CAMERA CALIBRATION APPROACHES
USING SINGLE IMAGES OF MAN-MADE OBJECTS
L. Grammatikopoulos a , G. E. Karras a , E. Petsa b
a Department of Surveying, National Technical University of Athens, GR-15780 Athens, Greece (lazaros, gkarras@central.ntua.gr)
b Department of Surveying, Technological Educational Institute of Athens, GR-12210 Athens, Greece (petsa@teiath.gr)
KEY WORDS: Non-Metric, Calibration, Orientation, Single-Image Techniques, Geometry, Algorithms, Accuracy
ABSTRACT
Single image techniques may be very useful for heritage documentation purposes, not only in the particular instances of damaged or
destroyed objects but also as auxiliary means for a basic metric reconstruction. In the general case, single images have unknown in
terior orientation, thus posing the fundamental question of camera calibration (as in several cases no ground control is available). To
this end, the known - or assumed - geometry of imaged man-made objects may be exploited. Recovery of the three main elements of
interior orientation, together with image attitude, requires the existence on the image of lines in three known non-coplanar directions,
typically orthogonal to each other (from the lines, radial lens distortion might also be estimated). Several approaches have been re
ported for the exploitation of this basic image geometry; however, the expected accuracy has not been adequately investigated. In this
contribution, three alternative algorithms are presented, based: on the direct use of the three basic image vanishing points; on the use
of image line parameters; and on the direct use of image point observations. The integration of radial distortion into the algorithms is
also presented. The reported results are evaluated, and promising conclusions are drawn regarding the performance and limitations of
such camera calibration methods, as compared to self-calibrating bundle adjustment techniques based on control points.
1. INTRODUCTION
Under certain circumstances photogrammetry is asked to handle
documentation questions for cultural items partly or totally da
maged. So, it happens that old (‘historic’) images can be the ex
clusive source for metric information; these may well be single
amateur photographs. Not taken for photogrammetric purposes,
they usually lack control information or camera data. Fortunate
ly enough, however, man-made objects usually contain straight
lines, thus being suitable for methods of line photogrammetry.
But single-image line photogrammetry is evidently not restricted
to old images; its uses include very diverse tasks like vehicle or
robot navigation and metric exploitation of surveillance cameras
(topics extensively studied in the field of computer vision). In
fact, what is more important is an understanding of the underly
ing image geometry, common to all monoscopic techniques. For
the purposes of this contribution, a single-image approach may
be regarded as consisting of three, albeit not independent, steps:
camera calibration; image orientation; object reconstruction.
Regarding ID measurements, one suitable vanishing point on an
uncalibrated image may be sufficient (Grammatikopoulos et al.,
2002). For 2D objects, e.g. planar facades, two vanishing points
of known angle permit to recover image rotations and the came
ra constant, and hence rectification (Karras et al., 1993). But if
the principal point cannot be ignored, rectification requires fur
ther information (a length proportion). Regarding 3D structures,
Gracie (1968) has derived all necessary equations for estimating
interior orientation parameters and camera attitude in a configu
ration with three vanishing points in orthogonal directions. Re
sults have been reported with this approach by both Brauer-Bur-
chardt & Voss (2001) and Petsa et al. (2001) regarding old pho
tographs (the former also address cases where one of the vanish
ing points is close to infinity by using appropriate length ratios).
To the same effect, van den Heuvel (2001) adjusted line obser
vations with constraints among lines for camera calibration.
Unlike approaches founded on vanishing points, Petsa & Patias
(1994) had presented an algorithm using image line parameters,
estimated previously; these are subsequently adjusted to recover
interior orientation and rotation matrix. This approach has been
successfully applied to uncalibrated photographs of both exist
ing buildings and a tom down theatre (Karras & Petsa, 1999).
Here, the particular problem of camera calibration is addressed.
Besides being a step towards the final goal of reconstruction, it
constitutes a problem in its own right: How reliable are simple
single-image calibration approaches, which do not rely on con
ventional control information but, merely, on object geometry?
Here, different formulations are discussed and evaluated against
a rigorous multi-image bundle adjustment approach.
In most instances, radial lens distortion is either neglected or is
estimated beforehand (as in Brauer-Burchardt & Voss, 2001) by
one of the simple methods at hand (Karras & Mavromati, 2001).
Here, radial distortion has also been introduced into the algo
rithms to allow camera calibration in one single step.
2. ALTERNATIVE FORMULATIONS
2.1 Use of vanishing points
As mentioned already, Gracie (1968) has given the formulae for
determining the three interior orientation elements (camera con
stant c and principal point x 0 , y 0 ) and the three to, cp, K image ro
tations from the vanishing points of three orthogonal directions,
which provide the six necessary equations. Thus, the adjustment
refers here to the estimation of vanishing points from individual
point measurements Xj, yj on converging image lines. The fitted
lines are constrained to converge to the corresponding vanish
ing point F(xp, yF) according to following observation equation:
Xi-x F -(yi-y F )t = 0 (1)
According to line direction, the equation can be also formulated
using slope t = Ay/Ax with respect to the x-axis. Having estima
ted vanishing point locations, subsequent determination of inte
rior orientation elements and rotation matrix R is then straight
forward. This is approach A.
