Lecture-5 - Lecture-5 Computing Camera Parameters Computing...

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1 Lecture-5 Computing Camera Parameters Computing Camera Parameters • Using known 3-D points and corresponding image points, estimate camera matrix employing pseudo inverse method of section 1.6 (Fundamental of Computer Vision). • Compute camera parameters by relating camera matrix with estimated camera matrix. – Extrinsic • Translation • Rotation – Intrinsic • Horizontal and vertical focal lengths • Translation o x and o y
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2 Comparison = 34 33 32 31 24 23 22 21 14 13 12 11 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ m m m m m m m m m m m m M + - + - + - + - + - + - + - + - = z y z y y y y y y y y x z x x x x x x x x T r r r o T T f o r r f o r r f o r r f o T T f o r r f o r r f o r r f M 33 32 31 33 23 32 22 31 21 33 13 32 12 31 11 Computing Camera Parameters: Estimating scale M M g = ˆ | | | | ˆ ˆ ˆ 2 33 2 32 2 31 2 33 2 32 2 31 g g = + + = + + r r r m m m Since M is defined up to a scale factor estimated + - + - + - + - + - + - + - + - = z y z y y y y y y y y x z x x x x x x x x T r r r o T T f o r r f o r r f o r r f o T T f o r r f o r r f o r r f m m m m m m m m m m m m 33 32 31 33 23 32 22 31 21 33 13 32 12 31 11 34 33 32 31 24 23 22 21 14 13 12 11 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ g Divide each entry of by . M ˆ | | g
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3 Computing Camera Parameters: estimating third row of rotation matrix and translation in depth 1 , ˆ 34 ± = = s s m T z 3 , 2 , 1 , ˆ 3 3 = = i m r i i s + - + - + - + - + - + - + - + - = z y z y y y y y y y y x z x x x x x x x x T r r r o T T f o r r f o r r f o r r f o T T f o r r f o r r f o r r f m m m m m m m m m m m m 33 32 31 33 23 32 22 31 21 33 13 32 12 31 11 34 33 32 31 24 23 22 21 14 13 12 11 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ g Computing Camera Parameters + - + - + - + - + - + - + - + - = z y z y y y y y y y y x z x x x x x x x x T r r r o T T f o r r f o r r f o r r f o T T f o r r f o r r f o r r f m m m m m m m m m m m m 33 32 31 33 23 32 22 31 21 33 13 32 12 31 11 34 33 32 31 24 23 22 21 14 13 12 11 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ g [ ] [ ] [ ] 33 32 31 3 23 22 21 2 13 12 11 1 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ m m m q m m m q m m m q = = = Let
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4 Computing Camera Parameters: origin of image ( 29( 29 ( 29( 29 ( 29( 29 ( 29( 29 x T x x x x x x x x x x x x x x x x x x x T o q q r r r o o r o r o r r r r o r o r o r r r r o r o r o r r r r r f r f r f r r r o r r f o r r f o r r f m m m m m m m m m m m m q q = + + = + + = = + -
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Lecture-5 - Lecture-5 Computing Camera Parameters Computing...

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