SEPARATION OF OVERLAPPED FINGERPRINTS

SEPARATION OF OVERLAPPED FINGERPRINTS
BY LAKSHMI PADMA Page 1
CHAPTER-1
INTRODUCTION
1.1 OVERVIEW:
Fingerprint is a commercially successful biometric utilized for human identification. In
2012, the market of automated fingerprint identification systems and related technologies
accounted for the greatest share of the global biometrics market and is forecasted to continue to
be the main source of overall market revenues from 2010 to 2015.
With growing demands for reliable personal authentication, supported by the recent
advancements in technology and data handling capacity, fingerprints are extensively used in
many civil, law enforcement and forensic applications such as access control systems,
transaction systems, cross-border security, and crime scene analysis. Civil applications such as
Indian government’s Aadhaar project, Department of Homeland Security’s USVISIT program,
and the UK Border Agency use rolled (nail-to-nail information) or slap (dap or flat) fingerprints
for authentication. Such fingerprints are used in recent large-scale applications. Extensive
research has been done in fingerprints captured using different methods. On the other hand,
forensic applications employ latent fingerprints for crime scene investigation. These fingerprints
are not directly visible to human eyes and after lifting using special procedures, they are used as
evidences in court proceeding.
Normally, fingerprint images contain a single fingerprint or a set of non overlapped
fingerprints. There may be situations where overlapped fingerprint can be obtained. It can be
frequently encountered in the latent fingerprint lifted from crime scenes. It is essential to separate
those overlapped fingerprint into its component fingerprints. The challenging work in separating
overlapped fingerprint is the separation of mixed orientation field into its component orientation
field.
1.2 HISTORY:
The science of fingerprint identification, or dactylography, began nearly 4,000 years ago
in the “Fertile Crescent,” the land between the Tigris and Euphrates Rivers in present day Iraq.

King Hammurabi (1955-1913 BC) used finger seals on contracts and law officers of the day
were authorized to secure fingerprints of arrested persons.
Little is known as to how the fingerprints were used. If actual point-to-point comparisons
were made, people of that day surely had exceptional eyesight —since optical magnifiers weren’t
invented until several millennia later.
More fingerprint work in South America led to the solution of a homicide using
fingerprint evidence — the first such case in recorded history. Police Inspector Alvarez of
LaPlatta, Argentina, solved the “Rojas Murder Case” with a bloody fingerprint found on a door.
In 1896, anthropometry was abandoned in Argentina in favor of fingerprint identification.
The use of fingerprint identification in the United States was slow to develop. Most
identification bureaus were locked into the Bertillon system until the now-famous Will West
case at Leavenworth prison. When Will West arrived to serve his sentence in 1903, identification
personnel insisted that he had been an inmate before. After being subjected to the Bertillon
measurements, officials found the file of one William West, whose measurements were virtually
identical to the person calling himself Will West. Even their photographs showed a remarkable
resemblance.
But William West was still in prison serving a murder sentence. Their respective
fingerprints were taken, compared, and they bore no resemblance. This unique case established
the value of fingerprint identification in this country. It is interesting to note that later research
indicates that Will and William West were most likely monozygote (identical) twins who were
separated at a young age.
In 1980, First computer data base of fingerprints was developed, which came to be
known as the Automated Fingerprint Identification System, (AFIS). In the present day, there are
nearly 70 million cards, or nearly 700 million individual fingerprints entered in AFIS.

CHAPTER-2
FINGERPRINTS
2.1 WHAT IS FINGERPRINT:
Fingerprint refers to the friction ridge skin of human finger or its impression. A
fingerprint is a type of oriented texture with locally smooth and intervening ridges and valleys.
Fingerprints are both unique and permanent, making it an ideal biometric trait for person
identification. Ridges of the skin that are created when we are still in the mother’s womb remain
the same for the rest of our lives. No two people have been found to have the same fingerprints --
they are totally unique. There's a one in 64 billion chance that your fingerprint will match up
exactly with someone else's.
Fingerprints are even more unique than DNA, the genetic material in each of our cells.
Although identical twins can share the same DNA -- or at least most of it -- they can't have the
same fingerprints.
2.2 HOW FINGERPRINTS ARE FORMED:
Fig 2.1: Baby in mother’s womb

