Abstract:
This paper presents an optimized method to reduce the points number
to be used in order to identify a person using fuzzy fingerprints. Two fingerprints
are similar if n out of N points from the skin are identical. We discuss the criteria
used for choosing these points. We also describe the properties of fuzzy logic and
the classical methods applied on fingerprints. Our method compares two matching
sets and selects the optimal set from these, using a fuzzy reasoning system. The
advantage of our method with respect to the classical existing methods consists in a
smaller number of calculations.
Keywords: fuzzy models, fingerprint authentication, cryptographic signature model.
1 Introduction
Fingerprint identification is the most mature biometric method being implemented at an early level
since 1960. The recognition of a fingerprint can be done with two methods: ”one-to-one” (verification)
and ”one-to-many” (1 : N identification). The first method is applied when we have two fingerprints
and we want to verify if they belong to the same person. The second one is used when we have one
fingerprint and we search it in a data base. The verification is much easier and faster because we have the
two fingerprints and we just need to compare them. On the other hand, the identification implies more
time for extracting the fingerprint because there are needed much more details.
The fingerprints are not compared with images, they use a method based on characteristic points
named ”minutiae”. These points are characterized by ridge ending (the abrupt end of a ridge), ridge
bifurcation (a single ridge that divides in two ridges), delta (a Y-shaped ridge meeting), core (a U-turn in
ridge pattern), etc. All these features are grouped in three types of lines: line ending, line bifurcation and
short line. After the minutiae points are localized, a map with all their locations on the finger is created.
Every minutiae point has associated two coordinates (x,y), an angle for orientation and a measure for the
fingerprint quality. The matching of two fingerprints depends on the position and on the rotation. For this
reason, every fingerprint is represented, not only, as a group of points with two coordinates, but also, as
a group of points with coordinates relative to other points. This allows obtaining an unique positioning
of a point regarding to other three points. The three selected points must not be collinear. When two
fingerprints are compared, first are compared the relative coordinates. If this stage ends successfully,
these coordinates are transformed in 2D coordinates and verified.
After verifying the fingerprints, the result will tell us if they are from the same person with a high
probability. Still, the cases when the belonging probability of a fingerprint is 0 (false) or 1(true) are
rarely. In most of the cases, the probability will be a number p ∈ [0,1]. This fact leads to a fuzzy logic.
The values in fuzzy logic can range between 0 and 1 (1 is for absolute truth, 0 for absolute falsity). A
fuzzy value for an element x will express the degree of membership of x in a set X. It is essential to
realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while
probability is a mathematical model of randomness.

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