A Flexible New Technique for Camera Calibration
Abstract
We propose a flexible new technique to easily calibrate a camera. It is well suited for use
without specialized knowledge of 3D geometry or computer vision. The technique only requires
the camera to observe a planar pattern shown at a few (at least two) different orientations. Either
the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens
distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a
nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and
real data have been used to test the proposed technique, and very good results have been obtained.
Compared with classical techniques which use expensive equipment such as two or three orthog-
onal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision
one step from laboratory environments to real world use.
Index Terms— Camera calibration, calibration from planes, 2D pattern, absolute conic, projective
mapping, lens distortion, closed-form solution, maximum likelihood estimation, flexible setup.
1 Motivations
Camera calibration is a necessary step in 3D computer vision in order to extract metric information
from 2D images. Much work h as been done, starting in the photogrammetry community (see [2,
4] to cite a few), and more recently in computer vision ([9, 8, 23, 7, 26, 24, 17, 6] to cite a few).
We can classify those techniques roughly into two categories: photogrammetric calibration and self-
calibration.
Photogrammetric calibration. Camera calibration is performed by observing a calibration object
whose geometry in 3-D space is known with very good precision. Calibration can be done very
efficiently [5]. The calibration object usually consists of two or three planes orthogonal to each
other. Sometimes, a plane undergoing a precisely known translation is also used [23]. These
approaches require an expensive calibration apparatus, and an elaborate setup.
Self-calibration. Techniques in this category do not use any calibration object. Just by moving a
camera in a static scene, the rigidity of the scene provides in general two constraints [17, 15]
on the cameras’ internal parameters from one camera displacement by using image informa-
tion alone. Therefore, if images are taken by the same camera with fixed internal parameters,
correspondences between three images are sufficient to recover both the internal and external
parameters which allow us to reconstruct 3-D structure up to a similarity [16, 13]. While this ap-
proach is very flexible, it is not yet mature [1]. Because there are many parameters to estimate,
we cannot always obtain reliable results.
Other techniques exist: vanishing points for orthogonal directions [3, 14], and calibration from pure
rotation [11, 21].
Our current research is focused on a desktop vision system (DVS) since the potential for using
DVSs is large. Cameras are becoming cheap and ubiquitous. A DVS aims at the general public,
who are not experts in computer vision. A typical computer user will perform vision tasks only from
time to time, so will not be willing to invest money for expensive equipment. Therefore, flexibility,
robustness and low cost are important. The camera calibration technique described in this paper was
developed with these considerations in mind.
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