point O F P P’ Z’ f Z CSE152, Spring 2011 Intro Computer Vision Thin Lens: Image Plane O F P P’ Image Plane Q’ Q A price: Whereas the image of P is in focus, the image of Q isn’t. CSE152, Spring 2011 Intro Computer Vision Deviations from the lens model Deviations from this ideal are aberrations Two types 1. geometrical 2. chromatic spherical aberration astigmatism distortion- pin-cushion vs. barrel coma Aberrations are reduced by combining lenses Compound lenses
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lec5 - Announcements HW1 has been posted See links on web...

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