lecture7 - EECS 442 Computer vision Stereo systems Stereo...

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EECS 442 – Computer vision Stereo systems •Stereo vision •Rectification •Correspondence problem •Active stereo vision systems Reading: [HZ] Chapter: 11 [FP] Chapter: 11
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Stereo vision Goal: estimate the position of P given the observation of P from two view points Assumptions : known camera parameters and position (K, R, T) p’ P p O 1 O 2
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Stereo vision Subgoals: - Solve the correspondence problem - Use corresponding observations to triangulate p’ P p O 1 O 2
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Correspondence problem p’ P p O 1 O 2 Given a point in 3d, discover corresponding observations in left and right images [also called binocular fusion problem]
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Triangulation Intersecting the two lines of sight gives rise to P p’ P p O 1 O 2
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• Epipolar Plane • Epipoles e 1 , e 2 • Epipolar Lines •Base l ine Epipolar geometry O 1 O 2 p’ P p e 1 e 2 = intersections of baseline with image planes = projections of the other camera center = vanishing points of camera motion direction
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O O P e 2 p p’ e 2 Parallel image planes KK x z v = v’ y Rectification: making two images “parallel” u v u v
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Parallel image planes = = × 0 0 0 0 0 0 0 ] [ T T R t E K 1 =K 2 = known x parallel to O 1 O 2 O O P e 2 p p’ e 2 KK x z y u v u v v = v’?
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Parallel image planes () () v T Tv v T T v u v u T T v u = = = 0 0 1 0 1 0 0 0 0 0 0 0 1 O O P e 2 p p’ e 2 KK x z y u v u v 0 p E p T =
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Making image planes parallel p’ P p OO H GOAL: Estimate the perspective transformation H that makes the images parallel
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Projective transformation i x i x H i i x H x = Now we don’t have the destination image /
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Making image planes parallel p’ P p OO H GOAL: Estimate the perspective transformation H that makes the images parallel Impose v’=v How? Map e to infinity
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Making image planes parallel T 2 1 T ] 1 e e [ T R K e = = T K e = p’ P p ee K K’ R,T [ ] P T R K P [] P 0 I K P OO
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Making image planes parallel 1. Map e to the x-axis at location [1,0,1] T [ ] T 1 0 1 H H 1 T R H = = T 2 1 ] 1 e e [ e p’ P p e e’ K K’ R,T [] P 0 I K P OO [ ] P T R K P
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Making image planes parallel 2. Send epipole to infinity p’ p [ ] T 1 0 1 e = [ ] T 0 0 1 e = = 1 0 1 0 1 0 0 0 1 H 2 P [ ] T 0 0 1 e OO Minimizes the distortion in a neighborhood (approximates id. mapping)
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Making image planes parallel 4. Align epipolar lines p’ p H = H 1 H 2 P e OO e’ 3. Define: H = H 1 H 2 Note: H is not unique!
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Projective transformation of a line (in 2D) l H l T = = b v t A H
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lecture7 - EECS 442 Computer vision Stereo systems Stereo...

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