# lecture5 - EECS 442 Computer vision Single view metrology...

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EECS 442 – Computer vision Single view metrology • Review calibration • Lines and planes at infinity • Absolute conic • Estimating geometry from a single image • Extensions Reading: [HZ] Chapters 2,3,8

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Calibration Problem j i i P M P = i i i v u p In pixels [ ] T R K M = = 1 0 0 v 0 u cot 1 0 0 0 0 0 0 1 K o o sin 1 θ β λ θα α World ref. system
Calibration Problem j i i P M P = i i i v u p Need at least 6 correspondences 11 unknown [ ] T R K M =

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Pinhole perspective projection Once the camera is calibrated. .. [] T R K M = C O w P p -Internal parameters K are known -R, T are known – but these can only relate C to the calibration rig Can I estimate P from the measurement p from a single image? No - in general / [P can be anywhere along the line defined by C and p]
Pinhole perspective projection Recovering structure from a single view C O w P p unknown known Known/ Partially known/ unknown

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Recovering structure from a single view Saxena et al, 05…
• Review calibration • Lines and planes at infinity • Absolute conic • Estimating geometry from a single image •Examp les

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Lines in a 2D plane 0 c by ax = + + -c/b -a/b l = c b a l If x = [ x 1 , x 2 ] T l 0 c b a 1 x x T 2 1 = x y
Lines in a 2D plane Intersecting lines l l x × = l l Proof l l l × l l l × 0 l ) l l ( = × 0 l ) l l ( = × l x x l x x is the intersecting point x x y

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Points at infinity (ideal points) 0 x , x x x x 3 3 2 1 = What happens if x 3 = 0 ? = × 0 a
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## This note was uploaded on 10/26/2010 for the course EECS 442 taught by Professor Savarese during the Fall '09 term at University of Michigan.

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lecture5 - EECS 442 Computer vision Single view metrology...

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