A two-stage fingerprint classification system
Raffaele Cappelli
Dario Maio
Davide Maltoni
Loris Nanni
DEIS, CSITE-CNR
University of Bologna
viale Risorgimento 2, Bologna - Italy
rcappelli@deis.unibo.it
dmaio@deis.unibo.it
dmaltoni@deis.unibo.it
lnanni@deis.unibo.it
police agencies are variants of the so-called Henry’s classification
scheme. Figure 1 shows the five classes (Arch, Tented arch, Left
loop, Right loop and Whorl) that are commonly used by today’s
fingerprint classification techniques. Fingerprints are not
uniformly distributed among these five classes: the proportions
are 3.7%, 2.9%, 33.8%, 31.7% and 27.9% for Arch, Tented arch,
Left loop, Right loop and Whorl, respectively.
ABSTRACT
In this paper we describe a fingerprint classification system based
on a two-stage sequential architecture: an MKL-based classifier is
first used to select the two-most-likely classes and then a second
classifier (specifically trained to discriminate between the two
classes) is then adopted for the final decision. The
experimentation performed on NIST Special Database 4, which is
one of the most important benchmarks in this area, shows that the
new approach yields an error rate lower than previously published
in the literature. In particular, the error rate is 4.8% and 3.7% for
the five-class problem and four-class problem, respectively.
Categories and Subject Descriptors
I.5.4 [Pattern recognition]: Applications – Computer vision
I.5.2 [Pattern recognition]: Design Methodology – Classifier
design and evaluation
Arch
Tented Arch
Left Loop
Right Loop
Whorl
Whorl
General Terms
Algorithms, Experimentation, Security.
Keywords
Fingerprint classification, classifier combination, directional
image, feature selection, subspace classifiers.
1. INTRODUCTION
The identification of a person with an AFIS (Automated
Fingerprint Identification System) requires the comparison of
his/her fingerprint with all the fingerprints in a database, which in
many applications may be very large (several millions
fingerprints). Adopting a classification approach is a common
strategy to reduce the number of comparisons during fingerprint
retrieval and, consequently, to reduce the response time of the
identification process. The first scientific studies on fingerprint
classification were made by Francis Galton [14], and Edward
Henry [16]. All the classification schemes currently used by
Figure 1. The five fingerprint classes (two examples are
reported for the whorl class, which is the most complex one).
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Automated fingerprint classification into these five classes is a
difficult pattern recognition problem, due to the small interclass
variability and the large intraclass variability [20] and to the noise
that often affects fingerprint images. For its relevance and its
intrinsic complexity, this classification problem has attracted the
interest of many researches during the last thirty years and several
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approaches have been proposed, based on a variety of
classification techniques: from syntactic [27] [28] [31] and
structural [6] [24] [25] methods to rule-based approaches [1] [12]
[13] [17] [22] [23], from neural networks [2] [4] [15] [18] [21]
[29] [30] [37] to classifier-fusion strategies [5] [7] [8] [19] [20]
[26] [32] [36] [38].
In this work we propose a fingerprint classification approach
based on a sequential (two-stages) architecture, where an MKL
classifier [7] [10] is used to find the two-most-likely classes and
an SPD (Subspace-based Pattern Discrimination) classifier
specifically trained to distinguish between the two classes is
selected for the final decision. SPD is a classification approach we
are developing within a more general framework; SPD
performance is very promising, especially for complex two-class
problems. The system described has been tested on NIST Special
Database 4 [34], which is one of the most used benchmarks for
fingerprint classification. The rest of the paper is organized as
follows: section 2 describes the feature extraction, section 3 the
general classification architecture and section 4 the SPD
classification approach. Finally, section 5 reports the results of the
experiments and section 6 draws some conclusions.
core point
Figure 2. The main feature extraction steps of the proposed
system.
