Kameda Yoshinari

Kitahara Itaru

Shishido Hidehiko

Suzuki Kenji

Xie Chun

亀田 能成

北原 格

宍戸 英彦

鈴木 健嗣

Tsukuba Repository

A Calibration Method for Large-Scale
Projection Based Floor Display System
著者 Xie Chun, Shishido Hidehiko, Kameda Yoshinari,
Suzuki Kenji, Kitahara Itaru
journal or
publication title
The 25th IEEE Conference on Virtual Reality
and 3D User Interfaces (IEEE VR 2018)
year 2018-03
URL http://hdl.handle.net/2241/00152113
A Calibration Method for  
Large-Scale Projection Based Floor Display System 
 
Chun Xie1  Hidehiko Shishido2      Yoshinari Kameda3  Kenji Suzuki4  Itaru Kitahara5  
University of Tsukuba, Japan 
 
 
ABSTRACT 
We propose a calibration method for deploying a large-scale 
projection-based floor display system. In our system, multiple 
projectors are installed on the ceiling of a large indoor space like a 
gymnasium to achieve a large projection area on the floor. The 
projection results suffer from both perspective distortion and lens 
distortion. In this paper, we use projector-camera systems, in which 
a camera is mounted on each projector, with the “straight lines have 
to be straight” methodology, to calibrate our projection system. 
Different from conventional approaches, our method does not use 
any calibration board and makes no requirement on the overlapping 
among the projections and the cameras’ fields of view. 
Keywords: Large-scale projection; projector-camera system; lens 
distortion; calibration; augmented reality. 
Index Terms: •Human-centered computing~Displays and imagers  
• Human-centered computing~Mixed / augmented reality • 
Computing methodologies~Camera calibration 
1 INTRODUCTION 
We deployed a large-scale floor projection system in a school 
gymnasium. One task in constructing a projection system that 
targets a large-scale space is to calibrate multiple projectors to align 
the projected images into one large projection. In our case, it is 
impossible to use chessboard based calibration method such as[3] 
to calibrate the system due to the large working distances of the 
devices. Self-calibration methods[4] also not work in our situation, 
because the number and locations of devices are usually limited by 
factors of realistic environment such as building structure, weight 
capacity and original purpose of the facility, therefore the 
projections and cameras' field of view are not sufficiently 
overlapped to generate reliable correspondences among devices. In 
this paper we introduce the calibration procedure we used on our 
projection system. We make use of projector-camera sets and 
“straight lines have to be straight”[2] methodology. Our calibration 
method does not require significant overlapping among projections, 
therefore, the number of projector can be minimized. 
2 SYSTEM SETUP 
As shown in Figure. 1, our projection system consists of multiple 
projector-camera systems with cameras mounted on top of the 
projector. This system is installed on the ceiling and content is 
presented on the floor. The total projection area of our system is 
around 120m2, and it can be extended by simply adding more 
projector-camera sets. 
3 CALIBRATION METHOD 
Camera lens distortion correction: Basing on “straight lines have 
to be straight”, the optimal lens distortion parameters can be found 
by minimizing the degree of distortion of straight lines in an image. 
In our method, we evaluate the degree of distortion for each line 
using the covariance matrix of their sample points. In case that there 
is no sufficient straight line in the camera view, we can use laser 
line pointer to project some straight lines on the projection plane. 
The optimization is done by an algebraic approach proposed by 
Alvarez [1]. 
 
 
Figure 1: Large-scale projection system comprised of multiple 
projector-camera systems 
Projector lens distortion correction:  We first use the projector 
to be calibrated to project some straight lines on the projection 
plane. Then we use the camera, which has been calibrated by the 
above procedure, to capture the projection result and evaluate the 
degree of distortion of the projected image. The distortion 
parameters of a projector can be then optimized by Broyden-
Fletcher-Goldfarb-Shanno (BFGS) algorithm, which iteratively 
finds the optimal values that produce the least distorted result in the 
camera image. To improve the accuracy and efficiency, the initial 
value of distortion center is roughly estimated by finding the 
intersection of the least distorted row and the column before 
optimization. Furthermore, to avoid projecting several patterns pre-
wrapped by new parameter values in each iteration, which is very 
time-consuming, we use line-shift structured light to generate the 
projector-to-camera pixels correspondences for each projector-
camera set with sub-pixel accuracy in advance. Doing this, for any 
further projections, we can get a camera coordinate in sub-pixel 
accuracy for every projector pixel, so that we can simulate the 
projecting and capturing in each iteration instead of performing 
them in the real world and thus reduce the processing time. 
Projective distortion correction: As the lens distortions have 
been corrected, the projective distortion can be corrected by pre-
wrapping the projector buffer by the projector-to-floor homography  
 
1      xie.chun@image.iit.tsukuba.ac.jp 
2,3,5 {shishido, kameda, kitahara}@ccs.tsukuba.ac.jp 
4      kenji@iit.tsukuba.ac.jp 
 
Figure 2: (a) and (b): Projection results of line grid and color block with only projective distortion correction. (c) and (d): The results with both projective 
distortion and lens distortion. 
 
