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height Yo through Eq. (4) from known widths AX (measured by
tape with an estimated accuracy of +2 cm). The final result was
Yo = 1.937 m with a standard deviation o — 42.7 cm. It is noted
that the actual camera height above the ground was about 1.8 m.
As pointed out above, the estimated Y, value is subject to frame
affinity (which here was about 8%). Subsequently, a total of 30
frames from ten different roads were chosen for assessing width
estimation from Eq. (4) against tape measurement. Fig. 4 shows
typical frames used for calibration and evaluation.
Figure 4. Video frames used for calibration and evaluation.
On every frame, separate Ax measurements were taken at five
different y-levels on the image, and their corresponding ground
widths were computed. The five AX estimates from each frame
were treated individually, giving a mean difference and an RMS
difference r from the corresponding reference AX values. For
the five measurements on each image the standard deviation c
was also computed. The overall results are presented in Table 5,
whereby d denotes the absolute mean difference.
Table 5. Lane width accuracy from 30 frames
mean difference RMS difference standard deviation
d - 2.3 cm r=4.7 cm o — £3.8cm
The above results are considered as satisfactory since individual
measurements of lane width are expected to have an accuracy r
better than 5 cm (the largest RMS difference was 7.1 cm), while
lane widths typically differ in steps of 25 cm. Image measuring
errors and small uncorrected parts of o-tilts, causing perspective
distortions, are considered as the main sources of inaccuracy, as
expressed in the repeatability o of measurement. Obviously, an
averaged width from more than one estimates per frame is gene-
rally expected to be closer to ground truth (d in Table 5). With
this camera, reliable measurements were possible within a depth
range of about 10—25 m in front of the vehicle.
It is clear that the reported accuracy characterises the particular
setup used, depending primarily on image resolution and scale.
Any other setup needs to be accordingly evaluated. On the other
hand, accuracy is practically independent of road slope, as the
camera axis is generally assumed to follow this slope, and small
relative tilts are corrected by means of the vanishing points. It
must be pointed out, however, that the validity of the approach
holds only for the object plane on which the vehicle proceeds.
In case of variable superelevation rates among lanes, the results
are valid only for the lane on which the camera platform moves.
As mentioned already, this approach has been widely used on a
routine basis (Psarianos et al., 2001). A different camera was
employed here, separately calibrated as regards its height Yo. In
Fig. 6 frames of this application are shown.
Figure 6. Typical video frames used in the actual application.
3. MEASUREMENT OF VEHICLE SPEED
The task was to develop a simple method for measuring vehicle
speed, a crucial variable when studying the traffic character of a
freeway to produce ‘fundamental diagrams’. Actually, the
traffic diagrams used in Greece stem from other countries, thus
being rather inconsistent with the road conditions in this country
and the temperament of its drivers.
Vehicle speed measurements on congested highways using an
uncalibrated camera have already been reported (Dailey et al.,
2000; Pumrin & Dailey, 2002). In these cases, the mean vehicle
dimensions were used for scaling purposes; thus, only estimates
for time-averaged mean vehicle speed were obtained. Contrary
to this, the task here was to measure the speed of individual cars
in order to obtain detailed information on speed distribution.
3.1 Full projective transformation with control points
The images used here had been acquired for a previous study of
the traffic character of freeways (Chorianopoulos, 2001).
Traffic flow had been recorded from a 10 m high structure over
a freeway with three lanes in each stream. A digital video came-
ra was used on different occasions, looking centrally along the
axis of one stream with a certain downward tilt against the hori-
zontal. The time interval between successive frames, whose
dimensions were 768 x 576, was known as 25 frames/sec. Thus,
speed in all three lanes could be estimated simply by measuring
the vehicle translation between frames (here again assuming flat
ground).
In order to measure distances covered by cars between frames,
Chorianopoulos (2001) has applied full 2D—2D projective trans-
formation based on ground control points to assess the potential
of a conventional photogrammetric approach. Using 20 geodetic
control points, adjustments for the 8 projective coefficients had
RMS errors not larger than 20 cm. One out of about every ten
frames were used for each vehicle to provide an average of six
successive speed estimates within an actual distance of about 75
m. Among the numerous cars having crossed the field of view
in the two full hours of recording, several hundreds of them
were measured. The overall standard deviation of o = +2 km/h
(assuming constant speed) is considered as very satisfactory and
represents the estimated precision of individual measurements.
Mean speeds for each vehicle are expected to be more accurate.
Indeed, the accuracy of photogrammetric speed estimation was
evaluated against speed measurements using a GPS system on a
moving vehicle which was imaged three times. The differences
of mean speeds were below 1 km/h. These experiments indicate
the potential of single image metrology. Yet, simpler procedures
with no need for control points are obviously required.
3.2 Affine transformation for 1D measurements
3.2.1 Affine rectification from two vanishing points Once the
image horizon of a plane is defined, the affine properties of this
image can be recovered. A horizon line is commonly identified
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