Instructors: Dr. George Bebis and Dr. Ali Erol.

1
Fingerprint ClassificationHandbook of
Fingerprint RecognitionChapter 5 (5-1 and
5-2) Fingerprint Classification by Directional
Image PartitioningRaffaele Cappelli, Alessandra
Lumini,Dario Maio and Davide Maltoni. IEEE
TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE
INTELLIGENCE, vol. 21, no. 5, pp. 402-421, 1999.

• Instructors Dr. George Bebis and Dr. Ali Erol.
• Presented by Milind Zirpe.
• CS 790Q (Fall 2005).

2
Overview

• Fingerprint Classification
• Introduction.
• Main classification techniques.

3
Introduction

• Need for fingerprint classification
• Database of fingerprints may be very large (e.g.
  several million fingerprints).
• Leads to long response time and hence unsuitable
  in real time applications.
• To reduce the number of comparisons.

4
Introduction

• What is fingerprint classification ?
• Fingerprint classification refers to the problem
  of classifying a fingerprint to a class in a
  consistent and reliable way.
• An approach
• A common strategy is to divide the fingerprint
  database into a number of bins, based on some
  predefined classes. A fingerprint to be
  identified is then required to be compared only
  to the fingerprints in a single bin of database
  based on its class.

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Introduction

• Galton-Henry classification (Galton, 1892 and
  Henry, 1900).

6
Introduction

• A difficult pattern recognition problem

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Introduction

• A difficult pattern recognition problem

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Classification Techniques
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Classification Techniques

• 1. Rule-based approaches
• Classification according to the number and
  position of the singularities (commonly used by
  human experts for manual classification).

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Classification Techniques

• a. Kawagoe and Tojo (1984)
• Derive a coarse classification using type and
  position of singular points.
• Finer classification is obtained by tracing the
  ridge line flow.

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Classification Techniques

• b. Karu and Jain (1996)
• An iterative regularization (smoothening
  orientation image with a 3x3 box filter) is done
  until a valid number of singular points are
  detected. This allows reducing noise and thus
  improves classification accuracy.

• Criteria for differentiating between tented
  arches and loops
• Connect the two singularities with a straight
  line and measure the avg. difference between the
  local orientations along the line and the slope
  of the line. A fingerprint is classified as a
  tented arch if

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Classification Techniques

• c. Hong and Jain (1999)
• A more robust technique is proposed the authors
  introduced a rule-based classification algorithm
  that uses the number of singularities along with
  the number of recurring ridges found in the
  image.
• The combination of these two distinct features
  leads to a performance better than that found in
  Karu and Jain (1996).

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Classification Techniques

• Problems with Rule-based approaches
• Although simple, some problems arise in presence
  of noisy or partial fingerprints, where
  singularity detection can be extremely difficult.
  (Addressed to some extent by Karu and Jain (1996)
  approach).
• May work well on rolled (nail to nail)
  fingerprint impressions scanned from cards, but
  are not suitable for dab (live-scan) fingerprint
  images, because delta points are often missing in
  these types of images.

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Classification Techniques

• 2. Syntactic approaches
• A syntactic method describes patterns by means of
  terminal symbols and production rules.
• Terminal symbols are associated to small groups
  of directional elements within the orientation
  image and represent a class.
• A grammar is defined for each class and a parsing
  process is responsible for classifying each new
  pattern (Fu and Booth, 1986a, b).

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Classification Techniques

• a. Rao and Balck (1980)
• A ridge line is analyzed and represented by a set
  of connected lines.
• These lines are labeled according to the
  direction changes, thus obtaining a set of
  strings that are processed through ad hoc
  grammars or string-matching techniques to derive
  the final classification.

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Classification Techniques

• Problems with Syntactic approaches
• Due to the great diversity of fingerprint
  patterns, syntactic approaches require very
  complex grammars whose inference requires
  complicated and unstable approaches.

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Classification Techniques

• 3. Structural approaches
• Based on the relational organization of
  low-level features into higher-level structures.
  This relational organization is represented by
  means of symbolic data structures (viz. trees and
  graphs), which allow a hierarchical organization
  of the information (Bunke, 1993).

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Classification Techniques

• a. Maio and Maltoni (1996)
• The directional image is partitioned into several
  homogenous regular-shaped regions, which are used
  to build a relational graph summarizing the
  fingerprint macro-features.
• Directional image is computed, over a discrete
  grid 32x32, using a robust technique proposed by
  Donahue and Rokhlin (1993).
• A dynamic clustering algorithm, Maio and Maltoni
  (1996), is adopted to segment the directional
  image.
• A relational graph is built by creating a node
  for each region and an arc for each pair of
  adjacent regions.
• An inexact graph matching technique, derived from
  Bunke and Allermann (1983), is used to compute a
  distance vector between the graph and each
  class prototype graph.

