Stereo - Introduction to Computer Version - Lecture Sli, Lecture notes of Computer Science

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Stereo, Continued

Depth from disparity

x’

z

f

x

C C’

X

baseline

f

(X – X’) / f = baseline / z

X – X’ = (baselinef) / z z = (baselinef) / (X – X’)

Outline

• Human stereopsis
• Stereograms
• Epipolar geometry and the epipolar constraint
  • Case example with parallel optical axes
  • General case with calibrated cameras

• Given p in left image, where can corresponding point p‟ be?

Stereo correspondence constraints

Stereo correspondence constraints

• Epipolar Plane

Epipole

Epipolar Line

Baseline

Epipolar geometry

Epipole

http://www.ai.sri.com/~luong/research/Meta3DViewer/EpipolarGeo.html

• Baseline : line joining the camera centers
• Epipole : point of intersection of baseline with image plane
• Epipolar plane : plane containing baseline and world point
• Epipolar line : intersection of epipolar plane with the image plane
• All epipolar lines intersect at the epipole
• An epipolar plane intersects the left and right image planes in epipolar lines

Epipolar geometry: terms

Why is the epipolar constraint useful?

Example

What do the epipolar lines look like?

Ol (^) Or

Ol (^) O r

Figure from Hartley & Zisserman

Example: parallel cameras

Where are the epipoles?

Docsity.com

Example: Forward motion

What would the epipolar lines look like if the camera moves directly forward?

Fundamental matrix

Let p be a point in left image, p’ in right image

Epipolar relation

• p maps to epipolar line l’
• p’ maps to epipolar line l

Epipolar mapping described by a 3x3 matrix F

It follows that

l l‟ p (^) p‟

Fundamental matrix

This matrix F is called

• the “Essential Matrix”
  • when image intrinsic parameters are known
• the “Fundamental Matrix”
  • more generally (uncalibrated case)

Can solve for F from point correspondences

• Each (p, p‟) pair gives one linear equation in entries of F
• 8 points give enough to solve for F (8-point algorithm)
• see Marc Pollefey‟s notes for a nice tutorial