INGENIEUR
The planar homography [6, 7] describing the
plane to plane projection can be resolved up to
the scale factor by employing the concept of least
square error as
[2.0]
Figure 3: The calibration rig (image captured from
the centre camera) is located about 10m from
the vehicle.
where Xi and Yi is the grid coordinate of the 3D
planar object (Zi is always equal to zero) and ui and
vi is the image pixel coordinate of the 2D image
plane of correspondence i. With the minimum of 4
correspondences, the value of planar homography
H can then be resolved.
Once the value of planar homography which
describes the 3D plane (world) to 2D plane (image)
projection is resolved, the distance between any
two points lying on the 2D image plane (e.g. the two
points on the surface of the road as shown in the
captured image with pixel coordinates coordinates
[u p1 v p1 ] and [u p2 v p2 ] ) can be measured as
Figure 4: The 16 points are automatically
selected.
Figure 5: Calibration rig detected by the system.
d=sqrt((X p1 –X p2 ) 2 +(Y p1 – Y p2 ) 2 ) [3.0]
where
By utilizing the planar homography, the width of
the road in the captured camera image (two image
coordinate points as annotated by the user) can
be measured accordingly [8].
Using the discussed planar homography, any
horizontal measurement (e.g. the width of a lane)
can be carried out by understanding the planar
project of road surface with respect to the region
in the captured camera image. A calibration rig
lying on the road surface (see Figure 3) can be
used to obtain the planar homography.
Using all the 16 points detected from the
captured image (see Figure 4), the value of the
planar homography is subsequently estimated
with Equation 2.0.
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Figure 6: Result of
measurement (orange
line). The obtained result is
1.0099 m (the actual length
of the object is around 1 m)
The estimated result is drawn on top on the
detected 16 points to allow the user to validate
the quality of the estimation (see Figure 5). The
better the estimation, the closer is the drawing
with respect to the actual calibration rig in the
image.
With the planar homograph value, horizontal
measurement on the surface of the road can then
be measured with Equation 3.0 (see Figure 6).
The achieved accuracy of the designed calibration
system is +/- 0.0168m.