Digital Signal Processing Reference
In-Depth Information
0 0
00
0
.
0
001
(2)
0 1
changes according to the mirror type and shape,
is the camera calibration
matrix and
is the rotation matrix of the mirror relative to the camera. The major-
ity of the catadioptric sensors commercially available have their mirror accurately
aligned with the camera. Therefore, the rotation matrix
. Generally, the
calibration of a central catadioptric system is to obtain mirror parameter
and the
intrinsic parameter matrix
.
2.2
Projection of Lines in Catadioptric Cameras
As shown in Figure 1(b), a line
in space intersect the unit sphere through the origin
creating a plane
,
,
,0
. The unit sphere based representation of line
is then defined as
,
,
. The image conic which is the catadioptric projec-
tion of line
in the canonical image plane is expressed as
1
1
1
1
(3)
In the catadioptric image plane, we have our conic image as
(4)
2.3
Computation of Catadioptric Line Images (CLIs)
For the computation of CLIs, we adopt the analytical process proposed by Bermudez-
Cameo et al [10]. If a point lies on a conic, their relationship can be expressed as
0
. When the catadioptric camera parameters are known, only two points are
required to fit a CLI. Suppose some points
is known to be lie on a CLI in the image
plane, these points are firstly transformed back to the canonical plane
using the
inverse of the collineation matrix
via
. For each point
,,
,
compute
1
(5)
If two points
,
,
and
,
,
are given in the canonical plane,
to estimate the normal
, we just need to solve the following linear system
0
0
(6)
Once
is estimated, the image conic is computed using equation (3) and (4).
