lecture6 - EECS 442 Computer vision Epipolar Geometry Why...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
EECS 442 – Computer vision Epipolar Geometry • Why is stereo useful? • Epipolar constraints • Essential and fundamental matrix • Estimating F •Examp les Reading: [AZ] Chapters: 4, 9, 11 [FP] Chapters: 10
Background image of page 1

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

View Full DocumentRight Arrow Icon
Pinhole perspective projection Recovering structure from a single view C O w P p Calibration rig Scene Camera K From calibration rig From points and lines at infinity + orthogonal lines and planes structure of the scene, K location/pose of the rig, K Knowledge about scene ( point correspondences, geometry of lines & planes, etc…
Background image of page 2
Pinhole perspective projection Recovering structure from a single view C O w P p Calibration rig Scene Camera K Why is it so difficult? Intrinsic ambiguity of the mapping from 3D to image (2D)
Background image of page 3

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

View Full DocumentRight Arrow Icon
Recovering structure from a single view Intrinsic ambiguity of the mapping from 3D to image (2D) Courtesy slide S. Lazebnik
Background image of page 4
Two eyes help!
Background image of page 5

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

View Full DocumentRight Arrow Icon
O 2 O 1 x 2 1 ? K =known Two eyes help! This is called triangulation K =known R, T
Background image of page 6
• Find X that minimizes ) , ( ) , ( 2 2 2 1 1 2 X P x d X P x d + O 1 O 2 x 1 2 X Triangulation
Background image of page 7

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

View Full DocumentRight Arrow Icon
Stereo-view geometry Scene geometry: Find coordinates of 3D point from its projection into 2 or images. Correspondence: Given a point in one image, how can I find the corresponding point x’ in another one ? Camera geometry: Given corresponding points in two images, find camera matrices, position and pose.
Background image of page 8
• Epipolar Plane • Epipoles e 1 , e 2 • Epipolar Lines •Base l ine Epipolar geometry O 1 O 2 x 2 X x 1 e 1 e 2 = intersections of baseline with image planes = projections of the other camera center = vanishing points of camera motion direction
Background image of page 9

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

View Full DocumentRight Arrow Icon
Example: Converging image planes
Background image of page 10
O 1 O 2 X e 2 x 1 x 2 e 2 Example: Parallel image planes • Baseline intersects the image plane at infinity • Epipoles are at infinity • Epipolar lines are parallel to x axis
Background image of page 11

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

View Full DocumentRight Arrow Icon
Example: Parallel image planes
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 50

lecture6 - EECS 442 Computer vision Epipolar Geometry Why...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online