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Classification Techniques
Class prototype graphs
Fig.3. Main steps. The intermediate results
produced during the classification of a Left Loop
fingerprint are shown.
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Classification Techniques

• Advantages
• The relational graphs are invariant with respect
  to displacement and rotation of image.
• The technique neither requires any position
  alignment nor any normalization.
• In principle, can be directly used for
  classification of partial fingerprints (i.e.,
  matching a graph with a sub graph).
• Problems with Structural approaches
• It is not easy to robustly partition the
  orientation image into homogenous regions,
  especially in poor quality fingerprints.
  (Resolved to some extent by Cappelli et al.
  (1999) using template-based matching).

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Classification Techniques

• 4. Multiple classifier-based approaches
• Different classifiers offer complementary
  information about the patterns to be classified.
  This motivates combining of different approaches
  for the fingerprint classification task.

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Classification Techniques

• a. Candela et al. (1995)
• Based on Neural Network and Rule-based
  approaches.
• The system is called as PCASYS (Pattern-level
  Classification Automation SYStem).
• A probabilistic neural network is coupled with an
  auxiliary ridge tracing module, specifically
  designed to detect whorl fingerprints.

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Classification Techniques
Fig. A functional scheme of the PCASYS.
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Classification Techniques

• b. Jain, Prabhakar, and Hong (1999)
• Two stage classification strategy based on
  Statistical and Neural Network approaches.
• Stage 1 A k-nearest neighbor classifier is used
  to find the two most likely classes from a
  FingerCode feature vector (section 4.6).
• Stage 2 A specific neural network, trained to
  distinguish between the two classes, is utilized
  to obtain the final decision. A total of 10
  neural networks are trained to distinguish
  between each possible pair of classes.

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Classification Techniques
27
Fingerprint Classification by Directional Image
Partitioning Raffaele Cappelli, Alessandra
Lumini,Dario Maio and Davide Maltoni. IEEE
TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE
INTELLIGENCE, vol. 21, no. 5, pp. 402-421, 1999.
28
Overview

• Fingerprint Classification by Directional Image
  Partitioning
• Introduction.
• The new approach.
• Fingerprint retrieval.
• Experimental results.
• Conclusion.

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Introduction

• The relational graph approach has some problems
  in obtaining analogous segmentation from similar
  directional images.
• Influenced too much by local ridge-line
  orientation changes, start point of clustering
  routines.
• The new approach uses dynamic masks for
  directional image partitioning.
• It is translation and rotation invariant and does
  not require the singularities to be detected.

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Introduction
Fig. 4. The segmentation of two Left Loop
fingerprints.
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The New Approach

• Overview of the new approach.
• Directional image computation and enhancement.
• Dynamic mask definition.
• Directional image partitioning with Dynamic
  masks.
• Generation of a set of Prototype masks.
• Classification.

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Overview of the new approach

• The basic idea of the new approach is to perform
  a guided segmentation of the directional image
  with the aim of drastically reducing the degrees
  of freedom during the partitioning process,
  conferring stability to the solutions.
• A set of dynamic masks, directly derived from the
  most common fingerprint classes, are used to
  guide the partitioning.
• The inexact graph matching step is simplified and
  embedded in the segmentation step.

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Overview of the new approach
Fig. 6. Classification of a Left Loop fingerprint
by means of the dynamic masks approach.
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Directional image computation and enhancement

• Directional image computation
• The finger area is separated from the background
  and its quality is improved by a filtering in the
  frequency domain.
• The R.M. Stock and C.W. Swonger (1969) method is
  applied to calculate directional elements. Each
  element is represented by a vector v.
• Directional image enhancement
• Regularization
• Regularization of directional elements by local
  averaging on 3x3 windows W.

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Directional image computation and enhancement

• Directional image enhancement (contd.)
• Attenuation
• Attenuation of the border elements by applying a
  Gaussian-like function which progressively
  reduces the element magnitude moving from the
  center towards the borders.

where distc(v) returns the distance in blocks of
v origin from the directional image center and s
determines the scale of the Gaussian function.
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Directional image computation and enhancement

• Directional image enhancement (contd.)
• Strengthening
• We use a strengthening function (str) which
  increases the significance of each element
  according to the irregularity degree of its 3x3
  neighborhood, without requiring the singularities
  to be explicitly detected.

returns 0 if all the vectors are parallel to each
other and its value approaches 1 when discordance
increases.
The resulting directional image is made up of
vectors ve such that
where is a weighting factor.
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Directional image computation and enhancement
Fig. 7. Enhancement of a directional image the
map in the arrow-box shows the most irregular
regions as revealed by the str function. The
parameters are s 9.6 and l 112.
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Dynamic mask definition

• Dynamic masks have been introduced in order to
  decrease the degrees of freedom during the
  partitioning process.
• Each mask is characterized by a set of vertices
  defining the borders of the regions which
  determine the segmentation.
• Some vertices can be locally moved to best fit
  the fingerprint image singularities, which can
  occupy different positions within fingerprints of
  the same class.

