ARTICLE IN PRESS
JID: NEUCOM [m5G; April 14, 2017;22:0 ]
Neurocomputing 0 0 0 (2017) 1–7
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Neurocomputing
journal homepage: www.elsevier.com/locate/neucom
Recovering the absolute phase maps of three selected
spatial-frequency fringes with multi-color channels
Yi Ding
a
, Jiangtao Xi
b
, Yanguang Yu
b
, Fuqin Deng
c
, Jun Cheng
d , ∗
a
School of Remote Sensing and Information Engineering, Wuhan University, 299 Bayi Road, Wuhan, China
b
School of Electrical Computer and Telecommunications Engineering, University of Wollongong, Wollongong, NSW, 2522, Australia
c
Han’s Motor, Headquarter, 9018 Beihuan Road, Shenzhen, China
d
Guangdong Provincial Key Laboratory of Robotics and Intelligent System, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068
Xueyuan Avenue, Shenzhen, China
a r t i c l e i n f o
Article history:
Received 23 October 2015
Revised 17 March 2016
Accepted 29 April 2016
Available online xxx
Keywords:
Instrumentation
Measurement and metrology
Three-dimensional image acquisition
Phase measurements
Color channels
a b s t r a c t
In a recent published work, we developed the technique to enhance the reliability of absolute phase maps
by using the fringes of three spatial frequencies. However, it is time-consuming to capture the fringe im-
ages of three spatial frequencies with single channel in time sequence. To increase the efficiency of our
proposed three-frequency technology, in this paper we propose a method to capture the fringe images of
three spatial frequencies with multi-color channels and 3CCD camera. The projected spatial frequencies
can be selected to guarantee the correctness of recovered fringe orders and avoid the chromatic aberra-
tion effect on frequency distortion. The cross talk among color channels can be eliminated effectively and
the measured object can be reconstructed with high accuracy. The effectiveness of this method is verified
by experimental results.
©2017 Elsevier B.V. All rights reserved.
1.
Introduction
Fringe projection profilometry (FPP) has become one of the
most promising technologies for non-contact 3D shape measure-
ment. The methods based on the phase maps of fringe patterns are
the most widely utilized. A challenging task associated with exist-
ing phase measurement technique in FPP is phase unwrapping op-
eration, which aims to recover the absolute phase maps from the
wrapped phase maps. Existing phase unwrapping methods include
spatial [1] , temporal [2] , and period coding [3] . However, recov-
ery of absolute phase maps is still a challenging task when the
wrapped phase maps contain noise, sharp changes or discontinu-
ities.
To achieve reliable and accurate phase unwrapping for FPP, a
variety of temporal phase unwrapping approaches have been pro-
posed. Huntley and Saldner [2] employ the multiple fringe patterns
which are projected onto the object in time sequence, phase un-
wrapping can be carried out by comparing the wrapped phases
of adjacent frequencies in order to avoid noise or boundaries and
thus achieving correct recovery of the absolute phase map. While
the method proposed in [2] is demonstrated to be effective for ac-
curate phase unwrapping, it also suffers from the drawback of re-
quiring many intermediate phase patterns, which is obviously not
∗
Corresponding author.
E-mail address: jun.cheng@siat.ac.cn (J. Cheng).
suitable for fast or real-time measurement. In order to increase the
efficiency, Zhao, et al. [4] propose to use two image patterns, one
of which has a very low spatial frequency in contrast to the other.
In particular, the low spatial frequency pattern only has a single
fringe. Such a pattern has its absolute phase value falling within
the range (−π , π ) , and hence can be used as a reference to cal-
culate the fringe number of the other fringe pattern, thus yielding
its absolute phase map. Li, et al. [5] also employ the phase map
of single fringe pattern as reference to unwrap high spatial fre-
quency fringe patterns, and it is shown that the spatial frequency
of the pattern to be unwrapped is determined by the level of noise.
Following the same method in [4] , Liu, et al. [6] project a single
fringe pattern and a high frequency pattern in one shot to accel-
erate the speed of 3D measurement. These method works well in
principle, but the gap between two spatial frequencies should be
restricted within a range based on the noise level or steps in the
low frequency phase maps. As the accuracy performance of FPP
requires the use of high frequency fringe patterns, these meth-
ods may not work well when the phase maps are noisy. Con-
sequently, multiple intermediate image patterns are still required
in order to reduce the frequency gaps among adjacent patterns.
Saldner and Huntley [ 7 , 8 ] study the multiple intermediate image
patterns, showing that to unwrap a phase map of frequency f ,
log
2
f + 1 sets of fringe patterns are required. A similar result is
also reached by Zhang [ 9 , 10 ], indicating that the spatial frequency
can be increased by a factor of 2 between two adjacent patterns.
http://dx.doi.org/10.1016/j.neucom.2016.04.074
0925-2312/© 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Y. Ding et al., Recovering the absolute phase maps of three selected spatial-frequency fringes with multi-color
channels, Neurocomputing (2017), http://dx.doi.org/10.1016/j.neucom.2016.04.074