circle center was varied while keeping the radius fixed at 60
mm. The levels of circle center (the principal point) were set
as (40, 40), (60, 60), (80, 80), (100,100), (120,120), (140,140),
(160,160), (180,180), (200,200), (220,220) and (240, 240) (mm
× mm). To simplify the presentation, the distance from the
circle center to the center of the plane where the circle center
is, represents the levels of the circle
center. The levels of circle center are
named as -141.42, -113.14, -84.85,
-56.57, -28.28, 0, 28.28, 56.57, 84.85,
113.14 and 141.42 mm. The results are
illustrated in Figure 8 c and 8d.
The accuracies of the camera pa-
rameters
c
,
x
0
,
y
0
,
k
1
is lower when the
circle size is very small (i.e., the circle
radius is less than 20
mm
). But the
results are still better than the ones ob-
tained by the method without ellipses.
Additionally, the maximum difference
of all the results is about three pixels.
Therefore, the different levels of the
circle size have relatively little impact
on the proposed approach.
Experiments of Real Data
Real Data
In experiments with real images, a
quantitative and qualitative evaluation
of the proposed approach is presented
by using two groups of 1,000 × 667 im-
ages, taken with a digital camera Canon
EOS 7D which has a zoom lens (18-135
mm focal length). The two settings of
the camera, i.e., 18 mm and 29 mm
focal length, were used to take wide-
angle and narrow-angle images, respec-
tively. At both settings, two images of
the same scenario were taken. The first
image is oblique, which contains three
main object directions. The second
image is the oblique façade, which only
contain two main object direc-
tions. All the images are shown in
Figure 9. Figure 9a and 9b are re-
spectively the wide-angle oblique
and façade images, taken by the
camera with 18 mm focal length.
Figure 9c) and 9d are respectively
the narrow-angle oblique and
façade images, taken by the camera
with 29 mm focal length. In the
experiments, the line segments are
extracted based on Line Segment
Detector (
LSD
) (von Gioi
et al
.,
2010), and the line segments ex-
tracted are clustered by J-Linkage
algorithm (Toldo and Fusiello,
2008)). Ellipses in the images are
fitted from a stable direct least
squares method (Halir and Flusser,
1998). The line segments of two/
three orthogonal directions and the
ellipse for calibration are marked
in Figure 9. To evaluate the quan-
titative results of the proposed
method, the method presented
by van den Heuvel has been used
for comparison. In addition, the
Camera Calibration Toolbox for
Matlab
(Bouguet, 2004.) has been
tested for comparison. The
Camera
(a)
(b)
(c)
(d)
Figure 9. Real images for experiments: (a) and (b) are wide-angle images by a Canon EOS 7D
with focal length of 18 m;
.
(c) and (d) are narrow-angle images taken by Canon EOS 7D with focal
length 29 mm)
(a)
(b)
(c)
(d)
Figure 8. Results of experiment 3 using simulated data: (a) through (b) represent the re-
sults with varying circle radius; and (c) and (d) represent resultswith varying circle center.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
May 2016
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