Single-sensor hand and footprint-based multimodal biometric ...

4 Preprocessing
4.4 Silhouette extraction
Having a binary m × n input image B with only one connected component as the hand
or foot object, the counter-clockwise contour polygon 〈S0, . . . , Sn〉 is traced as follows:
40
1. Estimation of starting point S0: depending on whether hands or feet are processed,
the starting point is found when intersecting the wrist or outside boundary
line of the foot with lines parallel to y-axis (and x-axis, respectively) through the
center of the (cropped) image. For hands, one can define:
S0 =
�
m
2
max{y ∈ {1, . . . , n} : B( m
m
, y) = 1 ∧ B( 2 2
For feet, the starting point is selected as:
S0 =
�
min{x ∈ {1, . . . , m} : B(x − 1, n
n
2
2
, y + 1) = 0}
n
) = 0 ∧ B(x, ) = 1} 2
�
�
; (4.13)
. (4.14)
2. Contour tracing: having selected S0, contour tracing involves a local decision of
the next contour pixel Sk+1 based on Sk and the current direction index dk within the
sequence 〈dm〉 referring to left-up, left, left-down, down, right-down, right, right-up,
up directions in counter-clockwise order:
〈dm〉 = 〈
�
−1
−1
�
,
�
−1
0
�
,
�
−1
1
�
,
�
0
1
�
,
�
1
1
�
,
�
1
0
�
,
�
1
−1
�
,
�
0
−1
�
〉.
(4.15)
Now, Sk+1 is selected with respect to the next counter-clockwise non-zero pixel within
an eight-neighbourhood starting at the pixel in direction of dk, i.e. the predecessor of
Sk. Finally, the resulting found direction is reversed, such that dk+1 points towards
the new predecessor Sk of Sk+1.
dk+1 = (dk + 4 + min{i ≥ 1 : B(Sk + d(dk+i) mod 8) = 1}) mod 8; (4.16)
Sk+1 = Sk − ddk+1 . (4.17)
The iteration stops, when Sn = S0 is reached. Initial directions are d0 = 3 = down
for hands and d0 = 1 = left for feet.