![](bg2.png)
(a) (b)
Figure 1: Two possible camera arrangements for soccer
scenes. Both arrangements have different properties. (a)
In the linear arrangement, all cameras are placed on a line
next to the long side of the pitch and have the same look-at
angle. (b) In the curved arrangement, all cameras are placed
around a corner of the pitch and point to a spot in the scene.
These multicamera matches might, however, be
unreliable. Therefore, we also present a filtering ap-
proach that is specifically tailored to cameras placed
next to each other, without a relative rotation around
their optical axes. Even large scale, curved cam-
era pathways can be properly handled by following a
piecewise linear approach over each triple of adjacent
camera views. We remove many outliers that would
not be removed with existing calibration tools, effec-
tively improving the calibration quality.
There are a number of existing camera calibration
methods available for outdoor sport scenes that do not
use calibration objects. Most of these methods use the
lines of the soccer area to determine camera locations
(Farin et al., 2003; Farin et al., 2005; Li and Luo,
2004; Yu et al., 2009; Hayet et al., 2005; Thomas,
2007). They are therefore only applicable if the scene
is a soccer pitch, where the lines are planar and visible
over all camera views. This is, however, not always
the case. The pitch is seldom a plane and cameras
with a small field of view do not always have lines in
their image stream. We therefore propose a solution
without this planar line assumption, which makes our
large-scale calibration solution more robust and more
widely applicable, with good self-calibration perfor-
mances (i.e. not requiring any specific calibration ob-
ject).
The rest of the paper is structured as follows. Sec-
tion 2 describes the used camera setup, with its geo-
metrical properties recorded into camera matrices, as
explained in section 3. Section 4 discusses the gen-
eration of the multicamera correspondences and their
propagation over adjacent cameras. Finally, section
5 describes our multicamera filtering approach to fur-
ther dismiss apparant outliers.
2 CAMERA SETUP
We do not present a camera calibration method for
Figure 2: The projective camera model. A camera center
and an image plane is defined. The image is formed by con-
necting a line between the camera center and the 3D point.
The intersection between this line and the image plane de-
fines the position of the projection for that 3D point.
all possible camera setups. Instead, we will present a
camera method for a large scale camera network, with
the following properties.
We considered two possible arrangements for the
cameras: a linear arrangement and a curved ar-
rangement with piecewise linear properties over large
scales. These camera topologies are shown in Fig-
ure 1. In both arrangements, the cameras are placed
around the pitch at a certain height to allow an
overview of the scene. Both the curved and linear ar-
rangement use cameras with a fixed location and ori-
entation. Some overlap between the camera images is
required to allow feature matching. Overlap between
every camera is, however, not required.
Our method requires that the cameras are synchro-
nized at shutter level, i.e. all cameras take an image at
the exact same time stamp. To provide this, we use
a pulse generator that periodically transmits a trigger-
ing pulse to all cameras at the same time.
3 REPRESENTATION OF
CAMERA PARAMETERS
In this section, we giveanoverviewof projectivecam-
eras and their matrix representations, commonly used
in computer vision applications.
A simple pinhole camera maps each 3D scene
voxel to a corresponding 2D image pixel, through
projection along the light rays traversing the pinhole.
Any real camera with a lens and finite aperture fol-
lows this basic voxel-to-pixel mapping principle and
can hence conveniently be modeled by an equivalent
pinhole camera. We will assume that all cameras fol-
low the pinhole projective camera model, as defined
by (Hartley and Zisserman, 2003, page 6) and shown
in Figure 2.
This projective process can be mathematically
represented in matrix notation as follows. Consider
a 3D point χ, represented in homogeneous coordi-
nates. In essence, homogeneous coordinates repre-
sent a point χ = [X,Y,Z]
T
, using four coordinates χ =
[WX,WY,WZ,W]
T
withW 6= 0 or χ = [X,Y, Z,1]
T
. A
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