Our fingerprints develop in the embryo before a baby is born. A person's fingerprints
are formed when they are a tiny developing baby in their mother's womb. Pressure on the fingers
from the baby touching, and their surroundings create what are called "friction ridges", the faint
lines you see on your fingers and toes. Ridges characteristics start to form around 3rd
month of a
fetus. These ridges are completely formed by the time a fetus is 6 months old, that's 3 months
before the baby is born! It consists of 98.7% water and 1.3% other substances (amino acids and
salt).
2.3 WHY DO WE HAVE FINGERPRINTS:
For over 100 years scientists have believed that the purpouse of our fingerprints is to
improve our ability to grip objects. But researchers discovered that fingerprints do not improve
grip by increasing frictionbetween the skin on our fingers and an object. In fact, finger[rints
actually reduce friction and ability to grasp smooth objects.
While testing the hypthesis of fingerprint friction,university of manchester researchers
discovered that skin behaves more like rubber than a normal solid. Several theories have arisen
suggesting that fingerprints help us to grasp rough or wet surfaces,protect our fingers from
damage, and increase touch sensitivity.
2.4 TYPES OF FINGERPRINTS:
Prints can be classified into categories. Three main classes:
1. Loops
2. Arches
3. Whorls.
60-65% of the population have loops, 30-35% have whorls and about 5% have arches.
2.4.1 LOOPS:
It must have one or more ridges entering from one side of the print, recurving and exiting
from the same side.
 If it opens toward the little finger, it is called an ulnar loop.
 If it opens toward the thumb, it is called a radial loop.

The main pattern that makes up the “loop” is surrounded by more lines, called type lines.
All loops have at least 1 delta, which is a triangular area usually shaped like a silt
formation near the mouth of a river flowing into the sea. All loops have a core. The core is the
center of the “loop” pattern. The distance between the core and the delta is often used to identify
a print.
Fig 2.2: Ulnar loop
Fig 2.3: Radial loop
ULNAR LOOP
Ulnar loop have at least one ridge that
starts on the little finger side, extends
across the finger and curves back to little
finger side.
RADIAL LOOP
Radial loop have at least one ridge that
starts on thumb finger side, extends
across the finger and curves back to
thumb finger side.

2.4.2 WHORLS:
Whorls are seen in about 25-35 % of fingerprint patterns encountered. In a whorl, some of
the ridges make a turn through at least one circuit. Any fingerprint pattern which contains 2
or more deltas will be a whorl pattern. There are four types of whorl patterns.
 Plain whorl
 Central pocket whorl
 Double loop whorl
 Accidental whorl
Plain whorl
Plain whorls consist of one or more ridges
which make or tend to make a complete circuit
with two deltas, between which an imaginary line
is drawn and at least one re-curving ridge within
the inner pattern area is cut or touched
Fig 2.4: plain whorl
Central loop whorl
Central pocket loop whorls consist of at least one re-
curving ridge or an obstruction at right angles to the
line of flow, with two deltas, between which when
an imaginary line is drawn, no re-curving ridge
within the pattern area is cut or touched.
Fig 2.5: central loop whorl

Fig 2.6: Double loop whorl
Fig 2.7: Accidental whorl
2.4.3 ARCHES
Arches are found in about 5% of fingerprint patterns encountered. The ridges run from one
side to the other of the pattern, making no backward turn. Ordinarily, there is no delta in an
arch pattern but where there a delta, no re-curving ridge must intervene between the core and
delta points. There are two types of arch patterns:
 Plain arch
 Tented arch
Accidental whorl
Accidental whorls consist of two different
types of patterns with the exception of the
plain arch, have two or more deltas or a pattern
which possess some of the requirements for
two or more different types or a pattern which
conforms to none of the definitions.
Double loop whorl
Double loop whorls consist of two separate
and distinct loop formations with two
separate and distinct shoulders for each core,
two deltas and one or more ridges which
make, a complete circuit.

Fig 2.8: Plain arch
Fig 2.9: Tented arch
Plain arch
Plain arches have an even flow of ridges from
one side to the other of the pattern; no
“significant up thrusts” and the ridges enter on
one side of the impression, and flow out the
other with a rise or wave in the center.
Tented arch
Tented arches have an angle, an up thrust, or
two of the three basic characteristics of the
loop.

