Signal Processing - May 2017 - 58

To maintain a minimum number of required images for
absolute depth recovery, several phase-shifting methods
using period coding have been proposed. The common idea is
to encode a period-specific signal into the fringe, and the phase
I 2 (u, v) - I 1 (u, v)
ambiguity is solved by decoding the embedded signal. In [25],
;
E
z (u, v) = arctan 3
. (4)
2I 3 (u, v) - I 2 (u, v) - I 1 (u, v)
Liu et al. embed a unit-frequency sinusoidal fringe into a highfrequency one. The high-frequency fringe plays the role of
The phase obtained by (4) ranges from -π to π, which results
phase shifting, while the unit-frequency fringe serves as period
in discontinuities in the phase map as shown in Figure 2(c).
codes. At least five images are needed to derive a phase pair.
Thus, a phase unwrapping procedure is needed to convert the
The unit-frequency phase has no ambiguity, as there is only
wrapped phase to the absolute phase as
a single period, so it can be used to disambiguate the wrapped
z abs (u, v) = z (u, v) + 2d (u, v) r,
(5)
high-frequency phase. To achieve a real-time performance, they
also propose a lossless table-lookup method for phase calculation
and 3-D point cloud generation. The 3-D reconstruction speed of
d
(
u
,
v
)
[
0
,
M
1
]
and
is an integer disparity within
where
their system can reach 228 fps at 640 × 480 pixels, though the
M is the number of periods of the fringe pattern. Once the
actual 3-D acquisition speed depends on the projector and the
absolute phase is obtained, the absolute depth at each scene
camera being used.
point can be calculated through triangulation between the
In [26], Wissmann et al. propose another phase-shifting
projector and the camera. An exemplar depth map is shown
method with period coding. Specifically, they embed a onein Figure 2(d).
dimensional (1-D) binary De Bruijn sequence into a four-step
Phase shifting belongs to time coding for structured light,
phase-shifting pattern set, where the embedded signal will not
as it uses multiple patterns. By concentrating the usable codeaffect the phase calculation. They also deword within a narrow fringe period and
sign a corresponding decoding strategy to
eliminating the influence of ambient illuDifferent depth sensors
extract the period index from the De Bruijn
mination and scene albedo, phase shifting
have complementary
sequence. One highlight of this work is the
can achieve higher accuracy compared
advantages, and a
cost-effective hardware design. Instead of
with other time-coding methods, especially
combined device could
using an off-the-shelf DLP projector, they
when high-frequency fringes are used [21].
outperform each single
develop a high-speed spatial light modulator
Nevertheless, due to the periodical nature
(SLM) for pattern generation. The four patof the fringe signal, a major problem of this
component.
terns are arranged around the rotational centechnique is the phase ambiguity. That is,
ter of the SLM. The SLM is illuminated by a light source and
only depth within a range equivalent to one fringe period can
imaged through a conventional camera lens. Pattern switching is
be measured directly, and depth exceeding this range will be
achieved via synchronized timing of camera exposure intervals,
wrapped. While high-frequency fringes are preferred for highintegrating the image of the rotating SLM during the rotation of
accuracy measurement, they also lead to severe ambiguity. To
a pattern segment. With this dedicated system, the 3-D acquisirecover the absolute depth, a prevalent solution is temporal
tion speed is claimed to be 50 fps, while the 3-D reconstruction
phase unwrapping using a large number of additional patspeed is 11 fps at 640 × 480 pixels.
terns, e.g., Gray code or multifrequency fringes [22], which
The aforementioned two methods solve the phase ambigugreatly limits the application of phase shifting in time-critiity using a relatively small number of images. However, one
cal scenarios.
drawback is that the amplitude of fringe needs to be reduced
Recently, the advancement of projector technology has
to accommodate the embedded period codes, which sacrienabled fast and accurate 3-D measurement with phase shiftfices the signal-to-noise ratio (SNR) and thus the accuracy
ing. One pioneering phase-shifting-based system is described
of phase shifting. To retain the SNR of phase shifting, Wang
by Zhang and Huang in [23]. To achieve real-time depth senset al. propose a period-coding strategy without reducing the
ing, they modify a color digital light processing (DLP) projecamplitude of the fringe in [27]. Their key observation is that
tor and use the red, green, and blue (RGB) channels to project
the spatial intensity efficiency of phase-shifted fringes is
three fringe patterns. Moreover, to avoid the time-consuming
less than 100%, leaving a margin of the available intensity
arctangent function when calculating the phase, they propose
dynamic range for adding a period cue signal. Given the step
a new phase-shifting method using trapezoidal fringes instead
of phase-shifting N and the number of periods of fringe M,
of sinusoidal fringes. The 3-D acquisition and reconstruction
speed of their system is up to 40 fps at 532 × 500 pixels. In
the period codes can be designed by following several basic
this work, spatial phase unwrapping [24] is applied to recover a
properties. It should be noted that a smaller N and a larger
continuous phase map from a wrapped one, yet it cannot solve
M will decrease the margin of intensity dynamic range and
the ambiguity when multiple isolated objects or abrupt depth
increase the difficulty of code design. If using four patterns,
changes are present. Although restricted in the scope of appli16 periods can be supported. In an extreme case of three patcation, this work demonstrates the feasibility of high-resolution,
terns, at most four periods can be used for reliable decodreal-time depth sensing with phase shifting.
ing. The computational cost of this method is low, and up to

and the phase z (u, v), so the theoretical minimum number
of fringe patterns required is three. Using the three captured
images together, the phase can be calculated as

IEEE SIgnal ProcESSIng MagazInE

May 2017

Table of Contents for the Digital Edition of Signal Processing - May 2017