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

4 Preprocessing
4.2.1 Fast Otsu Thresholding
Let pi refer to the probability of grey level i within the image B and let µ be the mean
intensity of the image. Otsu’s Method [29] is a global thresholding algorithm, i.e. a global
threshold t ∈ {0, . . . l + 1} is selected, such that the new binary image B ′ is given by:
B ′ (x, y) =
�
1 if B(x, y) ≥ t,
0 otherwise.
. (4.1)
Since light reflected by the sole of the foot or palm is converted into pixels with higher
intensities, this leads to a good separation of background (represented by the class C1
with grey levels {0, . . . , t − 1}) and sole/palm (represented by the class C2 with grey levels
{t, . . . , l}). For a given threshold t and class k ∈ {1, 2}, let ωk refer to the class probability
and µk refer to the mean for Ck [20]:
ωk := �
pi; (4.2)
i∈Ck
µk := 1 �
i pi. (4.3)
ωk i∈Ck
Otsu’s method chooses t ∗ , such that the between-class variance σ 2 B is maximised [20]:
σ 2 2�
B(t) := ωk(µk − µ)
k=1
2 2�
= ωkµk
k=1
2 − µ 2 ; (4.4)
t ∗ = arg max{σ
1≤t≤l
2 B(t)}. (4.5)
Since obtaining ωk and µk for each threshold t involve many recurring operations, an
improved fast threshold search can be implemented using lookup-tables of recursively
calculated zeroth- and first-order moments of pixel intensities u to v, as illustrated in
[20].
4.2.2 Canny-edge-detection based binarisation
In order to preserve foot edges for accurate shape feature extraction within the footprint
system, first Canny edge detection [2] with binary thresholding on the original image B
is employed. This step keeps the most significant edges only which reliably represent foot
contours. Then, within the obtained edge image B1, the interior of the foot is filled using
binary thresholding on B, i.e.
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B2(x, y) := max(B ′ (x, y), B1(x, y)); (4.6)