Spacecraft Stereo Imaging Systems

Group S3

Variables

• Separation of the cameras

• Height of the cameras – relative to the bench

• Angle – The direction cameras are facing relative to each other

Other Considerations

• Distance – Between the object and the cameras.

• Size of the object

Theory of stereo images

O

d

(x, y, z) f – focal length of the cameras.

),( ll yx ),( rr yx and

are the points in the two images,

produced by the cameras.

Theory of stereo images

z

dx

f

xl 2/

z

dx

f

xr 2/

z

y

f

y

f

y rl

By considering the geometry of the system we can obtain a set of 3 simultaneous equations

These equations can be rearranged to find equations for the coordinates of the object - x, y and z.

rl

rl

xx

xxdx

2

rl

rl

xx

yydy

2

rl xx

dfz

Theory of stereo images

rl

rl

xx

xxdx

2

rl

rl

xx

yydy

2

rl xx

dfz

Theory of stereo images

The quantity , which appears in all the equations is known as disparity.

rl xx

Stereo Views

Left Camera Right Camera

The objects are displaced in one image relative to the other. These displacements are known as DISPARITIES.

Producing Stereograms

• The optimal ratio of object distance to camera separation is 30/1.

• Separation of the camera the same as average human eyes.

• Displacement of objects inversely proportional to the distance

Initial Attempts at a Stereogram

Calibration• The demagnification of the camera was found at a range

of distances.

• This was done using a single camera.

s

h

s´

h´

Object Image

Calibration

where h is the height of the object h´ is the image height, s is the object distance and s´ is the image distance.

s

s

h

hionmagnificat

The image height h´ is given by

nwh where n is the number of pixels and w is the width of 1 pixel (a single sensor) inside the camera.

Calibration

sw

hsn

1.

By plotting a graph of the height in pixels, n, versus the distance s, for an object of known height, the constant s´/w can be found from the gradient, m.

Calibration Graph

Image Height Against Inverse Object Distance

y = 326.15x + 4.8214

R2 = 0.9999

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2

Inverse Object Distance / m^-1

Imag

e H

eig

ht

in P

ixel

s ±

2

Determination of Object Height and Range

Now the ratio h/s can be found by measuring the image height in pixels … but more information is needed to distinguish between a small object which is close and a large object which is far away.

rl

rl

xx

yydy

2

Finally

rl

rl

xx

xxdx

2

We took some measurements of position in each of the two images and used them to find the x position of the object. We will continue this in the next lab session.