Fig. 8. The singularity positions in three
different Left Loop fingerprints.
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Dynamic mask definition

• Formally, a dynamic mask is defined as a 6-tuple
• M ,
• where
• V is a set of vertices p.
• P is a set of polygonal regions
  whose vertices are in V.
• is a relation, encoding the dependency
  of the dependent vertices from the mobile ones.
  Each dependent vertex is anchored to exactly one
  mobile vertex.
• encodes a relation between some
  region pairs. For each pair Pi, Pj, whose
  orientation difference is significant,
  the triplet .
• is a function which associates to each
  mobile vertex a mobility window which limits the
  vertex movements during the mask adaptation.
• is a function which indicates, for
  each pair in the dependent vertex
  movement on the basis of the corresponding mobile
  vertex movement.

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Dynamic mask definition
Fig. 9. An example of dynamic mask definition.
Fixed vertices are denoted by empty circles, the
mobile ones by black circles, and the dependent
ones by gray circles. The dashed boxes denote the
mobility windows associated to the mobile
vertices. An arrow from a mobile vertex pi to a
dependent vertex pj indicates the dependence of
pj on pi.
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Directional image partitioning with Dynamic masks

• Let MT,Q be the steady mask obtained by the
  dynamic mask M as a result of the following
  transformations
• a global rotation-displacement T
  where and denote the global mask
  displacement and denotes the global mask
  rotation.
• a set of mobile vertex displacements Q (dx1,
  dy1), (dx2, dy2), ... (dxi, dyi) denotes the
  displacement of the vertex pi with respect to its
  initial position.
• The application of a steady mask MT,Q to a
  directional image D consists in superimposing
  MT,Q on D and deriving a segmentation R R1,
  R2, ..., Rn where each region Ri is made up of
  the directional elements internal to the polygon
  Pi.

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Directional image partitioning with Dynamic masks

• The cost Csm(MT,Q, D) of the application of MT,Q
  to D is given by the sum of two terms

where
First term Var(Ri) is proportional to the
variance of the directional elements in Ri and C0
is a parameter which introduces a penalty
proportional to the number of regions in M in
order to balance the possibility of obtaining
lower costs by segmenting the directional image
into several small regions. Second term
returns the difference between the avg.
orientations of regions Ri and Ri returns
the difference between qi, qj µ is the weight
of the orientation difference contribution, and
returns the number of triplets in .
43
Directional image partitioning with Dynamic masks

• The application cost of a dynamic mask M to a
  directional image D is computed by determining
  the minimum cost over all the possible steady
  masks MT,Q

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Directional image partitioning with Dynamic masks
Fig. 10. Adaptation of the mask defined in Fig. 9
to three different images of the same Left Loop
fingerprint.
45
Generation of a set of Prototype masks
Fig. 11. Prototype mask creation. The mask area
is larger than the directional image to allow the
border elements to be considered during the mask
displacement.
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Generation of a set of Prototype masks
Fig. 11 (contd.). Prototype mask creation. The
mask area is larger than the directional image to
allow the border elements to be considered during
the mask displacement.
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Generation of a set of Prototype masks
Fig. 12. The five prototype masks derived from
the classes Arch, Left Loop, Right Loop, Tented
Arch, and Whorl. The vertex positions, the
mobility windows, and the dependencies on mobile
vertices are graphically shown.
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Generation of a set of Prototype masks
Fig. 12 (contd.). Example of application of each
mask to a fingerprint belonging to the
corresponding class.
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Classification

• Let Mi, i 1..s be the prototype masks and D the
  directional image to be classified the feature
  vector wD resulting from the mask application is
• where low component values denote high
  similarity with the corresponding prototype mask.
• wD can be normalized as

• The normalization enables
• working within the fixed range 0, 1 this makes
  fingerprint indexing through spatial data
  structures easier.
• dealing with differently contrasted images The
  image contrast is related to the magnitude of the
  directional elements hence, it can determine an
  increase or a reduction of all the costs.

