Lecture-3-h - Lecture-3 Camera Model Camera Calibration...

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1 Lecture-3 Camera Model Camera Calibration Camera Model h Z X h GW R PCR C q f - - = • Camera is at the origin of the world coordinates first • Then translated (G), • then rotated around Z axis in counter clockwise direction, • then rotated again around X in counter clockwise direction, and • then translated by C.
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2 Camera Model h Z X h GW R PCR C q f - - = P = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 - 1 f 1 , R - Z = cos sin 0 0 - sin cos 0 0 0 0 1 0 0 0 0 1 R - X = 1 0 0 0 0 cos sin 0 0 - sin cos 0 0 0 0 1 , G = 1 0 0 - X 0 0 1 0 - Y 0 0 0 1 - Z 0 0 0 0 1 C = 1 0 0 - r 1 0 1 0 - r 2 0 0 1 - r 3 0 0 0 1 Camera Model h Z X h GW R PCR C - - = f r Z Z Y Y X X r Z Z Y Y X X f y f r Z Z Y Y X X r Y Y X X f x + + - - - + - - - - + - + - = + + - - - + - - - - + - = 3 0 0 0 2 0 0 0 3 0 0 0 1 0 0 cos ) ( sin cos ) ( sin sin ) ( sin ) ( cos cos ) ( cos sin ) ( cos ) ( sin cos ) ( sin sin ) ( sin ) ( cos ) ( 4 2 4 1 h h h h C C y C C x = =
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3 Camera Model h Z X h GW R PCR C q f - - = 4 2 4 1 h h h h C C y C C x = = = = 1 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 4 3 2 1 Z Y X a a a a a a a a a a a a a a a a Ch Ch Ch Ch AW C h h 44 43 42 41 4 4 24 23 22 21 2 4 14 13 12 11 1 a Z a Y a X a Ch y Ch a Z a Y a X a Ch x Ch a Z a Y a X a Ch + + + = = + + + = = + + + = Camera Model 0 0 44 43 42 41 24 23 22 21 44 43 42 41 14 13 12 11 = - - - - + + + = - - - - + + + y a Zy a Yy a Xy a a Z a Y a X a x a Zx a Yx a Xx a a Z a Y a X a 44 43 42 41 4 4 24 23 22 21 2 4 14 13 12 11 1 a Z a Y a X a Ch y Ch a Z a Y a X a Ch x Ch a Z a Y a X a Ch + + + = = + + + = = + + + =
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4 Camera Model 0 0 44 43 42 41 24 23 22 21 44 43 42 41 14 13 12 11 = - - - - + + + = - - - - + + + y a Zy a Yy a Xy a a Z a Y a X a x a Zx a Yx a Xx a a Z a Y a X a 0 0 0 0 0 0 44 43 42 41 24 23 22 21 2 44 2 2 43 2 2 42 2 2 41 24 2 23 2 22 2 21 1 44 1 1 43 1 1 42 1 1 41 24 1 23 1 22 1 21 44 43 42 41 14 13 12 11 2 44 2 2 43 2 2 42 2 2 41 14 2 13 2 12 2 11 1 44 1 1 43 1 1 42 1 1 41 14 1 13 1 12 1 11 = - - - - + + + = - - - - + + + = - - - - + + + = - - - - + + + = - - - - + + + = - - - - + + + n n n n n n n n n n n n n n n n n n n n y a y Z a y Y a y X a a Z a Y a X a y a y Z a y Y a y X a a Z a Y a X a y a y Z a y Y a y X a a Z a Y a X a x a x Z a x Y a x X a a Z a Y a X a x a x Z a x Y a x X a a Z a Y a X a x a x Z a x Y a x X a a Z a Y a X a M M One point n points 2n equations, 12 unknowns Camera Model = - - - - - - - - - - - - - - - - - - - - - - - - 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 44 43 42 41 24 23 22 21 14 13 12 11 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 a a a a a a a a a a a a y X y X y X y Z Y X y Z y X y X y Z Y X y Z y X y X y Z Y X x Z x Y x X x Z Y X x X x X x X x Z Y X x Z x Y x X x Z Y X n n n n n n n n n n n n n n n n n n n n M M 0 = CP
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5 Camera Model = - - - - - - - - - - - - - - - - - - n n n n n n n n n n n n n n n n n n n n y y y x x x a a a a a a a a a a a X y X y X y Z Y X Z y X y X y Z Y X Z y X y X y Z Y X Z x Y x X
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Lecture-3-h - Lecture-3 Camera Model Camera Calibration...

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