CHAPTER-3
FINGERPRINT ANALYSIS
3.1 WHERE FINGERPRINTS MAY BE FOUND:
Fingerprints can be found on practically any solid surface, including the human body.
Analysts classify fingerprints into three categories according to the type of surface on which they
are found and whether they are visible or not:
 Patent prints are easy to locate since they are visible to the naked eye. Patent prints
occur when someone has a substance on their fingers such as grease, paint, blood, or ink
that leaves a visible print on a surface.
 Plastic prints are also easy to locate but are less common than patent prints since they
occur when someone touches an object such as wax, butter, or soap and leaves a three-
dimensional impression of the finger on the object.
 Latent prints are the most common type of print and take the most effort to locate since
they are invisible. Latent prints occur when someone touches any porous or nonporous
surface. The natural oils and residue on fingers leave a deposit on surfaces which mirror
the ridges and furrows that are present on the individual’s finger
3.2 HOW FINGERPRINTS ARE COLLECTED:
The various fingerprint collection techniques is essential to successful cross-examination
of crime scene technicians and fingerprint examiners.
3.2.1 COLLECTING PATENT FINGERPRINTS:
Patent prints are collected using a fairly straightforward method: photography. These
prints are photographed in high resolution with a forensic measurement scale in the image for
reference. Investigators can improve the quality of the images by using low-angle or alternate
light sources and/or certain chemicals or dyes during photography, but this is usually not
necessary.

3.2.2 COLLECTING PLASTIC FINGERPRINTS:
Plastic fingerprints are 3D impressions of fingerprints left in a substance like wax, mud,
paint, soap, tar, drying blood, etc. They are generally easily visible. Plastic fingerprints are
generally preserved by casting. A liquid material (silicone rubber, plaster, or a metal alloy) is
poured over the fingerprint and hardened to make a cast of the impression. The cast is much
more durable than the plastic fingerprint and can be stored as evidence.
3.2.3 COLLECTING LATENT FINGERPRINTS:
One of the most common methods for discovering and collecting latent fingerprints is by
dusting a smooth or nonporous surface with fingerprint powder (black granular, aluminum
flake, black magnetic, etc.). If any prints appear, they are photographed as mentioned above
and then lifted from the surface with clear adhesive tape. The lifting tape is then placed on a
latent lift card to preserve the print.
However, fingerprint powders can contaminate the evidence and ruin the opportunity to
perform other techniques that could turn up a hidden print or additional information.
Therefore, investigators may examine the area with an alternate light source or apply
cyanoacrylate (super glue) before using powders.
3.3 WHO CONDUCTS THE ANALYSIS:
In criminal justice cases, computerized systems are used to search various local, state and
national fingerprint databases for potential matches. Many of these systems provide a value
indicating how close the match is, based on the algorithm used to perform the search. Fingerprint
examiners then review the potential matches and make a final determination.
Fingerprint examinations may be conducted by forensic scientists, technicians or police
officers; however, the examiner should have the proper training and experience to perform the
task. Currently many agencies require new examiners to have a four-year degree in science
(biology, chemistry or physics). In addition, agencies may require examiners to become certified
by the International Association for Identification (IAI). IAI’s website provides certification
requirements.

3.4 HOW AND WHERE THE ANALYSIS IS PERFORMED:
Fingerprint analysis is usually performed by law enforcement agencies or crime
laboratories; however, casework may be sent to private companies if there is a need, such as to
reduce backlogs, verify results, or handle high-profile cases.
Fingerprint examination involves looking at the quality and quantity of information in
order to find agreement or disagreement between the unknown print (from the crime scene) and
known prints on file. To conduct the examination, fingerprint examiners use a small magnifier
called a loupe to view minute details (minutiae) of a print. A pointer called a ridge counter is
used to count the friction ridges.
Fig 3.1: An examiner uses a loupe to view minute details of fingerprint

3.5 FINGERPRINT ANALYSIS PROCESS:
Fingerprint examiners use the ACE-V (analysis, comparison, evaluation and verification)
method to reach a determination on each print.
 Analysis involves assessing a print to determine if it can be used for a comparison. If
the print is not suitable for comparison because of inadequate quality or quantity of
features, the examination ends and the print is reported as not suitable. If the print is
suitable, the analysis indicates the features to be used in the comparison and their
tolerances (the amount of variation that will be accepted). The analysis may also
uncover physical features such as recurves, deltas, creases and scars that help indicate
where to begin the comparison.
 Comparisons are performed by an analyst who views the known and suspect prints
side-by-side. The analyst compares minutiae characteristics and locations to
determine if they match. Known prints are often collected from persons of interest,
victims, others present at the scene or through a search of one or more fingerprint
databases such as the FBI’s Integrated Automated Fingerprint Identification System
(IAFIS). IAFIS is the largest fingerprint database in the world and, as of June 2012,
held more than 72 million print records from criminals, military personnel,
government employees and other civilian employees.
 Evaluation is where the examiner ultimately decides if the prints are from the same
source (identification or individualization), different sources (exclusion) or is
inconclusive. Inconclusive results may be due to poor quality samples, lack of
comparable areas, or insufficient number of corresponding or dissimilar features to be
certain.
 Verification is when another examiner independently analyzes, compares and
evaluates the prints to either support or refute the conclusions of the original
examiner. The examiner may also verify the suitability of determinations made in the
analysis phase.