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Classification
Fig. 13. The figure shows the segmentation
obtained by applying the prototype masks defined
in Fig. 12 to some sample fingerprints (only one
example is provided for each class) the
corresponding normalized feature vectors are
shown on the right in the form of histograms.
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Classification
Fig. 13. (contd.)
52
Fingerprint retrieval

• Exclusive classification
• A neural network or a statistical classifier can
  be used to properly classify vectors .
• Continuous classification
• itself can be used as an access key for
  similarity searches. (Each fingerprint is
  characterized with a numerical vector).
• In order to evaluate the efficiency of continuous
  vs. exclusive classification for latent
  fingerprint retrieval, two different
  methodologies were proposed (A. Lumini, D. Maio,
  D. Maltoni, 1997), named A and B.
• Four different strategies AE, AC, BE, BC.

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Fingerprint retrieval

• Methodology A
• Methodology A assumes an error-free
  classification, so the search is restricted to
  the database fingerprints resembling analogous
  classification characteristics.
• AE
• The strategy AE can be implemented by searching
  the whole corresponding class of the latent
  fingerprint.
• The average portion of database considered
• The average retrieval error

Where, Pd(i) represents the database fraction
involved in the retrieval of a fingerprint of
class i and Pc(i) is the weighting factor
representing the probability to classify a latent
fingerprint as i.
Where, Pdc(ji) represents the conditional
probability that a database fingerprint,
corresponding to a latent fingerprint classified
as i, has been classified j in the database.
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Fingerprint retrieval

• Methodology A
• AC
• The strategy AC can be implemented by searching
  among those fingerprints which are less far from
  the feature vector w of the latent fingerprint
  than a fixed tolerance ?.
• Given a fixed ?,
• The average portion of database considered C?(AC)
  is determined by the average number of
  fingerprints inside the hyper-sphere with radius
  ?, centered in the latent fingerprint.
• The average retrieval error E?(AC) is determined
  by the average number of missed retrievals inside
  the search area.

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Fingerprint retrieval

• Methodology B
• Methodology B allows for misclassification to be
  taken into account to this aim, the search is
  carried out incrementally over the whole
  database, avoiding any possible retrieval error.
• This methodology requires the search to be
  terminated when a human expert finds a real
  correspondence between the latent fingerprint and
  a database fingerprint that has already been
  considered.
• BE
• The strategy BE can be implemented by starting
  the search from the latent fingerprint class, and
  incrementally extending it to the other classes.
• BC
• The strategy BC can be carried out by processing
  fingerprints according to their distance from the
  latent fingerprint feature vector w.

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Experimental results

• Databases used
• NIST Special Database 4 (Db4) contains 2,000
  fingerprint pairs, uniformly distributed in the
  five classes, in order to resemble a real
  distribution.
• NIST Special Database 14 (Db14) contains 27,000
  fingerprint pairs randomly taken, thus
  approximating the real fingerprint distribution
  only the last 2,700 fingerprint pairs have been
  employed in the simulation.
• The first 2,000 fingerprints of Db14 have been
  used as training set to derive the set of
  prototype masks and to optimize the parameters.
• MASK the dynamic mask method introduced in this
  paper.
• LUMINI the continuous classification approach
  described in A. Lumini, D. Maio, D. Maltoni
  (1997).
• PCASYS the exclusive approach by NIST (G.T.
  Candela, et al., 1995).

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Experimental results
Fig. 14. MASK results over Db4 (a) and Db14 (b)
the average portion of database considered C?(AC)
and the average retrieval error E?(AC) are
plotted as a function of ?.
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Experimental results
Fig. 15. Trade-off C?(AC)/E?(AC) varying ? for
the two continuous approaches MASK and LUMINI.
The point denotes C(AE)/E(AE) for the
exclusive classification approach PCASYS.
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Experimental results
TABLE 1 STRATEGY AC COMPARISON BETWEEN LUMINI
AND MASK.
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Experimental results
TABLE 2 COMPARISON AMONG PCASYS, LUMINI, AND
MASK FIXING THE AVERAGE PORTION OF DATABASE READ.
TABLE 3 COMPARISON BETWEEN THE AVERAGE
PERCENTAGES OF DATABASE SEARCHED (METHODOLOGY B).
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Experimental results
TABLE 5 CLASSIFICATION OF SOME FINGERPRINT
IMAGES SUBMITTED TO ARTIFICIAL PERTURBATIONS.
(Robustness).
62
Experimental results
TABLE 8 AVERAGE TIME SPENT FOR THE MAIN
PROCESSING STEPS.
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Conclusion

• Dynamic masks have been defined as a powerful
  instrument for a robust segmentation. (Noisy and
  partial fingerprint images).
• The experimental results prove the accuracy and
  robustness of the new method.
• The comparison with other techniques demonstrates
  its superiority for the continuous classification
  task, especially if fingerprints are classified
  only for improving the retrieval efficiency.
• Continuous classification does not enable to
  accomplish some tasks to be carried out, such as
  fingerprint labeling according to a given
  classification scheme.

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Thank you.