Graphics Reference
In-Depth Information
Also, a 2
d
projection operator can be define
P
[
x
]
=
(
x
1
/
x
3
,
x
2
/
x
3) so that it follows that
∇
z
=
P
[
n
]. The pixel intensity
c
i
(
x
,
y
) in the
i
th image, for
i
=
1
,...
3, can be defined as
n
=
l
i
c
i
(
x
,
y
)
E
(
λ
)
R
(
x
,
y
,λ
)
S
(
λ
) d
λ,
(1.17)
where
l
i
is the direction of a light source with spectral distribution
E
i
(
λ
), illuminating the
y
))
T
;
R
(
x
surface point (
x
,
y
,
z
(
x
,
,
y
,λ
) reflectance function, and
S
(
λ
) the response of the
sensor camera. The value of this integral is known as Albedo
ρ
, so the pixel intensity can be
defined as
l
i
c
i
=
ρ
n
.
(1.18)
ρ
Using linear constraints of this equation to solve for
n
in a least squares sense. The
∇
=
ρ
gradient of the height function
n
] is obtained and integrated to produce the function
z
. According to three source photometric stereo, when the point is not in shadow with respect
to all three lights, three positive intensities
c
i
can be estimated each of which gives a constraint
on
z
P
[
ρ
n
. Thus the following system can be defined as
L
−
1
c
ρ
n
=
.
(1.19)
If the point is in shadow, for instance in the 1
st
image, then the estimated of
c
1
cannot be
used as constraint. In this case, each equation describes a 3D plane, the intersection of the two
remaining constraints is a 3D line given by
c
2
l
3
)
T
n
(
c
3
l
2
−
=
.
0
(1.20)
In a general case, if the point is in shadow in the
i
th image, this equation can be arranged as
[
c
]
i
×
Ln
=
0
(1.21)
This equation is derived by Wolff and Angelopoulou (1994) and used for stereo matching
in a two view photometric. Fan and Wolff (1997) also used this formulation to perform
uncalibrated photometric stereo. Hernandez et al. (2011) used that for the first time in a least
squares framework to perform three source photometric stereo in the presence of shadows.
Figures 1.9 and 1.10 illustrate some reconstruction results with their proposed shading and
shape regularization schemes.
1.4.3 Structured Light
Structured light-based techniques are reputed to be precise and rapid. However, 3D imaging
of moving objects as faces is a challenging task and usually need more sophisticated tools
in combination with the existing patterns projection principle. The first strategy consists in
patterns projecting and capturing with a synchronized projecting device and camera at a very
high rate. The second is to motion modeling and compensation. Finally, the third fuses several
3D models from one or more projector-camera couples to complete them and corrects sensor
