Camera Self-Calibration with Lens
Distortion from a Single Image
Dan Liu, Xuejun Liu, and Meizhen Wang
Abstract
This paper presents an effective approach for self-calibration
with lens distortion using a single image combined with geo-
metric constraints including vanishing points and ellipses. To
improve the accuracy of self-calibration, radial distortion and
distortion center are included in the calibration procedure.
First, assuming image center as the symmetric center, the first
radial distortion coefficient and vanishing points are simulta-
neously optimized from line segments in the image. Second,
by utilizing the optimized vanishing points and extracted
ellipse, principal distance and principal point are estimated.
Last, distortion center is set as the current calculated prin-
cipal point, and the above steps are then repeated until the
principal point reaches a stable solution. Extensive quantita-
tive and qualitative studies of the approach are performed.
The experiments pertaining to simulated and real images
demonstrate that the approach is effective and suitable and
that the approach obtains satisfactory results.
Introduction
Camera calibration is a significant topic of research in Close-
Range Photogrammetry, which plays an essential role on
various tasks such as 3
D
reconstruction, geometric measure-
ment from images, and video surveillance. Camera calibration
is the procedure of estimating lens distortion coefficients and
camera interior orientation parameters including principal
distance, and principal point coordinates (Tsai, 1987). They,
together with exterior orientation parameters, are essential for
extracting 3
D
metric information in object space. In the 1970s,
self-calibration using bundle adjustment was first introduced
by Brown, which can extract camera parameters directly from
straightness in images of object space straight lines (Brown,
1971). Camera self-calibration methods from images are flex-
ible, efficient, and widely used. The classical self-calibration
methods require two or more images taken from different
viewpoints. They rely or partly rely on the corresponding re-
lationship between images (Faig, 1975; Hartley, 1994; Zhang,
2000; Remondino and Borlin, 2004). However, it is asked to
deal with a single image under certain circumstances. The
Internet or historic photos can be the exclusive source for 3
D
information of scenes. But these photos may well be not taken
for photogrammetric purposes, but taken by the public or
amateur photographers. So there usually exists only a single
image of the scene. In addition, when calibrating with the
classical methods which requires multiple images, parts of
the scene appear only in one single image due to occlusion
or lack of corresponding features between images
.
Therefore,
camera calibration from a single image is extremely useful for
recovering 3
D
metric information.
Unlike camera calibration using multiple images, camera
calibration can be performed from a single image with prior
geometrical information. According to the geometrical infor-
mation, methods for camera calibration from a single image
mainly include the following categories: camera calibration
using a single image based on vanishing points/vanishing
lines (Caprile and Torre, 1990; Grammatikopoulos
et al
.,
2007), based on circles/ellipses (Chen
et al
., 2004; Colombo
et
al
., 2006), based on symmetry (Hong
et al
., 2004) and based on
coplanar points/coplanar lines (Shang
et al
., 2005; Park, 2007).
Because of the advantages of its simple and easy-to-
achieve, camera calibration based on vanishing points has
been subsequently reported in
Photogrammetry and Com-
puter Vision
. In the computervision community, Caprile and
Torre (1990) first proposed a technique for camera calibration
using three mutually orthogonal vanishing points from a sin-
gle image of a cube. The cube was replaced with other calibra-
tion patterns to generate orthogonal vanishing points, such as
a parallelepiped (Wildenauer
et al
., 2005), a rectangular prism
(Avinash
et al
., 2008). Wildernauer and Hanbury (2012) pre-
sented a
RANSAC
-based method to estimate vanishing points
and principal distance from a set of four lines in single image
of Manhattan world. In the photogrammetry community, van
den Heuvel (1999 and 2001) estimated the interior orienta-
tion parameters and lens distortion in a least squares adjust-
ment using parallelism and perpendicularity constraints. The
calibration process was split into two steps. In the first step,
vanishing points and radial distortion were estimated based
on parallelism constraint. In the second step, the interior
orientation parameters were estimated from perpendicular-
ity constraints. Grammatikopoulos
et al
. (2003) presented the
technique for camera calibration based on three basic image
vanishing points. Grammatikopoulos
et al
. (2007) proposed
one-step approach for camera calibration, in which vanish-
ing points, the interior orientation parameters, and radial
distortion were estimated simultaneously. González-Aguilera
(2008) presented a complete procedure for camera calibration
from a single image using three orthogonal vanishing points.
González-Aguilera and Gómez-Lahoz (2009) and Garcia-Gago
et al
. (2014) respectively performed historic building recon-
struction and forensic photogrammetric analysis from a single
image based on vanishing points. Although these methods
based on vanishing points are useful for camera calibration,
vanishing points are sensitive to noise, which makes the ac-
curacy of these methods relatively low.
Some camera self-calibration methods, especially methods
based on vanishing points, depend on the assumption of an
ideal pinhole camera model. However, most modern digital
cameras contain lens distortion, particularly radial distortion
which is the most significant type of distortion, so that the
Key Laboratory of Virtual Geographic Environment (Nanjing
Normal University), Ministry of Education, Nanjing, Jiangsu
210023, China;Jiangsu Center for Collaborative Innovation
in Geographic Information Resource Development and
Application, Nanjing, Jiangsu 210023, China; and College of
Geographic Sciences, Nanjing Normal University, Nanjing,
Jiangsu 210023, China (
)
Photogrammetric Engineering & Remote Sensing
Vol. 82, No. 5, May 2016, pp. 325–334.
0099-1112/16/325–334
© 2016 American Society for Photogrammetry
and Remote Sensing
doi: 10.14358/PERS.82.5.325
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
May 2016
325
