Graphics Reference
In-Depth Information
I
j
,
j
=
1
, ...
3, are the recorded intensities,
I
0
is the background and
I
mod
is the signal
amplitude.
φ
(
x
,
y
) is the recorded phase value, and
θ
is the constant phase shift. The phase
x
p
ω
value corresponds to projector coordinates computed as
φ
=
2
π
N
, where
x
p
is the projector
x
-coordinate,
the horizontal resolution of the projection pattern, and
N
the number of periods
of the sinusoidal pattern. The wrapped phase is estimated as
ω
arctan
tan
2
I
1
(
x
,
y
)
−
I
3
(
x
,
y
)
ˆ
φ
(
x
,
y
)
=
,
(1.23)
2
I
2
(
x
,
y
)
−
I
1
(
x
,
y
)
−
I
3
(
x
,
y
)
I
1
(
x
,
y
)
+
I
2
(
x
,
y
)
+
I
3
(
x
,
y
)
I
0
(
x
,
y
)
=
,
and
(1.24)
3
(
I
3
(
x
2
I
2
(
x
y
)
2
y
))
2
,
−
,
−
,
,
y
)
−
I
0
(
x
,
y
)
I
1
(
x
y
)
I
3
(
x
I
mod
(
x
,
y
)
=
+
.
(1.25)
3
9
Using the estimated phase, the depth is calculated on the basis of triangulation between
camera and projection device.
•
Motion estimation: Figure 1.12 shows a planar surface and its effects on phase estimation.
P
0
is the location observed by the camera at time
t
0
and
P
1
at
t
1
. Assuming that
=
t
t
0
−
t
−
1
=
t
1
−
t
0
, is a known constant value. If
P
0
and
P
−
1
are known, the distance vector
Δ
s
Δ
c
P
-1
t
-1
P
0
P
1
n
t
0
t
1
Figure 1.12
A planar surface moving towards the camera and its effect on phase estimation (Weise
et al. (2007)). Here three images are captured at three time steps. The velocity of the surface along its
normal is estimated on the basis of the normal motion displacement
δ
s
as the projection of
δ
c
, the distance
vector, onto the surface normal
n
. Copyright
C
2007, IEEE