This analysis process is manual process which is done by the examiner. It takes large
amount of time and there may be a chance of inaccuracy in the analysis process.
3.6 USE OF FINGERPRINT ANALYSIS:
Fingerprints can be used in all sorts of ways:
 Providing biometric security (for example, to control access to secure areas or
systems) Identifying amnesia victims and unknown deceased (such as victims of
major disasters, if their fingerprints are on file)
 Conducting background checks (including applications for government employment,
defense security clearance, concealed weapon permits, etc.).
3.7 IS IT POSSIBLE TO REMOVE FINGERPRINT:
Yes, it is possible to remove fingerprint. The relative simplicity of identifying and
copying a fingerprint, for legal or illegal purposes, is what has raised interest in how one could
remove or change their fingerprints today. However, when you take a look at some of the
possible techniques to do so, the options quickly dwindle.
Scarring: One method used to change one’s prints is to heavily scar the fingertip. This would
require cutting or burning it enough to create a permanent scar that mars the entire surface of the
fingertip, which would be quite painful when done at home. Furthermore, this strategy only
changes the fingerprint, it doesn’t remove it entirely. This means it is still a unique identifier, it
would just need to be updated in any databases where your fingerprints are stored.
Complete Removal: Though more popularized in entertainment, such as the above scene from
Men in Black where Will Smith’s fingerprints are permanently removed, there is at least one
example of someone completely removing his fingerprints in real life. In the mid-1900s, Roscoe
Pitts had skin from his chest grafted onto his fingertips. The skin on the chest is smooth, so this
eliminated Pitts’ prints. However, police were still able to eventually identify him using prints
taken from the sides of his fingers.

CHAPTER-4
Fingerprint images contain a single fingerprint or a set of non overlapped fingerprints. There
may be situations where overlapped fingerprint can be obtained. It can be frequently encountered
in the latent fingerprint lifted from crime scenes. It is essential to separate those overlapped
fingerprint into its component fingerprints. The challenging work in separating overlapped
fingerprint is the separation of mixed orientation field into its component orientation field.
Forensic scientists have proposed a method to separate overlapped fingerprints using the
gold material. This technology is very interesting and is not convenient since it works only for
some specific fingerprints. Fan et al. proposed an algorithm to separate overlapped fingerprints
based on image enhancement using a manually marked orientation field. However, it is tedious
and time consuming for us to manually mark the orientation field of each component fingerprint
in the overlapped fingerprint image.
Geng et al. proposed to use morphological component analysis to separate overlapped
fingerprints. Experimental results showed that their algorithm can only separate that component
fingerprint which dominates the overlapped image. Singh et al. suggested the use of independent
component analysis (ICA) to separate overlapped fingerprints, but they did not provide a
separation algorithm.
So with the advancement of the technology, an algorithm is proposed to separate the
overlapped fingerprints and evaluated it using both real overlapped latent fingerprints and
simulated overlapped fingerprints. The algorithm is based on two assumptions which are both
reasonable and practical.
1. The overlapped fingerprint image consists of at most two fingerprints.
2. There exist differences between the orientation fields of the two component fingerprints
in the overlapped area.
The proposed algorithm consists of the following four steps:
1. Region segmentation

2. Initial orientation field estimation
3. Orientation field separation
4. Fingerprint separation
Fig 4.1: A flow model for proposed algorithm
4.1 REGION SEGMENTATION:
The region masks are manually marked for the two overlapped fingerprints. Manually
marking region mask is a common practice in latent fingerprint community. The overlapped
fingerprint image consists of two regions, the overlapped region and the non overlapped region
of two component fingerprints. The overlapped region is the common region of the two masks
and it contains the overlapped part of the two fingerprints and the non overlapped region
contains only one fingerprint.

