Biomedical Engineering Reference
In-Depth Information
Similarly, we can get all the other needed values in (5.59), namely,
q
xx
,
q
y
,
q
yy
,
Z
x
,
Z
y
,
Z
xx
,
Z
yy
,
I
xx
, and
I
yy
. Notice that, in (5.61), the partial derivatives
p
x
,
p
xx
, and
p
yy
are approximated by linear terms in their Taylor series.
In order to accelerate the computational process, the hierarchical imple-
mentation has been used in Zheng-Chellappa's algorithm. The lowest layer of
the image is 32
×
32
,
the higher one is 64
×
64, etc. For a detailed discussion
about the hierarchical method and its implementation, we refer the readers to
[70].
The whole algorithm can be described by the following procedure.
Step 1.
Estimate the original parameters of the reflectance map.
Step 2.
Normalize the input image. This step can be used to reduce the
input image size to that of the lowest resolution layer.
Step 3.
Update the current shape reconstruction using Eqs. (5.56)-(5.59),
and (5.61).
Step 4
. If the current image is in the highest resolution, the algorithm
stopped. Otherwise, we will increase the image size and expand the shape
reconstruction to the adjacent higher resolution layer; reduce the normal-
ized input image to the current resolution. Then go to step 3.
The following is the pseudocodes used to realize Zheng-Chellappa's method.
Algorithm 3:
Zheng-Chellappa's method
Input Z
min
(mindepthvalue),
Z
max
(maxdepthvalue),
(
x
,
y
,
z
) (direction of the light source),
I
(
x
,
y
)(input image)
D
←
x
2
+
y
2
+
z
2
,
sx
←
x
/
D
,
sy
←
y
/
D
,
sz
←
z
/
D
.
p
0
←
q
0
←
Z
0
←
0
δ
pq
←
0
.
001
,µ
←
1
.
0(
µ
will be used in Eqs. (5.57) and (5.58))
sin
γ
←
sin(arccos (
lz
))
,
sin
τ
←
sin (arctan (
sy
/
sx
))
,
cos
τ
←
cos(arctan (
sy
/
sx
))
.
for
i
=
1to
w
idth
(
I
)do
for
j
=
1to
height
(
I
)do
calculate
(
p
x
,
p
xx
,
p
y
,
p
yy
,
q
x
,
q
xx
,
q
y
,
q
yy
,
Z
x
,
Z
xx
,
Z
y
,
Z
yy
)
R
←
(
ρ
cos
γ
−
p
(
i
,
j
) cos
τ
sin
γ
−
q
(
i
,
j
) sin
τ
sin
γ
)
/
sqrt
(1
+
p
(
i
,
j
)
2
+
q
(
i
,
j
)
2
)
,
R
p
←
R
(
p
(
i
,
j
)
+
δ
pq
,
q
(
i
,
j
))
−
R
(
p
(
i
,
j
)
,
q
(
i
,
j
))
calculate
(
δ
p
,δ
q
,δ
Z
) using Eqs. (5.57) and (5.58)
p
←
p
0
+
δ
p
,
q
←
q
0
+
δ
q
Z
←
Z
0
+
δ
Z
