Fingerprint recognition and synthesis

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Fingerprint recognition and synthesis

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Title: Fingerprint recognition and synthesis

1
Fingerprint recognition and synthesis advanced
techniques

Biometric Course CPSC 601

2
Overview

Advanced Matching
Correlation-based techniques
Minutiae-based techniques
Point-pattern matching
Minutiae with pre-alignment
Classification
Syntactic
Structural
Statistical
Retrieval
Synthesis

3
Correlation-based techniques

Let T and I be the two fingerprint images
corresponding to the template and the input
fingerprint respectively. A measure of the
diversity is the sum of squared differences (SSD)
between the intensities of the corresponding
pixels
SSD(T, I) T I 2 (T I)T(T I) T
2 I 2 2TTI
If the terms T 2 and I 2 are constant,
the diversity between the two images is minimized
when the cross-correlation (CC) between T and I
is maximized
CC(T, I) TTI

4
Correlation-based techniques

Due to the displacement and rotation that
characterize two impressions of a given finger,
their similarity cannot be simply computed by
superimposing T and I.
Let I(?x, ?y, ?) represent a rotation of the
input image I by an angle ? around the origin and
shifted by ?x, ?y pixels in directions x and y
respectively. Then the similarity between the two
fingerprint images T and I can be measured as
S(T, I) max?x, ?y, ? CC(T, I (?x, ?y,
?))

5
Distortions

Non-linear distortion makes impressions of the
same finger significantly different in terms of
global structure.
Skin condition and finger pressure cause image
brightness, contrast and ridge thickness to vary
significantly across different impressions.
A direct application of the last equation is
computationally very expensive.

6
Distortion
7
Correlation

The correlation theorem states that computing
the correlation in the spatial domain is
equivalent to performing a point-wise
multiplication in the Fourier domain in
particular,

Where F(.) is the Fourier transform of an image,
F-1(.) is the inverse Fourier transform,
denotes the complex conjugate and X denotes the
point by point multiplication of two vectors. The
result is a correlation image whose value at the
pixel x, y denotes the correlation between T
and I when the displacement is ?x x and ?y y.
Computing the maximum correlation need not
necessarily be done in a sequential, exhaustive
manner multi-resolution approaches,
space-searching techniques (gradient descent),
and other heuristics can be adopted to reduce the
number of evaluations.
The Fourier-Mellin transform may be used instead
of Fourier transform to achieve rotation
invariance in addition to translation invariance.
The approach proposed by Wilson, Watson and Paek
partitions both T and I into local regions and
computes the maximum correlation (in the Fourier
domain) between any pair of regions. This method
suffers from border effects because of the
partial overlapping between the different blocks,
but can considerably speed up the matching
process.
Correlation between two signals can be computed
by an optical system that uses lenses to derive
the Fourier transform of the images and a joint
transform correlator for their matching.

8
Minutiae-based Methods

Minutiae matching is certainly the most
well-known and widely used method for fingerprint
matching. Let T and I be the representation of
the template and input fingerprint respectively.
Each minutia may be described by a number of
attributes, including its location in the
fingerprint image, orientation, type etc. Most
common minutiae matching algorithms consider each
minutia as a triplet m x, y, ? that indicates
the x, y minutia location coordinates and the
minutia angle ?
T m1, m2,,mm, mi xi, yi,
?i, i 1..m
I m'1, m'2,,m'n, m'j x'j,
y'j, ?'j, j 1..n,
where m and n denote the number of minutiae in T
and I respectively.
Aligning the two fingerprints is a mandatory step
in order to maximize the number of matching
minutiae. Correctly aligning two fingerprints
certainly requires displacement and rotation to
be recovered, and likely involves other geometric
transformations
Scale has to be considered when the resolution
of the two fingerprints may
vary.
Other distortion-tolerant geometrical
transformations could be useful to match minutiae
in case one or both of the fingerprints is
affected by severe distortions.