The proposed system uses the fingerprint directional image as
initial feature. A directional image is a discrete matrix whose
elements represent the local average directions of the fingerprint
ridge lines (figure 2); it summarizes the information contained in a
fingerprint pattern and can be reliably computed from noisy
fingerprints. Furthermore, the local directions within a damaged
area can be restored by means of a regularization process. For
these reasons, most of the existing classification methods make
use of fingerprint directional images.
3. CLASSIFIER ARCHITECTURE
In our previous studies ([7] [8] [9]) we found that a classifier
based on the multi-space generalization of the KL transform
(MKL [10]) was able to achieve very good results on this
problem. The basic idea of the MKL-based classifier is to
represent each class with one or more low-dimensional subspaces
and classify patterns according to the distance-from-space metric
(the reader should refer to [7] and [10] for a throughout
treatment).
As in [7], the following steps are performed to obtain the feature
vector of a given fingerprint (figure 2):
•
•
Directional image
Enhanced dir. image
2. FEATURE EXTRACTION
•
Enhanced fingerprint
Input fingerprint
image enhancement: the grey-level image enhanced through a
filtering in the frequency domain: this step is performed as in
[5];
First stage
directional image computation and alignment: the Stock and
Swonger method [33] is used to calculate the orientations
over a 28x30 grid; then the directional image is aligned with
respect to the core point [5], which is determined by using the
Poincarè method [23] and by iteratively smoothing the
directional image until a valid number of cores is found (as in
[22]); in case the core point is not found with the above
method, the R92 algorithm [35] is used for detecting a valid
reference point for the fingerprint;
Second stage
10 SPD
classifiers
two-mostlikely
MKL-based classes
classifier
directional image enhancement: the technique initially
proposed in [6] is adopted to increase the importance of the
discriminant elements.
Classifier
selection
Feature vector
Selected SPD
classifier
Hypotized class
Figure 3. The general architecture of the proposed
classification system: the feature vector is first submitted to
the MKL-based classifier, which returns the two most-likely
classes (first stage). Then an SPD classifier trained to
discriminate between these two classes makes the final decision
(second stage).
The enhanced directional image is treated as a single vector of
dimension 1680, by simply concatenating its rows (as in [5], each
element of the 28x30 directional matrix is encoded as a pair
[q‚cos 2θ, q‚sin 2θ], where θ is the orientation and q an estimate
of the direction reliability).
A further analysis on the results obtained with the MKL-based
classifier on NIST DB4 [34] showed that if the second-choice of
the classifier is taken into account, the error drops to 0.9%; in
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other words, the probability that the correct class is one of the
two-most-likely classes is 99.1%. This suggested that a two-stage
architecture analogous to that proposed in [20] could allow very
interesting results to be achieved: an MKL-based classifier is here
employed in the first stage, to determine the two-most-likely
classes. This strategy allows to decompose a difficult five-class
problem into ten two-class problems: for instance, if for a give
fingerprint the two-most-likely classes according to the MKLbased classifier are Arch and Left loop, then an SPD classifier
specifically trained to distinguish Arch and Left loop fingerprints
is adopted in the second stage.
both classes wA and wB and the similarity score is computed using
the corresponding QDFs. The final classification rule consists in
selecting the class with the highest average similarity score
(calculated over all its clusters).
The rationale behind SPD classification is that it is often very
difficult to find good discriminant features for all the patterns in a
class (especially when the intra-class variance is very high, as in
fingerprint classification). Dividing a class into clusters makes it
possible to find specific features that, although not well suited to
discriminate all the patterns, are optimal to distinguish a subset of
patterns in a class from the other class. An example in the
fingerprint domain may be the following: a complex class such as
Whorl contains fingerprints which are very different one from the
other. Consider for instance the fingerprints in figure 3: the
features that are optimal for discriminating Whorl fingerprint A
from Left loop fingerprint B are not necessarily the best suited to
discriminate fingerprint C from B.
Figure 3 summarizes the general architecture of the proposed
system.
4. SPD CLASSIFIER
This section describes the SPD training and classification
procedures.
