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

This preview shows pages 1–18. Sign up to view the full content.

EECS 442 – Computer vision Stereo systems •Stereo vision •Rectification •Correspondence problem •Active stereo vision systems Reading: [HZ] Chapter: 11 [FP] Chapter: 11

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
Stereo vision Subgoals: - Solve the correspondence problem - Use corresponding observations to triangulate p’ P p O 1 O 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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]
Triangulation Intersecting the two lines of sight gives rise to P p’ P p O 1 O 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
• 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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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’?
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 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Making image planes parallel p’ P p OO H GOAL: Estimate the perspective transformation H that makes the images parallel
Projective transformation i x i x H i i x H x = Now we don’t have the destination image /

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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!
Projective transformation of a line (in 2D) l H l T = = b v t A H

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 68

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

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online