Fig 4.2: Procedure to divide the regions
An overlapped fingerprint image is segmented into non overlapping blocks of 16x16
pixels. The block in the overlapped region is called overlapped block and the block in the non
overlapped region is called non overlapped block. There exists one dominant orientation in the
non overlapped block and two dominant orientations in the overlapped block.
4.2 INITIAL ORIENTATION FIELD ESTIMATION:
A Fingerprint orientation field is a matrix, whose value at (x, y) denotes the dominant
ridge orientation at point (x, y). The orientation field of an overlapped fingerprint image is
different from that of the orientation field of a single fingerprint image in that it contains one
dominant orientation in the non overlapped region and two dominant orientations in the
overlapped region. In this paper, we have assumed that the region masks of the component
fingerprints have been manually marked.
After the creation of region mask we have used Local Fourier analysis method in order to
extract the initial orientation field. We have taken the input overlapped fingerprint image and
then is divided in to non overlapping blocks of 16x16 pixels. The ridge present in an each block

can be represented by a 2D sine wave. Centered at each block, the local image in the 64x64
window is then multiplied by a Gaussian function (σ = 16). The discrete Fourier transform (DFT)
F(u,v) of the resulted image is computed and the amplitude of the low frequency components is
set to zero. Also, the local maxima points with the largest amplitude are found in the frequency
domain. Each point can be represented by a 2D sine wave
w(x,y)= a. sin(2Πf(sin(θ)x + cos(θ)y) + Φ),
where a, f, θ, Φ represents the amplitude, frequency, orientation and phase respectively.
Fig 4.3: Estimation of two dominant orientations in a overlapped block
4.3 ORIENTATION FIELD SEPARATIONS:
The algorithm is proposed in order to reconstruct the orientation fields. The method used is
Relaxation labeling method.
The Proposed algorithm is given below:
Initialization: set t=0, obtain initial label probabilities:
P(0) = (p1(0),p2(0),.....,pN(0)).
While true do
1) Selection of labels :
For i= 1,2,...,N do
Choose a label at random based on the current label probabilities pi(t).
End
2) Calculation of responses:

For i= 1,2,.....,N do
Let q be the label selected for Oi in step 1) and compute the response βiq
to Oi as
Βiq = (1/N) ΣjRij(q,sj),
Where sj is the label selected for object Oj in step 1).
End.
3) Updating of label probabilities:
For i= 1,2,...,N do
Let q be the label selected for Oi in step 1) and Pi(t) is updated as
Piq(t+1) = Piq(t) + αβiq(1 – Piq(t)),
Pir(t+1) = Pir(t) - αβiqPir(t), r≠q.
End
4) Iteration:
If probability vectors have converged then
Break.
End
Else
t = t+1.
End
End
Fig 4.4: (a) and (b)correspond one merger, while (c) and (d) correspond to another one.

4.4 FINGERPRINT SEPARATION:
Contextual filtering using 2D Gabor filters is very effective for fingerprint enhancement.
Two important parameters of 2D Gabor filters are local ridge orientation and frequency. When
the ridge orientation field and ridge frequency map are obtained, Gabor filtering can connect the
broken ridges and remove intervening ridges. Finally, two overlapping fingerprints have been
successfully separated.
Fig 4.5: Separated orientation fields of overlapped fingerprint
Fig 4.6: First enhanced fingerprint and second enhanced fingerprint

CHAPTER-5
ADVANTAGES AND DISADVANTAGES
5.1 ADVANTAGES:
The proposed algorithm can be applied in the fields such as:
 Forensics.
 Crime investigation department.
 Security and defense.
 Improves the accuracy of overlapping fingerprints separation, especially for the practical
scenario of poor quality overlapped latent image.
 The model based separation method proposed here provides a very useful interactive tool
for examiners.
5.2 DISADVANTAGES:
 It is assumed that there are not more than two overlapped fingerprints.
 The algorithm needs manually marked region.
 A fully automated system could be developed.