Training
Each SPD classifier is trained, through the following steps, using
a training set X={x1,x2,…,xn} of feature vectors xi∈ℜd and
belonging to two classes wA and wB.
1.
Feature orthogonalization and reduction: vectors in X are
transformed in order to minimize correlation and decrease
their dimensionality without loosing too much information.
Any dimensionality reduction technique that produces
orthogonal features may be used for this task; in this work we
simply calculated a KL transform on the whole training set
and reduced the vectors from d=1680 to r=80 features.
A) Whorl
B) Left Loop
C) Whorl
Figure 3. Two Whorl fingerprints (A and C) and a Left loop
fingerprint (B).
Clustering: classes wA and wB are independently partitioned
into clusters to group together similar patterns. Let A and B
be the subsets of X containing vectors of class wA and wB,
respectively (obviously A∪B=X), and let ℘A={A1,A2,…,ANa}
and ℘B ={B1,B2,…,NNb} be the partitioning of A and B, in
Na and Nb clusters, respectively. We found that a fuzzy CMeans [3] algorithm is a good choice for this step, but in
principle any reasonable clustering approach may be
adopted.
5. EXPERIMENTAL RESULTS
3.
Feature selection: a different subspace is defined for each
cluster Ai or Bi, by determining an optimal subset of features.
To this purpose, in this work we used a simple featureranking technique which selects the features that maximize
the distance between the centroid of the cluster Ai (or Bi) and
the centroid of the whole set of patterns belonging to the
other class B (or A).
The classification error of the proposed system is 4.8%; the
confusion matrix is reported in table 1. Please note that the rows
of table 1 do not sum up to 400; in fact, some ambiguous
fingerprints are assigned to two classes in the database; in such
cases, when any one of the two labels matches the output of our
classifier, the result is assumed to be correct.
4.
Learning of cluster-specific metrics: the similarity between
an unknown pattern x and a given cluster Ai (or Bi), is
computed thought a quadratic discriminant function (QDF
[11]), whose parameters are tuned to maximize
discrimination between the cluster itself and all the patterns
belonging to the other class B (or A); all the patterns
involved in the learning are first projected into the subspace
corresponding to the cluster Ai (or Bi).
2.
The experimentation was performed on NIST DB4 [34], which
consists of 4000 fingerprint images from 2000 fingers, equally
distributed in the five classes. Two different fingerprint instances
(named ”F” and “S”) are present for each finger: the images are
numbered from F0001 to F2000 and from S0001 to S2000. We
used the 2000 images from the first 1000 fingers (F0001-F1000
and S0001-S1000) as a training set and we tested the system on
the remaining 2000 images (F1001-F2000 and S1001-S2000).
Table 1. Confusion matrix on NIST DB4.
True
Hypotized class
class
A
L
R
W
T
7
10
1
15
387
A
Classification of an unknown pattern
Given an unknown pattern x, its dimensionality is first reduced
from d to r, then it is projected into the subspace of each cluster of
97
L
3
373
2
4
4
R
4
1
381
9
3
W
0
4
7
391
0
T
6
3
7
5
373
It is worth noting that many errors are due to the classification of
some Tented arch fingerprints as Arch: in fact, these two classes
have a substantial overlap and it is very difficult to separate them,
even for human experts. For this reason, in some previous works,
Arch and Tented arch are merged into a single class (four-class
problem): in this case the error rate of the system decreases to
3.7%.
four-class problem. The SPD classifier we adopted for the second
stage proved to be a promising classification approach, although
more experiments in other real-world pattern recognition
problems are needed to better assess its effectiveness.
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Since NIST DB4 contains an equal number of fingerprints for
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Table 2 reports the results of published classification approach
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The error rate of both the five-class and four-class problems are
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Table 2. Error rates on NIST DB4 for the five-class problem
and the four class-problem, in the non-weighted / weighted
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n.a. / n.a.
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analogous architecture: a k-NN classifier for the first stage and ten
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problems. Consider that, in [20], the output of the first stage (twomost-likely classes) was 98% correct and the neural networks in
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