Q
local
FDA
=
⎪
⎨
⎪
⎩
A
F
max
+ C (A
F
max
−1
+ A
F
max
+1
)
, if F
max
= A
1
orF
max
= A
|A|
P
|A|/2
F =1
A
F
1, otherwise
15 APRIL 28, 2016 DRAFT - FOR COMMENT - DO NOT EXCERPT
5 10 15 20 25 30
50
100
150
200
250
Block x−index
Mean intensity
0 1/16 1/8 3/16 1/4 5/16 3/8 7/16
0
200
400
600
800
1000
1200
1400
1600
Cycles/pixel
Magnitude
100 200 300 400 500 600
100
200
300
400
(a) (b) (c) (d)
Figure 3: Processing steps of fda quality algorithm. (a) central area of input block; (b) ridge-valley profile; (c) dft of ridge-valley profile;
(d) map of Q
local
FDA
.
Computing the local Frequency Domain Analysis quality score The local fda quality score, Q
local
FDA
is computed as:
⎧
(12)
wher
e C
=
0
.
3
according to the definition appearing in ISO/IEC TR 29794-4:2010. The effect of the constant is to retain an
attenuated amplitude of the frequency bands immediately surrounding the band with the maximum amplitude A
F
max
.
The value of Q
local
FDA
is set to 1 when maximum frequency amplitude bin is F
max
= A
1
or F
max
= A
|A|
as both positions will
result in accessing out of bounds elements in A due to the use of attenuated neighboring bins.
4.3 Local Clarity Score
lcs [2, 5] computes the block-wise clarity of ridge and valleys by applying linear regression to determine a gray-level
threshold, classifying pixels as ridge or valley. A ratio of misclassified pixels is determined by comparing with the nor-
malized ridge and valley width of that block.
Particular regions inherent in a fingerprint will negatively affect Q
LCS
. For example, ridge endings and bifurcations or
areas with high curvature such as those commonly found in the vicinity of core and delta points.
A visual overview of the algorithm outputs are depicted in fig. 4.
Algorithm 4: Local Clarity Score algorithm
Input: Fingerprint image I
Output: lcs quality score Q
LCS
1 for each block V in I do
2 rotate V such that dominant ridge flow is perpendicular to x-axis
3
crop V such that no invalid regions are included
4 with V obtain the ridge-valley signature T (eq. (11))
5
Determine DT using linear regression on T
6 For each element T(x) set threshold P(x) of x being ridge or valley based on
(
DT
1, if T(x) < P(x)
7
Predict columns in V as ridge (1) or valley (0) with S(x) =
0, otherwise
8
Determine ridge-valley transition vector C from S
9
Compute the vector W containing ridge and valley widths from C
10
Determine normalized ridge width and valley width
¯
W
and
¯
r
W
v
(eqs. (15) and (16))
11
Determine proportion of misclassified pixel β and α in the ridge and valley regions (eqs. (13) and (14))
12
Compute the local quality score Q
local
LCS
(eq. (19))
13 end
15
lcs[2,5]通过线性回归确定灰度阈值，将像素划分为脊线或谷线，计算脊线和谷线的块级清晰度。通
过与该块的归一化脊宽和谷宽的比较，确定了误分类像素的比例。
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