June 10, 2009 / Vol. 7, No. 6 / CHINESE OPTICS LETTERS 479
A robust photometric calibration framework for
projector-camera display system
Wenhai Zou (邹邹邹文文文海海海)
∗
and Haisong Xu (徐徐徐海海海松松松)
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China
∗
E-mail: zwh gd2001@yahoo.com.cn
Received August 4, 2008
A novel photometric calibration framework is presented for a projector-camera (ProCam) display system,
which is currently under booming development. Firstly, a piecewise bilinear model and five 5-ary color
co ding images are used to construct the homography between the image planes of a projector and a camera.
Secondly, a photometric model is proposed to describe the data flow of the ProCam display system for
displaying color images on colored surface in a general way. An efficient self-calibration algorithm is
corresp ondingly put forward to recover the model parameters. Aiming to adapt this algorithm to different
types of ProCam display system robustly, a 3×7 masking coupling matrix and a patches image with 1024
color samples are adopted to fit the complex channel interference function of the display system. Finally,
the experimental results demonstrate the validity and superiority of this calibration algorithm for the
ProCam display system.
OCIS codes: 100.5010, 100.2000, 120.2040, 330.0330.
doi: 10.3788/COL20090706.0479.
In the last decade, projectors have broken out of the tra-
ditional role as awkward, simplex output devices and
have been transformed to be portable
[1]
, environment-
sensing, interactively-communicating, and multifunc-
tional display systems. A good example of these display
systems is the projector-camera (ProCam) display sys-
tem, of which the basic unit is a projector attached with
a camera. Depending on the modern vision art, the Pro-
Cam display system has been commonly used in many
developed applications, such as keystone correction
[2]
,
smart presentations
[3]
, and tiled display
[4]
. Moreover,
current efforts in this area have made it clear that the
application outlook of the ProCam display system will
be highly exploited in the near future by new ideas
like controlling the appearance of three-dimensional (3D)
object
[5]
, iLamp and radion frequency identity and ge-
ometry (RFIG) lamp
[6]
, 3D multi-spectral scanner
[7]
, etc.
Without exception, the ProCam display systems involved
in these applications are all needed to be geometrically
and photometrically pre-calibrated to achieve the inner
characteristics of the display system, and to ensure the
expected accurate results. Moreover, the screen for the
ProCam display system is not constrained to a high-
quality white screen but has been extended to an or-
dinary curved and colored surface
[5,7]
.
Concerned about the photometric calibration problem
of the ProCam display system, there are much existed
work on the projector’s and the camera’s calibration, re-
spectively. In Refs. [8, 9], several general methods were
introduced to estimate the input transfer function of a
camera and the precision optical instruments, for exam-
ple, photometers or colorimeters were naturally used to
obtain the transfer function of the projectors. However,
due to the limited range of the measurement at a time
using the precision optical instruments, these methods
are inefficient and cannot recover the spatial variation
of projectors accurately. Therefore, the calibrated cam-
eras are recently introduced to estimate the projector’s
transfer function and several techniques have been de-
veloped to calibrate the ProCam display system
[10,11]
. In
these methods, the projector is calibrated beforehand us-
ing the precision optical instrument and meanwhile the
camera is pre-calibrated under ideal environment, and
then the calibrated camera is used to estimate the pro-
jector’s transmission function on a perfectly-white screen.
These techniques can obtain relatively accurate calibra-
tion results but require fussy processes. More recently,
online self-calibration techniques were developed, which
did not depend on other calibration aids but extracted
the calibration information from the user-projected im-
agery and their camera-outputs at different settings
[5,12]
.
These techniques show high efficiency but suffer from the
simple assumptions of color mixing between the projector
and the camera or being only applied to the monochrome
display surfaces and grayscale images. In this letter, a
general model and a novel algorithm are proposed to ex-
tend the photometric calibration method to be adaptive
to different types of ProCam display system, such as its
projector operating in different modes for displaying color
images on colored surface for different application pur-
poses.
The ProCam display system is composed of a projec-
tor (VGA NEC LT 30+) with a native resolution of 1024
× 768 pixels and a camera (HITACHI HV-D30) with a
resolution of 768 × 576 pixels. The images are projected
onto the screen via a display card (RADEON R9200SE),
and those images from the camera are captured by an 8-
bit Matrox Meteor II/Multi-channel frame-grabber. We
assumed that the color channel numbers of the projector
and camera both were three (e.g., red (R), green (G),
blue (B)).
Before photometric calibration, the geometric map-
ping, which is defined as m(x, y) = (u, v) from the pixel
(x, y) in the image plane of the projector to the cor-
responding pixel (u, v) of the camera, should be con-
structed. If m is divided into proper numbers of subsec-
1671-7694/2009/060479-04
c
° 2009 Chinese Optics Letters