9
Minutiae-based Methods
Let map(.) be the function that maps a minutia
m'j (from I) into m"j according to a given
geometrical transformation for example, by
considering a displacement of ?x, ?y and a
counterclockwise rotation ? around the
origin map ?x, ?y, ?(m'j x'j, y'j, ?'j)
m"j x"j, y"j, ?'j ?, where
10
Minutiae-based Methods
11
Approaches to point pattern matching
Relaxation The relaxation approach iteratively
adjusts the confidence level of each
corresponding pair of points based on its
consistency with other pairs until a certain
criterion is satisfied. At each iteration r, the
method computes m . n probabilities pij
(probability that point i corresponds to point
j)
where c(i,jh,k) is a compatibility measure
between the pairing (i, j) and (h, k), which can
be defined according to the consistency of the
alignments necessary to map point j into i and
point k into h. The above equation increases the
probability of those pairs that receive
substantial support by other pairs and decreases
the probability of the remaining ones. At
convergence, each point i may be associated with
the point j such that pij maxspis, where s is
any other point in the set. Algebraic and
operational research solutions This is based on
the restrictive hypothesis that n m and that an
exact alignment may be recovered under an affine
transformation.
12
Approaches to point pattern matching
Tree Pruning It attempts to find the
correspondence between the two point sets by
searching over a tree of possible matches while
employing different tree-pruning methods to
reduce the search space. Energy minimization
These methods define a function that associates
an energy with each solution of the problem.
Optimal solutions are then derived by minimizing
the energy function by using a stochastic
algorithm such as genetic algorithm or simulated
annealing. Hough Transform This method
converts point pattern matching to the problem of
detecting peaks in the Hough space of
transformation parameters.
13
Minutiae matching with pre-alignment

Storing pre-aligned templates in the database and
pre-aligning the input fingerprint before the
minutiae matching can speed up the 1N
identification.
The two main approaches for pre-alignment are-
Absolute pre-alignment
Relative pre-alignment

14
Minutiae matching with pre-alignment
The M82 method, developed for minutiae-based
fingerprint matching performs a coarse absolute
pre-alignment according to the core position
(detected through R92 method) and the average
orientation of two regions located at the two
sides of the core.
15
Minutiae matching with pre-alignment
After the course absolute pre-alignment of both T
and I minutiae, M82 determines a list of
candidate minutiae pairs by considering the
minutiae that are closer than a given distance
the matching degree of each candidate pair is
consolidated according to the compatibility with
other pairs. The list is sorted with respect to
the degree of matching the top pair is selected
as the principal pair and all the remaining
minutiae are translated accordingly. In a second
stage, a deformation tensor, which allows the
matching to tolerate small linear distortion and
rotations, is determined.
16
Minutiae matching with pre-alignment
Jain, Hong and Bolle (1997) proposed a minutiae
matching approach that exploits ridge features
for relative pre-alignment. The relative
pre-alignment is based on the observation that
minutiae registration can be performed by
registering the corresponding ridges. In fact,
each minutia is associated with a ridge during
the minutiae extraction stage, when a minutia is
detected and recorded, the ridge on which it
resides is also recorded. The ridge is
represented as a planar curve, with its origin
coincident with the minutia and its x-coordinate
being in in the same direction as the minutia
direction. Also, this planar curve is normalized
(in scale) with respect to the average ridge
frequency. By matching these ridges, the
parameters (?x, ?y, ?) may be recovered. The
ridge matching task proceeds by iteratively
matching pairs of ridges until a pair is found
whose matching degree exceeds a certain
threshold. The pair is then used for relative
pre-alignment.
17
Minutiae matching with pre-alignment
18
Avoiding alignment
Fingerprint alignment is a critical and
time-consuming step. Bazen and Gerez (2001)
introduced an intrinsic coordinate system (ICS)
whose axes run along hypothetical lines defined
by the local orientation of the fingerprint
pattern. First, the fingerprint is partitioned in
regular regions (i.e. regions that do not contain
singular points). In each regular region, the ICS
is defined by the orientation field. When using
intrinsic coordinates instead of pixel
coordinates, minutiae are defined with respect to
their position in the orientation field.
Translation, displacement and distortion move
minutiae with the orientation field they are
immersed in and therefore do not change their
intrinsic coordinates.
19
Galton-Henry classification
The five most common classes of the Galton-Henry
classification scheme are Arch An arch
fingerprint has ridges that enter from one side,
rise to a small bump and go out the opposite
side Arches do not have loops or deltas. Tented
Arch Similar to (plain) arch, except that at
least one ridge exhibits a high curvature and one
loop and one delta are present. Loop Has one or
more ridges that enter from one side, curve back,
and go out the same side they entered. There can
be left loops and right loops. Whorl and Whorl
with a twin loop Contains at least one ridge
that makes a complete 360-degree path around the
center of the fingerprint.
20
Galton-Henry classification
21
Galton-Henry classification
22
Galton-Henry classification
23
Classification Techniques

The features of a fingerprint image used for
identification are-
Ridge line flow
Orientation image
Singular points
Gabor filter responses

