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and the surface shape at each pixel. According to Horn's formulation of SFS problem, the
brightness equation arises as:
,
=
,
,
I
(
x
y
)
R
(
n
(
x
y
))
(1.4)
where, (
x
y
) are the coordinates of a pixel;
R
, the reflectance map and
I
the brightness
image. Usually, SFS approaches, particularly those dedicated to face shape recovery, adopt
the Lambartian property of the surface. In which case, the reflectance map is the cosine of the
angle between light vector
,
L
(
x
,
y
) and the normal vector
n
(
x
,
y
) to the surface:
L
|
L
n
|
cos(
L
R
=
,
n
)
=
·
|
,
(1.5)
n
|
L
and
where
R
,
y
). Since the first SFS technique developed by Horn, many
different approaches have emerged; active SFS which requires calibration to simplify the
solution finding has achieved impressive results.
n
depends on (
x
,
1.2.3 Depth from Time of Flight (ToF)
Time of flight provides a direct way to acquire 3-D surface information of objects or scenes
outputting 2.5 D, or depth, images with a real-time capability. The main idea is to estimate the
time taken for the light projected by an illumination source to return from the scene or the object
surface. This approach usually requires nano-second timing to resolve surface measurements
to millimeter accuracy. The object or scene is actively illuminated with a nonvisible light
source whose spectrum is usually nonvisible infrared, e.g. 780 nm. The intensity of the active
signal is modulated by a cosine-shaped signal of frequency
f
. The light signal is assumed
to have a constant speed,
c
, and is reflected by the scene or object surface. The distance
d
is estimated from the phase shift
θ
in radian between the emitted and the reflected signal,
respectively:
c
2
f
2
d
=
(1.6)
π
While conventional imaging sensors consists of multiple photo diodes, arranged within a
matrix to provide an image of, e.g., color or gray values, a ToF sensor, for instance a pho-
ton mixing device (PMD) sensor, simultaneously acquires a distance value for each pixel in
addition to the common intensity (gray) value. Compared with conventional imaging sensors,
a PMD sensor is a standard CMOS sensor that benefits from these functional improve-
ments. The chip includes all intelligence, which means that the distance is computed per
pixel. In addition, some ToF cameras are equipped with a special pixel-integrated circuit,
which guarantees the independence to sunlight influence by the suppression of background
illumination (SBI).