Hpf. This homography is calculated from the projector-to-camera 
homography Hpc and the camera-to-floor homography Hcf. Hpc can 
be estimated by finding the coordinate correspondences between 
the projector and the camera, and similarly, Hcf  can be estimated 
by finding the coordinate correspondences between  the camera and 
the floor.  
4 EXPERIMENTS 
4.1 Quantitative experiment 
We performed a quantitative experiment by simulation. We 
generated three projector camera coordinate maps with white noise 
[-0.1,0.1], [-0.3,0.3] and [-0.5,0.5] (unit: pixel). The ground truth 
values and calibration results based on these three maps are shown 
in Table 1.  
Table 1: Projector lens distortion estimation results 
Variables k1’ 
(1e-7) 
k2’ 
(1e-14) 
Distortion center 
(unit: pixel) 
Ground truth -1.023 4.387 (512, 384) 
Noise = ±0.1 -1.025 4.428 (512.104, 383.858) 
Noise = ±0.3 -1.024 4.404 (511.214, 383.966) 
Noise = ±0.5 -1.012 4.138 (512.726, 384.681) 
Both k1’ and k2’ are converging to the ground truth, while k2’ is 
less stable because its effect on the lens distortion is much weaker 
than k1’. The estimation errors of the distortion center for all three 
maps are less than 1 pixel. 
4.2 Projection Experiment 
In this experiment, we use four projectors whose projections are 
approximately aligned on the floor. We projected two kinds of 
images to evaluate the appearance of the projection result: a grid 
pattern that only consists of 1-pixel lines and a color block pattern. 
Figure 2(a) shows that for the line grid image, some lines are bent, 
and noticeable line misalignments occurred around adjacent edges 
between two projections. Figure 2(b) shows that for the color block 
images, the gap between two projections is much more obvious 
than line bending and misalignment. Note that since adjacent edges 
are curved, the gaps cannot be solved by linear transformation. 
Figure 2(c) and 2(d) give the corrected results of the line grid as 
well as the color block generated by our method. In these results, 
distorted lines are straightened, and misalignment and gaps around 
adjacent edges can barely be observed. Although it is not seamless 
since there is very narrow overlapping between two adjacent 
projections where the projection intensity is higher than the 
surrounding areas, the problem can be solved by additional 
intensity normalization. 
5 CONCLUSION 
In this paper, we proposed a calibration method for a projector-
camera system in a large-scale space. Using the “straight lines have 
to be straight” methodology, our method corrects the projective and 
lens distortions of both the projector and the camera without 
moving them or the projection plane. Although our method’s 
optimization is based on projecting and capturing iterations, which 
is time-consuming, by generating a projection camera pixel map in 
advance, projecting and capturing can be performed virtually to 
reduce the processing time. 
The quantitative experiment shows that the estimation results of 
projector lens distortion parameters are very close to the ground 
truth values. Our projection experiment shows that compared with 
a result where only projective distortion correction was performed, 
our method gave a more seamless projection result. 
This work was partially supported by JST CREST Grant Number 
JPMJCR14E2, Japan. 
REFERENCES 
[1] L.Alvarez, L.Gómez, and JR.Sendra. An algebraic approach to lens 
distortion by line rectification. Journal of Mathematical Imaging and 
Vision 35, 1, 36-50, 2009 
[2] F.Devernay, and O.Faugeras. Straight lines have to be straight. 
Machine vision and applications 13, 1, 14-24, 2001. 
[3] D. Moreno and G. Taubin, Simple, accurate, and robust projector– 
camera calibration, Proceedings of 3DIMPVT2012, Zurich, pp. 464–
471, 2012. 
[4] S. Willi and A. Grundhöfer. Robust Geometric Self-Calibration of 
Generic Multi-Projector Camera Systems. Proceedings of 
ISMAR2017, Nantes, pp. 42-51, 2017. 


A Calibration Method for Large-Scale Projection Based Floor Display System

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A Calibration Method for Large-Scale Projection Based Floor Display System

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