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Calibration–Free Hand–Eye Calibration:
A Structure–from–Motion Approach
Jochen Schmidt
, Florian Vogt
, and Heinrich Niemann
Lehrstuhl f¨ur Mustererkennung, Universit¨at Erlangen-N¨urnberg,
Martensstr. 3, 91058 Erlangen, Germany
{jschmidt, vogt, niemann}@informatik.uni-erlangen.de
Abstract. The paper presents an extended hand-eye calibration approach that, in
contrast to the standard method, does not require a calibration pattern for determin-
ing camera position and orientation. Instead, a structure-from-motion algorithm
is applied for obtaining the eye-data that is necessary for computing the unknown
hand-eye transformation. Different ways of extending the standard algorithm are
presented, which mainly involves the estimation of a scale factor in addition to
rotation and translation. The proposed methods are experimentally compared us-
ing data obtained from an optical tracking system that determines the pose of an
endoscopic camera. The approach is of special interest in our clinical setup, as the
usage of an unsterile calibration pattern is difficult in a sterile environment.
1 Introduction
Hand-eye calibration algorithms [9, 10, 7, 5] solve the following problem that originated
in the robotics community: Given a robot arm and a camera mounted on that arm, com-
pute the rigid transformation from arm to camera (hand-eye transformation). Knowl-
edge of this transformation is necessary, because the pose of the robot arm is usually
provided by the robot itself, while the pose of the camera is unknown but needed for vi-
sual guidance of the arm. However, if the hand-eye transformation is known the camera
pose can be computed directly from the pose data provided by the robot.
Usually, the camera (eye) poses are computed using a calibration pattern and stan-
dard camera calibration techniques. In contrast to that, a method for hand-eye cali-
bration is presented in this paper, where no calibration pattern is needed. Instead, the
camera poses are obtained solely from an image sequence recorded using a hand-held
camera by applying structure-from-motion methods.
Hand-eye calibration is also interesting for applications that are not directly related
to robotics, but where similar problems arise. Instead of a robot we used an optical
tracking system that provides hand data, and a camera, where the camera poses (eye)are
computed using a calibration pattern for standard hand-eye calibration, and structure-
from-motion for the extended hand-eye calibration described in this paper. The camera
may in general be an arbitrary hand-held video camera. For our application—the recon-
struction of high-quality medical light fields [11]—we used an endoscope with a rigidly
This work was partially funded by the European Commission 5th IST Programme - Project
VAMPIRE. Only the authors are responsible for the content.
This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG) under grant
SFB 603/TP B6. Only the authors are responsible for the content.
W. Kropatsch, R. Sablatnig, and A. Hanbury (Eds.): DAGM 2005, LNCS 3663, pp. 67–74, 2005.
c
Springer-Verlag Berlin Heidelberg 2005
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