spacecraft stereo imaging systems group s3. variables separation of the cameras height of the...
Post on 21-Dec-2015
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Variables
• Separation of the cameras
• Height of the cameras – relative to the bench
• Angle – The direction cameras are facing relative to each other
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
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
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