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ICCV
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GIM,
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eying
IMAGE-VARIANT INTERIOR ORIENTATION AND SENSOR MODELLING OF HIGH-
QUALITY DIGITAL CAMERAS
H. Hastedt*, Th. Luhmann, W. Tecklenburg
Institute for Applied Photogrammetry and Geoinformatics, University of Applied Sciences Oldenburg,
Ofener Strafe 16/19, D-26121 Oldenburg, Germany - iapg(a)fh-oldenburg.de/*h.hastedt(g)vermes.fh-oldenburg.de
Commission V, WG V/1
KEY WORDS: camera calibration, image-variant interior orientation, finite elements, distortion, accuracy, bundle adjustment,
guideline VDI/VDE 2634
ABSTRACT:
Nowadays digital high-resolution consumer cameras are increasingly used in closerange photogrammetry. These partial-metric
cameras do not meet photogrammetric requirements as (conventional) metric cameras do. Especially the mechanical constructon of
these cameras is instable. Therefore extended mathematical models for camera calibration are required to model all instabilities and
influences sufficiently. An approach including image-variant interior orientation for camera modelling is discussed. A correction
model with finite elements is added to the mathematical model that provides the correction of remaining errors in sensor space. All
parameters are estimated simultaneously in a bundle adjustment. Based on the German guideline VDI/VDE 2634 foracceptance and
reverification test of optical 3D measuring systems the discussed camera modelling is tested by different camera lens combinations
and configurations of imaging. The results express the importance of the camera model and the investigationsconcerning verification
tests as described in this paper. Significant improvements of accuracy have been achieved with respect to conventional calibration
techniques within self-calibration bundle adjustment.
1. INTRODUCTION
High quality digital cameras are increasingly used for industrial
metrology and machine vision applications. Most of these
cameras are designed for photo-journalism purposes and do not
meet photogrammetric requirements as conventional metric
cameras do (Shortis et al. 1998; Luhmann & Wendt 2000). In
particular these partial-metric cameras show high instability
concerning the fixed CCD-array with respect to the lens. The
system’s accuracy mainly depends on image resolution, image
scale, image measurement precision and network design (Fraser
et al. 1998). Relative precision of 1:50000 up to 1:80000 is
required for most industrial applications. Internal accuracy up to
1:100000 can be achieved using a Kodak DCS 460 (Shortis et
al. 1998). Image measurement precision of 0.02 — 0.05 Pixel,
respectively 0.25um in image space can be achieved, hence it is
fundamental for the accuracy of the photogrammetric bundle
adjustment.
The calibration of still-video cameras like the Kodak DCS 460
or the Fuji S1 Pro is necessary to consider and elimirate
systematic errors (Shortis et al. 1998). Conventional mathema-
tical models for camera calibration assume a stable interior
orientation for one set of images over the whole period of image
acquisition. Principal distance (c;) principal point (xjy;),
radial-symmetric lens distortion (a;,a,,a3), decentring of lenses
by tangential and asymmetric distortion (b,,b,) and global
sensor properties such as affinity and sheering (cı,c,) are
estimated within self-calibrating systems.
Different investigations have been made to take deformations of
film and sensor plane into account (e.g. CAP). Munji (1986)
reports on the application of finite elements for the determi
nation of local imaging errors of partia-metric cameras. The
behaviour of the principal point for Kodak cameras with
assumed fix principal distance based on several sets of images is
exposed at Shortis et al. (1998). Fraser et al. (1992) and Dold
(1997) report on the influence of variation of distortion within
the photographic field and gained improvement in accuracy for
special applications.
It can not be assumed that camera parameters remain stable over
the whole period of image acquisition. Gravity takes effect with
different viewing directions. Long periods of image acquisition
yield to heat the camera with increasing influences on the
photogrammetric system (Jantos et al. 2002). The camera is
subject to intense mechanical influences by the user; especially
hand-held shots are influenced by the users handling and can
yield to varying strains of the camera body (Tecklenburg et al.
2000).
These effects are investigated by the discussed extended model
for camera calibration. An image-variant interior orientation is
added to the camera model which describes variation in
principal distance and principal point. As a major result the
possible displacement and rotation of the lens with respect to
the image sensor are compensated by this model, similar to the
approach of Maas (1998). In order to compensate sensor based
influences (especially sensor unflatness) as well as all remaining
lens effects not considered within radia-symmetric lens
distortion, a finite-elements correction grid has been chosen.
This raster-wise correction grid based on anchor points is
distributed according to an a priori grid width.
This approach is verified by various sets of images of a testfield
based on the German guideline VDI/VDE 2634. Different
photogrammetric projects are accessable of an own control field
with reference points for comparability and quality of the
camera and its parameters. Mainly two cameras (Kodak DCS
460 and Fuji S1 Pro) are tested by different sets of images of the
described testfield. The results are presented and discussed.
2. MATHEMATICAL MODEL
2.1 Image-variant parameters
Usually camera parameters are applied identically for all images
of a photogrammetric project. Distortion parameters are defined
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