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Science, 
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79 
CALIBRATION OF STATIONARY CAMERAS BY OBSERVING OBJECTS OF EQUAL HEIGHTS 
ON A GROUND PLANE 
Jochen Meidow 
Institute of Photogrammetry, University of Bonn 
Nußallee 15, D-53115 Bonn, Germany 
meidow@ipb.uni-bonn.de 
KEY WORDS: Camera, Calibration, Estimation, Measurement, Scene, Accuracy. 
ABSTRACT 
With the increasing number of cameras the need for plug-and-play calibration procedures arises to realize a subsequent 
automatic geometric evaluation of observed scenes. An easy calibration procedure is proposed for a non-zooming station- 
ary camera observing objects of initially equal and known heights above a ground plane. The image coordinates of the 
corresponding foot and head points of these objects serve as observations. For the interior and exterior orientation of the 
camera a minimal parametrization is introduced with the height of the camera above the ground plane, its pitch and roll 
angle and the principal distance. With the idea of corresponding foot and head trajectories being homologue, the situation 
can be reformulated with a virtual second camera observing the scene. Therefore a plane induced homography can be 
established for the observation model. This special planar homology can be parametrisied with the unknown calibration 
quantities. Initially the calibration is estimated by observing foot and head points of objects with known heights. In the 
subsequent evaluation phase the height and positions of unknown objects can be determined. With the same procedure 
the calibration can be checked and updated if needed. The approach is evaluated with a real scene. 
1 INTRODUCTION 
Motivation. Metric scene reconstruction is the subject of 
many vision tasks. With the increasing number of video 
cameras there is a demand of quick and easy calibration 
procedures which lower the expenses of camera installa- 
tions while guaranteeing the desired measurement accu- 
racy. In this paper a calibration procedure is presented 
for stationary, non-zooming cameras as a contribution to 
the realization of plug-and-play video cameras. The ap- 
proach uses the observed foot and head points of object 
with equal heights on a ground plane. The formulas for the 
solution of the problem will be assembled and explained 
and the achievable accuracies for the calibration will be 
determined as well. 
Approach. With a straight line preserving pinhole cam- 
era a minimal parametrization is introduced: For the intrin- 
sic camera parameters the principal distance is the crucial 
parameter which determines the reconstruction. The ex- 
terior orientation is realized by the pitch and roll angle of 
the camera as well as the distance of the projection center 
to the ground plane (height above ground). For the cor- 
responding foot and head points of imaged objects a so- 
called plane induced homography (Hartley and Zisserman, 
2000) can be introduced which maps the foot points into 
the corresponding head points. Assuming that the head 
and foot points are identical in the object space, the situa- 
tion can be reformulated with the help of a second, virtual 
camera observing the same points. This idea allows to ex- 
ploit a stereo approach: The motion between both cameras 
induces a planar homology as a special homography and 
enables the formulation of constraints between the obser- 
vations and the unknown parameters. The latter are esti- 
mated in a combined adjustment for which in principle no 
approximation values are needed. 
1067 
Procedure. The realization of the approach consists of 
two stages: (1) Initialization: Since photogrammetry ac- 
quires angles, metric information has to be provided in an 
initial calibration phase by observing objects of equal and 
known height. After the collection of sufficient data the 
initial calibration is performed and then the determination 
of the height and positions of unknown objects is possible. 
(2) Parameter update: Due to environmental influences the 
calibration parameters may vary, especially the principal 
distance, therefore, the parameters have to be checked and 
updated. By assuming that the camera height above ground 
is constant, this can be achieved by the observation of pos- 
sibly other objects of equal but unknown heights. 
Notation. We denote vectors of the image and the cam- 
era coordinate systems with small boldface letters, e. g. 
x, and coordinates in the object coordinate system with 
capital boldface letters, e. g. X. Vectors and matrices are 
denoted with slanted letters, matrices sans-serif, thus x or 
R. Homogeneous vectors and matrices, which represent 
the same object when multiplied with a scalar A # 0, are 
denoted with upright letters, e. g. x or K. We use the skew 
symmetric matrix 
0 —X3 Fao 
Siz)= +13 0 —q1 
—Ko +I 0 
of a 3-vector x = (14. x5, £3)! to represent the cross prod- 
uct by a x b = S(a)b. The Euclidean normalization of a 
vector x is preformed by the operator N(x) = x/||æ||. 
2 MODELLING 
2.1 Parametrisations and Observations 
Coordinate Systems. The orientation of the camera in 
the object coordinate system can be described by the pitch