CHAPTER-6
APPLICATIONS
Fingerprints are especially important in the criminal justice realm. Investigators and analysts
can compare unknown prints collected from a crime scene to the known prints of victims,
witnesses and potential suspects to assist in criminal cases. For example:
 A killer may leave their fingerprints on the suspected murder weapon
 A bank robber’s fingerprints may be found on a robbery note
 In an assault case, the perpetrator may have left fingerprints on the victim’s skin
 A burglar may leave fingerprints on a broken window pane
 A thief’s fingerprints may be found on a safe
In addition, fingerprints can link a perpetrator to other unsolved crimes if investigators
have reason to compare them, or if prints from an unsolved crime turn up as a match during a
database search. Sometimes these unknown prints linking multiple crimes can help investigators
piece together enough information to zero in on the culprit.
In the absence of DNA, fingerprints are used by the criminal justice system to verify a
convicted offender’s identity and track their previous arrests and convictions, criminal
tendencies, known associates and other useful information. Officers of the court can also use
these records to help make decisions regarding a criminal’s sentence, probation, parole or
pardon.

CHAPTER-7
CONCLUSION
Every human being carries with him from his cradle to his grave certain physical marks
which do not change their character by which he can always be identified and that without shade
of doubt or question these marks are his signature…and this autograph cannot be counterfeited,
nor can he disguise it or hide it away. This ‘signature’ is each man’s very own — there is no
duplicate of it among the swarming populations of the globe. This autograph consists of the
delicate lines or corrugations with which Nature marks the insides of the hands and the soles of
the feet.
Fingerprint refers to the friction ridge skin of human finger or its impression. A
fingerprint is a type of oriented texture with locally smooth and intervening ridges and valleys.
Fingerprints are both unique and permanent, making it an ideal biometric trait for person
identification. Fingerprint recognition has been successfully deployed in various applications,
such as entry control, time and attendance, computer login, forensics, and airport security. One
challenging problem now-a-days is the processing and matching of overlapped fingerprints.
When the same location of a surface is touched by two or more fingerprints at different times, the
developed latent image may contain overlapped fingerprints. It may also occur in the live scan
fingerprint images when the surface of fingerprint sensors contains residue of preceding
fingerprints.
Overlapped fingerprints which are encountered from the crime scenes are not of good
quality. However, separating the overlapped fingerprints is a very challenging problem for the
existing algorithms. We have proposed a relaxation labeling algorithm for separating overlapped
fingerprints. By applying the relaxation labeling algorithm over the initial orientation field output
obtained from the Local Fourier analysis we obtain two separated orientation fields. Then the
two component fingerprints are separated by filtering the overlapped fingerprint image using the
Gabor filter.

CHAPTER-8
FUTURE SCOPE
This study can be extended along the following directions:
1. The proposed algorithm assumes that the component orientation fields should be
different or completely separable in the overlapped region. This may not always
be the case. The algorithm needs to be improved to handle the more general case.
2. The current algorithm requires manually marked region masks (region of interest
or ROI) and singular points as input. There is a plan to develop a fully automatic
overlapped fingerprint separating algorithm.
3. Image quality of the overlapped fingerprints used in the current experiments is
relatively good. We are in the process of collecting additional latent overlapped
fingerprints of various quality that are lifted using different latent development
methods.

CHAPTER-9
BIBILIOGRAPY
1. F.Chen, J.Feng, A.K.Jain, J.Zhou and J.Zhang,”Separating overlapped fingerprints,”
IEEE Trans. On Information forensics and security, vol.6, no.2, June 2011.
2. D. Maltoni, D. Maio, A.K.Jain, and S. Prabhakar, Handbook of Fingerprint Recognition
(Second Edition). New York: springer, 2009.
3. L. Hong, Y. Wan, and A.K.Jain, “Fingerprint image enhancement: Algorithm and
performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell., vol.20, no.8, pp.777-
789, Aug.1998.
4. A.K. Jain and J. Feng,” Latent palm print matching,” IEEE Trans. Pattern Anal. Mach.
Intell., vol.31, no.6, pp.1032-1047, Jun 2009.
5. M.Pelillo, F.Abbattista, and A. Maffione,” Evolutionary learning for relaxation labeling
processes,” in Proc. AI*IA, 1993, pp.230-241.
6. M.Pelillo and M. Refice,”Learning compatibility coefficients for relaxation labeling
processes,” IEEE Trans. Pattern Anal. Mach. Intell., vol.16, no.9, pp.933-945, sep.1994.
7. J.Zhou and J. GU,” A model – based method for the computation of fingerprints,” IEEE
Trans. Image Process. vol. 13, no.6, pp.821-835, Jun.2004.

SEPARATION OF OVERLAPPED FINGERPRINTS

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