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# lecture4 - EECS 442 Computer vision Camera Calibration...

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EECS 442 – Computer vision Camera Calibration • Review camera parameters • Camera calibration problem • Example Reading: [FP] Chapter 3 [HZ] Chapter 7 Some slides in this lecture are courtesy to Profs. J. Ponce & F-F Li

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Pinhole perspective projection Projective camera f O c f = focal length
Pinhole perspective projection x y x c y c C=[u o , v o ] f O c Projective camera f = focal length u o , v o = offset

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f O c Units: k,l [pixel/m] f [m] [pixel] , α β Non-square pixels Projective camera f = focal length u o , v o = offset non-square pixels , α β
x y x c y c C=[u o , v o ] θ f O c Projective camera non-square pixels , f = focal length u o , v o = offset α β θ = skewness

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f O c Projective camera = 1 z y x 0 1 0 0 0 v 0 0 u cot P o o sin θ β θ α α K has 5 degrees of freedom! P c P’ f = focal length u o , v o = offset non-square pixels , α β θ = skewness
f O c Projective camera P c O w i w k w j w R,T [ ] w c P T R P = P’ f = focal length u o , v o = offset non-square pixels , α β θ = skewness R,T = rotation, translation

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f = focal length u o , v o = offset non-square pixels , α β f O c Projective camera P O w i w k w j w R,T w P M P = [ ] w P T R K = Internal parameters External parameters θ = skewness R,T = rotation, translation P’
Goal of calibration w P M P = [ ] w P T R K = Internal parameters External parameters Estimate intrinsic and extrinsic parameters from 1 or multiple images

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Goal of calibration w P M P = [ ] w P T R K = Estimate intrinsic and extrinsic parameters from 1 or multiple images Note: To simplify notation let P = P w = 1 0 0 v 0 u cot K o o sin θ β θ α α = T 3 T 2 T 1 R r r r = z y x t t t T
Calibration Problem •P 1 … P n with known positions in [O w ,i w ,j w ,k w ] •p 1 , … p n known positions in the image Goal : compute intrinsic and extrinsic parameters j Calibration rig

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Calibration Problem
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