el to the
gonal to
H to the
(6)
remain-
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nally:
(7)
g aspect
ation. A
ove' the
ring it).
g to the
(8)
| size of
Eq. (6),
(9)
one step
vanish-
> image,
red only
allelism
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inishing
ntioned
je recti-
und X-
nd p on
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1€ Cross
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ments d
se lines
patch is
as been
rmation
is possible only on the line of the known length. On the right,
one may see the outcome of affine rectification from two known
lengths, described above. Here, parallelism has been restored in
all directions. Angles can be restored only if the angle between
the two directions is known. Measurement is here possible on
all lines along the correctly scaled y-direction.
Figure 8. Vanishing point F, from lengths a, b on parallel lines.
Figure 9. Rectification with one and two vanishing points.
This approach, requiring a second known length on the ground,
is important as it bypasses the constraint on camera orientation.
In the present case, however, images were assumed to have only
a tilt about the horizontal x-axis, hence the approach with one
vanishing point and one known distance was actually applied.
3.3 Practical evaluation
The performance of the approach, laid out in section 3.2.2, for
1D measurement based on one finite vanishing point (that in the
direction of the road axis, with the second assumed at infinity)
has been evaluated against 2D-2D measurement (section 3.1). A
total of 11 vehicles in all three lanes were followed, and their
speed was found from 4-8 frames. Three independent estima-
tions were made, based on three different known distances (seen
in Fig. 10) to establish the repeatability of results.
Figure 10. Known distances a, b, c used for speed estimation.
The vehicle's shadow was manually measured on the first frame
and was then automatically followed in subsequent frames with
a simple correlation technique. This has been facilitated by the
use of rectified images. In Fig. 11, the affine transformations of
three frames are shown.
S
ik
Figure 11. Affine rectifications of successive frames.
The results are seen in Table 12, which presents mean speed d
and standard deviation o from all frames of each vehicle. Only
very few outlying estimates have been rejected, namely from
the far end of the road where image scale is too small and
measuring errors cause very large displacements.
Table 12. Speed estimation in km/h from 1D measurements
using three different known distances a, 5b, c (11 vehicles)
ID 2D
a b C
d o d o d o d o
95 +2 94 +2 95 +2 95 +]
110 +2 110 +2 110 +2 109 +1
118 +2 117 +2 118 +2 118 +2
99 +2 99 +2 100 +2 98 +1
115 +1 115 +1 116 +1 116 +1
122 +2 122 +2 120 +2 122 +2
146 +3 146 +3 146 +3 144 +2
103 +1 102 +1 103 +1 103 +1
133 +2 132 +2 133 +2 133 +1
132 +1 131 +1 132 +1 131 +2
156 +3 156 +3 157 +3 155 +1
The results indicate that the simple approach of affine rectifica-
tion using one vanishing point and one known distance (under
the assumption that the image plane is parallel to the X-axis of
the road) compare very well with metric data derived from full
2D-2D projective transformation (the validity of which has been
established with GPS measurements).
4. CONCLUDING REMARKS
In this contribution methods have been presented for extracting
metric data form single uncalibrated images (in the specific con-
text of road and traffic scenes). Based on a combination of pho-
togrammetric and computer vision approaches, the methods are
very simple requiring minimal external information (one known
distance) if ‘reasonable’ assumptions are adopted. In both cases
images are subject to affine deformations, yet ID measurements
are possible in the properly scaled direction. It has been further
demonstrated that both methods are capable of providing metric
results of satisfactory accuracy.
Of course, important questions still wait to be addressed. For in-
stance, lane width estimation is limited to linear road segments.
2:5.
