Plane-based calibration of a projector-camera system
Gabriel Falcao, Natalia Hurtos, Joan Massich
VIBOT Master 2008
Accuracy and simplicity of system calibration is a key challenge in 3D computer vision tasks. A calibration method by
a planar checkerboard to minimize calibration complexity and cost is proposed. This method is based in considering
the projector as an inverse camera which maps 2D image intensities into 3D rays, thus making the calibration of a
projector the same as that of a camera. In this way, having the 2D projected points and its 3D correspondences the
system can be calibrated using a standard camera calibration method such as the one implemented in Bouguet’s
Calibration Toolbox. A projector-camera system has been calibrated by this method, and a good 3D reconstruction
quality has been achieved by the calibrated system.
1. Introduction
This report addresses the problem of system calibration which is crucial for any 3D computer vision
system and in particular for any 3D shape measurement system. Placed in this context, system
calibration involves the calibration of a camera, which have been extensively studied over the years,
and the calibration of a projector. Theoretically, a data projector can be seen as a dual of a camera. In
practice, there are two main differences that make the calibration of a projector more complicated than
that of a camera. The first one is obvious: projectors cannot image the surface that they illuminate so
that the correspondence between the 2D projected points and the 3D illuminated points cannot be
made without the use of a camera. The second one is that it is difficult to retrieve the co-ordinates of
the 3D points because the calibrating pattern is projected and not attached to the world coordinate
frame in general. This can explain that, to this date, there have been very few practical methods to
compute the intrinsic parameters of a data projector.
In this work, we present a method of plane-based calibration for projector-camera systems which aims
to be both accurate and easy-to-use. This method has been implemented as an extension to Bouguet
Camera Calibration Toolbox.
In section 2 the principle of the proposed method is presented. In sections 3,4,5 the main steps of the
method are described. In section 6 a tutorial on the use of the toolbox for calibrating a Camera-
Projector system is provided. Finally in section 7 some experimental results using 3D reconstruction
with structured light demonstrate the performance of the method and in section 8 the conclusions and
future work is discussed.
2. Overview of the method
The goal of the presented method is to obtain the intrinsic and extrinsics parameters for both the
camera and projector of the system. Both image capture and projection is generally described by a
standard pinhole camera model with intrinsic parameters including focal length, principle point, pixel
skew factor, and pixel size; and extrinsic parameters including rotation and translation from a world
coordinate system to a camera or projector coordinate system.
The key point of the proposed calibration method is to consider the projector as an inverse camera
(mapping intensities of a 2D image into 3D rays) thus making the calibration of a projector the same as
that of a camera. In this way we can make use of any standard calibration procedure for cameras in
order to calibrate the projector. So the main concern of our method is to find the 3D points of the
projected pattern in order to use them together with the 2D points of the image we are projecting to
finally obtain the intrinsics and extrinsics of the projector.
The proposed method to achieve the whole calibration of the system is divided in several steps:
• Calibrate the camera using Zhang’s method
• Recover calibration plane in camera coordinate system
• Project a checkerboard on calibration board and detect corners
• Apply ray-plane intersection to recover 3D position for each projected corner
