In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C. Tournaire O. (Eds). 1APRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
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PANORAMA-BASED CAMERA CALIBRATION 
Bertrand Cannelle, Nicolas Paparoditis, Olivier Tournaire 
Université Paris-Est. Institut Géographique National, MATIS Laboratory 
73 Avenue de Paris. 94165 Saint-Mandé Cedex, France 
firstname.lastname@ign.fr 
Commission III/l 
KEY WORDS: Camera calibration, panorama, self-calibration, bundle adjustment 
ABSTRACT: 
This paper presents a method to calibrate a camera from panoramas. Camera calibration using panoramas has two main advantages: 
on the one hand it requires neither ground control points or calibration patterns and on the other hand the estimation of intrinsic and 
distortion parameters is of higher quality due to the loop constraint and to a decorrelation of tied parameters due to the fixed perspective 
center. 
The paper is organised as follow. The first pail presents the acquisition process and our mathematical estimation framework. The 
second part explores with simulated data sets the impact of noisy measures, of geometry of acquisition and of unmodelled parallaxes on 
the calibration results. A comparison with a traditional calibration method (i.e by using a 3D target network) is then studied. The final 
section presents results in a real case and compares the results obtained with our panorama approach against the classical calibration. 
The results are very promising. 
INTRODUCTION 
In photogrammetric surveys, the camera calibration is most of 
the time performed prior to the survey and the extrinsic param 
eters of the poses of the survey are obtained by bundle adjust 
ment. A '’classical’* photogrammetric camera calibration meth 
ods (Tsai, 1986. Zhang, 2000) consists in taking images of a 
topometrically surveyed 2D or 3D target network, in measuring 
manually or automatically the positions of the projection of the 
targets (the observations) in image space and finally in estimating 
the set of parameters of a mathematical projection model (usu 
ally the collinearity equation) minimising the distance in image 
space between the observations and the projection of the corre 
sponding targets given the set of parameters. In ’'classical” sur 
veys where images are parallel to the surfaces of the objects or 
landscapes to be surveyed, the extrinsic parameters determined 
through a bundle adjustment can absorb/compensate errors of the 
camera calibration. In image sets with loops, like in panoramas 
or when turning around objects, these errors can unfortunately 
not be compensated. In order to perform a better estimation and 
decorrelation of intrinsic (and distortion parameters) and extrinsic 
parameters, some other techniques have been developed using ro 
tating images (Hartley, 1994), or using panoramas (Ramalingam 
et al., 2010). Some woks using the same acquisition framework 
already exist ((Agapito et al., 2001. Tordoff and Murray. 2004)). 
However the distortion modeling is different than ours. 
Our calibration approach consists in carrying out a self-calibration 
from panoramas, i.e. to estimate intrinsic and extrinsic parame 
ters at the same time while closing a loop and with a fixed per 
spective center to decorrelate some tied parameters and limit the 
number of unknowns to estimate (we only need to estimate a ro 
tation between our different images). This approach has many 
advantages: it is fully automatic, it does not need a qualified op 
erator to acquire images with a ’’good geometry” (with targets in 
the comer, etc.), it does not need any ground control point and 
calibration patterns (any detail or texture of a scene becomes a 
tie point) and it is thus ultra-portable. Indeed, the calibration can 
be realised close to the survey thus for example in the same ther 
mal conditions knowing that temperature has a relatively strong 
impact on the intrinsic and the distortion parameters. 
Our panoramas are acquired with a low cost motorised pan-tilt 
device thus with a gross angular accuracy (around 0.1) which is 
insufficient to measure the perspective bundle in a direct way (ray 
by ray by observing a point while turning the camera) but which 
is sufficient enough to provide initial solutions for rotations and 
limit the search space for homologous points. 
Our work present a method to calibrate camera without ground 
point. One of the main advantage to work in a panoramic geom 
etry is that we only needs to estimate a rotation between images. 
Another interesting particularity is that it requires neither ground 
points nor geometric information extracted from the images. 
We will first start by presenting our acquisition process, our ge 
ometric camera model, and our mathematical estimation frame 
work (Section 1). Then we will present some experiments with 
synthetic data to study the influence of noise on the estimation 
of intrinsic parameters and distortion (Section 2). A comparison 
with a ’’classical” calibration with ground control points will then 
be presented in Section 3. Finally, Section 4 presents results on a 
real dataset. 
1 OUR METHODOLOGY 
In this section we present our calibration framework. We first 
discuss the acquisition process and the matching of tie points be 
tween images. Then, we present our camera geometrical model 
and introduce the mathematical bundle adjustment framework in 
which the calibration is embedded, and we explain how to solve 
it. 
1.1 Acquisition process 
Our pan-tilt device which is controlled by a computer is presented 
on Fig. 1. Mechanically, it provides two rotation axes (from left 
to right and top to bottom) and can support any reasonable weight 
camera. In our framework, images are taken with an overlap ra 
tio around 50% in order to have enough measures of homologous