stereoscopic foundamental

8/3/2019 Stereoscopic foundamental

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Stereo matching usingcorrelation

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Stereo Vision

Left Right

baseline

Matching correlation

windows across scan lines

depth

),(),(

y xd

B f y x Z

Z (x , y ) is depth at pixel (x , y )d (x , y ) is disparity

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Basic Stereo Geometry

L W R

(X, Y, Z)

x L x R d d

B f

d

B f

Z Z

Z

B f x xd

Z B X f x

Z

B X f x

R L

R

L

ˆ

2 /

2 /

f

B

How do matching errors affectthe depth error?

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Stereo disparity

• Stereo disparity is the difference in positionbetween correspondence point in two images

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Basic methods

• Correlation based corresponding: checking if one location in on image looks/seems likeanother one image

• Feature based: finding features in the imageand seeing if the layout of subset of features issimilar in the two images

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Basic stereo matching problem

• For each pixel x in the first image – Find corresponding epipolar line in the right image

– Check all pixels x’ on the epipolar line and pick the bestmatch

– Compute disparity x-x’ and set depth(x) = 1/(x-x’)

• Simplest case: epipolar lines are scanlines – Image planes of cameras are parallel to each other and to

the baseline

– Camera centers are at the same height

– Focal lengths are the same

– Then, epipolar lines fall along the horizontal scan lines of theimages

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Stereo matching using correlation

• Stereo matching is the correspondence problem

• For a point in image #1, where is the correspondingpoint in image #2

•

Image rectification makes the correspondence problemeasier and reduce computation time

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Image rectification•

A transformation process used to project two-or more imagesonto a common image plane. It corrects image distortion bytransforming the image into a standard coordinate system.

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Epipolar Geometry

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Epipolar plane

Epipolar line

Epipole



Epipolar Geometry

f

x x’

BaselineB

z

O O’

X

f

10

Epipolar line



Stereo matching

Left Right

u u

Rectified images

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Matching along epipolar line

Matching value

The best match estimates the “disparity” • In this case, horizontal disparity only (since images were rectified)

u i

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Stereo matching by correlation– Correlate left image patch along the epipolar line in the right

image– Best match = highest value

Normalized correlation would be better!

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Non local constraints• Uniqueness

– For any point in one image, there should be atmost one matching point in the other image

• Ordering

– Corresponding point should be in the same orderin both views

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stereoscopic foundamental

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