CALIBRATION OF A PROJECTOR WITH A PLANAR GIRD
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Jun Tao ^ , Ruifang Zhai ^, Zuxun Zhang ', Jianqing Zhang *
“Wuhan University, College of Remote Sensing and Information Engineering,
#129 Luoyu Road, Wuhan, Hubei, P.R.China 430070
Jqzhang@supresoft.com.cn, martintao@etang.com, zxzhang@supresoft.com.cn
KEY WORDS: Photogrammetry, Calibration, Image, Sequences, Parameters, Platform
ABSTRACT:
The projector is being frequently used in broad range of the photogrammetric measurements with the development of non-contact
measurement in the close-range photogrammetry, because a projector can project any pattern onto the measured object for
controlling and calculating. Before using a projector, the interior parameters of it have to be calibrated first. Hence, the projector
calibration is a necessary and important preceding step. The paper proposes a flexible technique to make the calibration of a
projector with a planar grid. This technique only requires an ordinary projector, a digital camera and a planar grid. The planar grid
provides the main control ground and the camera takes photos as the image data. The camera demands to be calibrated or its intrinsic
parameters are known. The algorithm with 2D direct linear transformation (2D-DLT) and collinear equations is used to calibrate the
projector. The operation method in detail and the algorithm are addressed systematically and entirely. First, the image coordinates of
the projector are designed carefully and the space coordinates of the projector are computed by the image data and the intrinsic and
extrinsic parameters of the digital camera. Then, the decomposition of initial values of the projector intrinsic and extrinsic
parameters using the correspondence of 2D-DLT and collinear equation is deduced. Finally, the projector calibration parameters are
worked out by the whole adjustment. The feasibility and the exactness of the calibration technique of a projector put forward in this
paper are verified by the results of real experimentations and data.
1. INTRODUCTION
1.1 Advantages of a Projector
The use of the ordinary projector becomes familiar and frequent,
because a projector can project any pattern onto the measured
object. It can provide the points of interest conveniently and
simply. The pattern can be designed differently according to all
kinds of requirements of the measured object. These points
projected on the surface of the object are stable, high contrast
and quality. They have no inhere target thickness. Their size
can grow up and their intensity can decrease down as the
projector gets further from the measured object. Hence the
projected points can be adjusted to suit for a good measurement.
At same time, the projector is set far enough away the surface
of the measured object so that it is convenient and easy to be
installed and is almost not affected by the special object such as
high temperature iron block or quickly moving bus. Because of
the advantages of the ordinary projector above, it is being used
in broad range of the close-range photogrammetric
measurements. In order to take full advantage of the projector
in the procedures of diverse photogrammetric measurements,
the intrinsic parameters of the projector have to be calibrated in
advance. Namely, the projector needs to be calibrated at first.
Hence, the projector calibration 1s a necessary and important
preceding step.
1.2 Calibration of a Projector
In this paper a flexible technique is proposed to calibrate the
ordinary projector easily. The technique only requires an
ordinary projector, a digital camera and a planar grid. The
projector illuminates a target grid slide onto the planar grid.
The digital camera is used to take the images of the planar grid
from a few (at least two) different orientations. The camera has
already been calibrated or its intrinsic parameters are known
first. The planar grid functions as a control ground to provide
the coordinates of space points. Using the correspondence of
collinear equations and 2D direct linear transformation, the
intrinsic parameters of the projector can be worked out. By this
time, the projector is calibrated entirely.
Compared with other techniques, which use the expensive
equipment and the complex algorithm, the proposed technique
is easy to realize and flexible. It is hardly affected by the space
factor or time factor. It paves the path for the using in future of
an ordinary projector, which is calibrated. The feasibility and
the correctness of the projector calibration technique proposed
in this paper are verified by the results of real data.
1.3 Using of a Calibrated Projector
After a projector has been calibrated correctly, it can be used to
control on and project to the measured objects as the same
function as a camera. Especially, it can supply the points of
interest on the surface of the objects which are lack of the
texture. Using these points, all kinds of values of the measured
objects can be computed easily. When the intrinsic parameters
of a projector are correct, the using of it and the calculation
with its parameters are effective and exact.
2. METHODOLOGY AND ALGORITHM
2.1 Equipment and Method
An ordinary projector, a digital camera and a planar grid are the
main equipments required in this technique. For the projector, a
* E-mail: martintao@etang.com; Tel: 86-27-87664509(D), 86-27-87654319(0), 86-27-84764339(H)
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