Stereo Vision: Triangulation and Image Rectification - Prof. Marshall Tappen, Study Guides, Projects, Research of Computer Science

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Depth from Stereo

CAP 5415

Fall 2009

Triangulating Points

●

Remember epipolar geometry?

(Image from Forsyth and Ponce)

But it can be easier

●

Image planes are parallel

●

Also parallel to line connecting the two optical

centers

O

O'

P

Baseline

Overhead view

P

O O'

●

Now triangulation is much easier

P

O O'

Z

f

P

O O'

Z

f B d

P

O O'

Z

f Disparity

Image Rectification

●

All we need to calculate the depth is the

distance between corresponding points

●

Would be easier to implement if the epipolar

lines corresponded with scanlines

●

Image rectification transforms the images so

they have this property

Intuitions on Rectification

●

Let's look in 2D

●

If I change the position of my camera, then the

location of the point depends on depth

P

Intuitions on Rectification

●

Let's look in 2D

●

If I change the position of my camera, then the

location of the point depends on depth

P

P'

Image Rectification

P

Baseline

O

O'

●

I can rotate views to be parallel to each other

and baseline

Lines up Epipolar lines with scanlines

(Image from Loop and Zhang)

Interesting Connections to

Fundamental Matrix

●

After rectification, it should have this form

Implication