24
Syntactic approaches
A syntactic method describes patterns by means of
terminal symbols and production rules. A grammar
is defined for each class and a parsing process
is responsible for classifying each new
pattern. The approach introduced by Rao and
Black(1980) is based on the analysis of ridge
line flow, which is 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.
25
Syntactic approaches
26
Structural approaches
Structural approaches are based on the relational
organization of low-level features into
higher-level features. The relational
organization is represented by means of symbolic
data structures, such as trees and graphs, which
allow a hierarchical organization of the
information. Maio and Maltoni (1996) partition
the orientation image into regions by minimizing
a cost function that takes into account the
variance of the element orientations within each
region. An inexact graph matching technique is
then used to compare the relational graphs with
class-prototype graphs.
27
Structural approaches
28
Structural approaches
In Chappelli et al. (1999), a template-based
matching is performed to guide the partitioning
of the orientation images. The main advantage
of this approach is that, because it relies only
on global structural information, it is able to
deal with partial fingerprints, where some
singular points are not available, and it can
also work on very noisy images.
29
Structural approaches
30
Statistical approaches

One of the most widely adopted statistical
classifiers is the k-nearest neighbor examples
of its application in the fingerprint-classificati
on domain can be found in Fitz and Green(1996),
where wedge-ring features obtained from the
hexagonal Fourier transform are used as input,
and in Jain, Prabhakar and Hong(1999), where the
first step of a two-stage classification
technique is performed by means of the k-nearest
neighbor rule.
Many approaches directly use the orientation
image as a feature vector, by simply nesting its
rows. By encoding each element of the orientation
image with the two components rcos2?, rsin2?, a
typical 30 X 30 orientation image results in a
vector of 1800 elements. Training a classifier
with such high-dimensional vectors would require
large amounts of training data, memory and
computation time. For this reason, statistical
dimensionality reduction techniques are often
applied to reduce the dimensionality of the
feature vector.

31
Statistical approaches
32
Example of the system
A functional scheme of PCASYS (Candela et al.,
1995)
33
Retrieval strategies
If an exclusive classification technique is used
for indexing, these retrieval strategies can be
used Hypothesized class only Fixed search
order Variable search order
34
Retrieval strategies
35
Performance of retrieval strategies
36
Synthetic Fingerprint generation
The strategy is to generate a master fingerprint
first. Then several synthetic impressions can be
derived from the master fingerprint by explicitly
tuning displacement, rotation, distortion, skin
condition and noise.
37
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39
Generation of a master fingerprint

Creating a master fingerprint involves the
following steps
Fingerprint area generation
Orientation image generation
Frequency image generation
Ridge pattern generation

40
Generation of a master fingerprint

Fingerprint area generation
Depending on the finger size, position and
pressure against the acquisition
sensor, the acquired fingerprint images have
different sizes and external
shapes.

41
Generation of a master fingerprint
A simple model based on four elliptical arcs and
a rectangle and controlled by five parameters can
handle most of the variations present in real
fingerprint shapes. The following figure shows
some examples of fingerprint shapes generated by
this model by varying the five parameters.
42
Generation of a master fingerprint
Orientation image generation The orientation
model proposed by Sherlock and Monro (1993)
allows a consistent orientation image to be
computed from the knowledge of the position of
the fingerprint singularities (loops and deltas)
alone. In this model, the image is located in the
complex plane and the local ridge orientation is
the phase of the square root of a complex
rational function whose singularities (poles and
zeros) are located at the same place as the
fingerprint singularities (loops and deltas).
43
Generation of a master fingerprint
44
Generation of a master fingerprint
45
Generation of a master fingerprint

Frequency image generation
The steps are-
A feasible overall frequency is randomly selected
according to the distribution of ridge line
frequency in real fingerprints an average
ridge/valley period of nine pixels is used this
simulates a 500 dpi sensor.
The frequency in the above-described regions is
slightly decreased according to the positions of
the singularities.
The frequency image is randomly perturbed to
improve its appearance.
A local smoothing by a 3 X 3 averaging box filter
is performed.

46
Generation of a master fingerprint
47
Ridge pattern generation

Given an orientation image and a frequency image
as an input, a deterministic generation of a
ridge line pattern, including consistent
minutiae, is not an easy task. One could try to
fix a priori the number, the type, and the
location of the minutiae, and by means of an
explicit model, generate the gray-scale
fingerprint image starting from the minutiae
neighborhoods and expanding to connect different
regions until the whole image is covered.

48
Ridge pattern generation
Gabor filters They are an effective tool for
fingerprint enhancement. SFINGE uses equal values
for the standard deviations of the Gaussian
envelope along the x and y axes sx sy
s The filter applied at each pixel x, y has
the form
49
Ridge pattern generation
50
Perturbation and global translation/rotation

Perturbation and global translation/rotation
The perturbation phase sequentially performs the
following steps
Isolate the white pixels associated with the
valleys into a separate layer. This is simply
performed by copying the pixels brighter than a
fixed threshold to a temporary image.
Add noise in the form of small white blobs of
variable size and shape. The amount of noise
increases with the inverse of the fingerprint
border distance.
Smooth the resulting image with a 3 X 3
averaging box filter.
Superimpose the valley layer to the resulting
image.
Rotate and translate the image.