Computer vision
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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

Computer Vision

Stereo Vision


Pinhole camera

Pinhole Camera


Perspective projection

Perspective Projection


Stereo vision

Stereo Vision

  • Two cameras.

  • Known camera positions.

  • Recover depth.

scene point

p

p’

image plane

optical center


Correspondences

Correspondences

p

p’


Matrix form of cross product

Matrix form of cross product

a=axi+ayj+azk

a×b=|a||b|sin(η)u

b=bxi+byj+bzk


The essential matrix

The Essential Matrix

Essential matrix


Stereo constraints

Epipolar Line

p’

Y2

X2

Z2

O2

Epipole

Stereo Constraints

M

Image plane

Y1

p

O1

Z1

X1

Focal plane


A simple stereo system

disparity

Depth Z

Elevation Zw

A Simple Stereo System

LEFT CAMERA

RIGHT CAMERA

baseline

Right image:

target

Left image:

reference

Zw=0


Stereo view

Stereo View

Right View

Left View

Disparity


Stereo disparity

Stereo Disparity

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


Parallel cameras

Parallel Cameras

P

Z

xl

xr

f

pl

pr

Ol

Or

Disparity:

T

T is the stereo baseline


Finding correspondences

Finding Correspondences


Correlation approach

(xl, yl)

Correlation Approach

LEFT IMAGE

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


Correlation approach1

Correlation Approach

RIGHT IMAGE

(xl, yl)

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


Correlation approach2

Correlation Approach

RIGHT IMAGE

(xr, yr)

dx

(xl, yl)

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


Computer vision

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Most

popular

Comparing Windows


Computer vision

Comparing Windows

Minimize

Sum of Squared

Differences

Maximize

Cross correlation


Correspondence difficulties

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 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

Stereo results

  • Data from University of Tsukuba

Scene

Ground truth

(Seitz)


Results with window correlation

Results with window correlation

Estimated depth of field

(a fixed-size window)

Ground truth

(Seitz)


Results with better method

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)


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