Graphics Reference
In-Depth Information
code word. Therefore, before triangulating, it is necessary to calculate either the center of
every stripe or the edge between two consecutive stripes. The latter has been shown to be
the best choice.
N
-ary codes.
The main drawback of binary codes is the large number of patterns to be
projected. However, the fact that only two intensities are projected eases the segmentation
of the imaged patterns. The number of patterns can be reduced by increasing the number of
intensity levels used to encode the stripes. A first mean is to use multilevel Gray code based
on color. This extension of Gray code is based on an alphabet of
n
symbols; each symbol is
associated with a certain RGB color. This extended alphabet makes it possible to reduce the
number of patterns. For instance, with binary Gray code,
m
patterns are necessary to encode
2
m
stripes. With an
n
-ary code,
n
m
stripes can be coded using the same number of patterns.
•
Phase shifting.
Phase shifting is a well-know principle in the pattern projection approach
for 3D surface acquisition. Here, a set of sinusoidal patterns is used. The intensities of a
pixel
p
(
x
•
,
y
) in each pattern is given by:
I
1
(
x
,
y
)
=
I
0
(
x
,
y
)
+
I
mod
(
x
,
y
)
cos
(
φ
(
x
,
y
)
−
θ
)
,
I
2
(
x
,
y
)
=
I
0
(
x
,
y
)
+
I
mod
(
x
,
y
)
cos
(
φ
(
x
,
y
))
,
(1.9)
I
3
(
x
,
y
)
=
I
0
(
x
,
y
)
+
I
mod
(
x
,
y
)
cos
(
φ
(
x
,
y
)
+
θ
)
.
I
0
(
x
,
y
) is the background or the texture information,
I
mod
(
x
,
y
) is the signal modulation
amplitude, and
I
1
(
x
,
y
),
I
2
(
x
,
y
) and
I
3
(
x
,
y
) are the intensities of the three patterns.
φ
(
x
,
y
)
2
3
is the phase value and
θ
=
is a constant. Three images of the object are used to estimate
a wrapped phase value
ˆ
φ
(
x
,
y
) by:
arctan
√
3
I
1
(
x
,
y
)
−
I
3
(
x
,
y
)
ˆ
φ
(
x
,
y
)
=
(1.10)
2
I
2
(
x
,
y
)
−
I
1
(
x
,
y
)
−
I
3
(
x
,
y
)
The wrapped phase is periodic and needs to be unwrapped to obtain an absolute phase
value
φ
(
x
, where
k
is an integer representing the period or the
number of the fringe. Finally the 3D information is recovered based on the projector-camera
system configuration. Other pattern configurations of these patterns have been proposed.
For instance, Zhang and Yau proposed a real-time 3D shape measurement based on a
modified three-step phase-shifting technique (Zhang et al., 2007) (Figure 1.6). They called
the modified patterns 2+1 phase shifting approach. According to this approach, the patterns
and phase estimation are given by
,
y
)
=
φ
(
x
,
y
)
+
2
k
π
y
)
cos
−
2
I
1
(
x
,
y
)
=
I
0
(
x
,
y
)
+
I
mod
(
x
,
φ
(
x
,
y
)
,
I
2
(
x
,
y
)
=
I
0
(
x
,
y
)
+
I
mod
(
x
,
y
)
cos
(
φ
(
x
,
y
))
,
(1.11)
I
3
(
x
,
y
)
=
I
0
(
x
,
y
)
,
arctan
I
1
(
x
,
y
)
−
I
3
(
x
,
y
)
ˆ
φ
(
x
,
y
)
=
.
(1.12)
,
−
,
I
2
(
x
y
)
I
3
(
x
y
)
