Digital Signal Processing Reference
In-Depth Information
is a circle if
is affine (i.e.
0
and
1
), it can be calculated from the
calibration parameters. The centre of the horizo
n circle
is the image centre
,
, its radius
is obtained using
1
. Hence, the validity of
the estimated VPs can be checked by measuring if they lie on or close to the horizon
circle. In this way, the conics which are not orthogonal to the mirror axis are eliminat-
ed. The conics are grouped simply by checking their VPs distance to the other
validated VPs.
4
Experiment
The proposed method is tested on real images. The omnidirectional image database
from the University of Amsterdam [12] is used. These omnidirectional images were
taken by a central catadioptric system consisting of a perspective camera and a hyper-
bolic mirror. The image size is 1024×768 pixels. The elevation angle (i.e. FOV above
horizon) of the catadioptric system is 0.4887 radians. The mirror parameter
is given
by the manufacturer as 0.9886. The rest of the camera and geometric parameters
calibrated for the catadioptric system is shown in Table 1.
(a)
(b)
Fig. 3.
(a) The results of conic fitting: green conic is detected using constrained method and the
blue conic section is detected using unconstrained method; (b)The detected CLIs and VPs:
different sets of conics are shown in different colour.
Table 1.
Camera and geometric parameters obtained from real images
Average value 1764.8 451.93 530.79 389.16
Standard deviation ± 4.07 ± 1.04 ± 1.69 ± 1.44
For conic fitting, the results from unconstrained method to constrained method (i.e.
introduced in Section 2.3) are highly different as shown in Figure 3(a). The uncon-
strained approach can be unreliable and inaccurate when edge points are not well
distributed along their corresponding conic. Figure 3(b) shows an example of grouped
CLIs and their corresponding vanishing points. The accuracy of the vanishing points
