# Computer Vision - PowerPoint PPT Presentation

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Computer Vision. Stereo Vision. Pinhole Camera. Perspective Projection. Stereo Vision. Two cameras. Known camera positions. Recover depth. scene point. p. p’. image plane. optical center. Correspondences. p. p’. Matrix form of cross product. a =a x i +a y j +a z k.

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Computer Vision

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## Computer Vision

Stereo Vision

### Stereo Vision

• Two cameras.

• Known camera positions.

• Recover depth.

scene point

p

p’

image plane

optical center

p

p’

### Matrix form of cross product

a=axi+ayj+azk

a×b=|a||b|sin(η)u

b=bxi+byj+bzk

Essential matrix

Epipolar Line

p’

Y2

X2

Z2

O2

Epipole

M

Image plane

Y1

p

O1

Z1

X1

Focal plane

disparity

Depth Z

Elevation Zw

LEFT CAMERA

RIGHT CAMERA

baseline

Right image:

target

Left image:

reference

Zw=0

Right View

Left View

Disparity

### Stereo Disparity

• The separation between two matching objects is called the stereo disparity.

### Parallel Cameras

P

Z

xl

xr

f

pl

pr

Ol

Or

Disparity:

T

T is the stereo baseline

(xl, yl)

### Correlation Approach

LEFT IMAGE

• For Each point (xl, yl) in the left image, define a window centered at the point

### Correlation Approach

RIGHT IMAGE

(xl, yl)

• … search its corresponding point within a search region in the right image

### Correlation Approach

RIGHT IMAGE

(xr, yr)

dx

(xl, yl)

• … the disparity (dx, dy) is the displacement when the correlation is maximum

?

=

g

f

Most

popular

Comparing Windows

Comparing Windows

Minimize

Sum of Squared

Differences

Maximize

Cross correlation

### Correspondence Difficulties

• Why is the correspondence problem difficult?

• Some points in each image will have no corresponding points in the other image.

(1) the cameras might have different fields of view.

(2) due to occlusion.

• A stereo system must be able to determine the image parts that should not be matched.

### Structured Light

• Structured lighting

• Feature-based methods are not applicable when the objects have smooth surfaces (i.e., sparse disparity maps make surface reconstruction difficult).

• Patterns of light are projected onto the surface of objects, creating interesting points even in regions which would be otherwise smooth.

• Finding and matching such points is simplified by knowing the geometry of the projected patterns.

### Stereo results

• Data from University of Tsukuba

Scene

Ground truth

(Seitz)

### Results with window correlation

Estimated depth of field

(a fixed-size window)

Ground truth

(Seitz)

### Results with better method

• A state of the art method

• Boykov et al., Fast Approximate Energy Minimization via Graph Cuts,

• International Conference on Computer Vision, September 1999.

Ground truth

(Seitz)