After obtaining the descriptor for the two images the next
step is to find the matching points using the descriptors. During the process
of feature vector building or pore descriptor estimation we have considered the
neighboring pixels of the pores so as to get a region sufficient enough for
comparing with the other pore descriptor. So the size of the block centered on
the pore plays an important role. Also the block-size should be of odd values
so that equal neighboring pixels are taken into account. Also the neighboring
ridge valley pattern should be considered. Basically in the field of object
detection block-size of 9*9, 11*11 and 15*15 is used. Considering the high
resolution fingerprint image we have used a block-size of 41*41.
While comparing the pore descriptor of the first image with
the pore descriptor of second image, the one with least difference is considered
as a matched pore and the location of the two pores are recorded. This done by locating
the coordinates of the matching pore. There are different approaches used for
finding the similarity between the two feature vectors. The metrics we use for
estimating the matching points are Sum of Absolute Difference (SAD) and Sum of
Squared Differences (SSD).
1 Sum of
Squared Differences
For matching, the each feature vector of first image is
compared with all the other feature vector of second image. Given the pore
descriptor for pores on two fingerprint images, we can now compare them
pair-wise and establish a correspondence between them. Suppose {P1i | i = 1, 2….M}
and {P2j | j = 1, 2….N} are the sets of pores on two fingerprint images, P1i
and P2j are the descriptors on pores. The length of the two descriptors may not
be same. The correspondences between two
pores Pi and Pj is established using the following expression:
Here M is the length of the descriptor P1. The one with
least difference forms the matching point. The coordinates of the two matching
forms the correspondence between the pores.
2. Sum of
Absolute Differences
Another method used for finding the matching points using
two feature vectors is Sum of Absolute Differences. Here instead of taking the
square of the differences, the absolute difference between them is computed. Considering
{P1i | i = 1, 2….M} and {P2j | j = 1, 2….N} sets of pores on two fingerprint,
we find for each pore on the first fingerprint, a pore which is the most
similar one to it among all the pores on the second fingerprint using SAD. If P1ik
has its most similar pore as P2jk and P1ik is also the most similar pore of
P2jk, then a correspondence is established between them which are given as
Ck =
(P1ik,P2jk).
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Fig.1: Results of direct pore
matching; (a) and (b) two fingerprints to be matched; (c) and (d) pore
extracted using DoG method; (e) and (f) matched pores using SSD.
|
Finally we will get k pairs of corresponding pores between
the fingerprint images. An example result of direct pore matching using SSD is
shown in Fig.1. Fig.2 shows the example of direct pore matching between the two
images whose extracted pores are shown by red circles. The matching pores
between two images are shown by the yellow lines. The two ends of lines are on
the matching pores.
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Fig.2:
Example of direct pore matching; (a) and (b) two pore extracted image block using DoG filter; (c) matching
between two images in (a) and (b).
|
So here we have presented a direct pore matching approach
using the two metrics namely Sum of Squared Differences (SSD) and Sum of
Absolute Differences. (SAD). The above
example testified that an efficient pore matching was done using the proposed
pore matching.
