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Pair Wise Distance Histogram Based Fingerprint

Minutiae Matching Algorithm

- Developed By Neeraj Sharma
- M.S. student,
- Dongseo University, Pusan
- South Korea.

Contents

- Introduction
- Why Fingerprints some facts
- Essential Preprocessing (Feature Extraction etc.)
- Abstract
- Previous Work
- Problem Simulation
- Steps of Algorithm
- Flow Chart
- Local Matching
- Global Matching
- Results
- Comparison with Reference method (Wamelen et al)
- Future work
- Publications

Introduction

- Fingerprints are most useful biometric feature in

our body. - Due to their durability, stability and uniqueness

fingerprints are considered the best passwords. - In places of access security, high degree

authentication, and restricted entry,

fingerprints suggests easy and cheap solutions.

Biometric Modalities

Market Capture by different Biometric

modalities

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Different fingerprints of two fingers

Different Features in a Fingerprint

Ridge Ending

Feature points extracted

Feature Extraction with CUBS-2005 algorithm

(Developed by SHARAT et al)

Minutia features

Extraction of minutiae

Image skeleton

Gray scale image

Feature points pattern of same finger

High level description of algorithms in FVC

(Fingerprint Verification Competition)2004

Abstract

- Thesis proposes a novel approach for matching of

minutiae points in fingerprint patterns. - The key concept used in the approach is the

neighborhood properties for each of the minutiae

points. - One of those characteristics is pair wise

distance histogram, that remains consistent after

the addition of noise and changes too.

Previous Work

- Fingerprint Identification is quite mature area

of research. Its almost impossible to describe

all the previous approaches in a short time here. - The previous methods closely related to this

approach and also taken in reference are by Park

et al.2005 and Wamelen et al.2004. - Park et al. used pair wise distances first ever

to match fingerprints in their approach before

two years. - Wamelen et al. gave the concept of matching in

two steps, Local match and Global match.

Problem Simulation

Input Pattern

- The input fingerprint of the same finger seems to

be different while taken on different times. - There may be some translational, rotational or

scaling changes, depending upon situation. - Our aim is to calculate these changes as a

composite transformation parameter T. - The verification is done after transforming the

input with these parameters, new transformed

pattern should satisfy desired degree closeness

with template pattern.

Template

Minutiae matching-Aligning two point sets

Template

Input

Algorithm Steps

- The algorithm runs in two main steps-
- (i) Local matching
- (ii) Global matching
- In local matching stepwise calculations are

there - Calculate k nearest neighbors for each and

every point in both patterns. - Calculate histogram of pair wise distances in the

neighborhood of every point. - Find out the average histogram difference between

all the possible cases. - Set the threshold level of average histogram

difference - Compare the average histogram differences with

the threshold level.

Flow Chart

Calculation of k Nearest neighbors (Local

match)

- For the given input fingerprint pattern and the

template pattern, calculate k nearest neighbors

in order to distances. - Here k is a constant can be calculated with the

formula given by wamelen et al.(2004)

Histogram Calculation (Local Match)

- Histogram of pair wise distances in their

neighborhood for each and every point is

calculated here. It describe the variety of

distances of particular point in its

neighborhood. - Here for one point P1
- P1n1, P1n2, P1n3, P1n4, P1n5 are five

nearest neighbors. - Note step size is 0.04unit, here.

P1n2

Average Histogram Difference and

Threshold Setting (Local Match)

- To calculate average histogram differences for

two points, first subtract the their histograms.

It comes in a form of matrix. To calculate

average, just normalize it on corresponding

scale. - H14 2 0 0 2 0 1 2 3 1
- H21 3 2 5 0 0 2 3 0 1
- H1 - H2 3 -1 -2 -5 2 0 -1 -1 3 0
- Average histogram diff.(?H avg)(1/10)S(

H1 - H2 i) - Setting of threshold depends on the size of

point pattern. Larger the number of points,

smaller the threshold count. - Every matching pair is related with a

transformation function. That transformation

parameter is calculated mathematically.

Threshold check for a 20 points pattern input

0 1.2 2 2.4 1.2 1.6 0.8 1.6 1.6 0.8 2.8 2 2.8 2.4 2.8 2.4 1.6 2.8 2.8 2.8 1

1.2 0.4 1.2 1.6 0.8 1.2 1.2 1.6 2 1.2 2.8 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 2 2

2 1.2 0.8 1.2 1.6 1.2 2.4 2.4 2.4 1.6 2.4 1.2 1.2 1.2 1.6 1.6 2.8 1.6 0.8 1.6 3

2.4 1.6 0.8 0.4 1.6 0.8 2.4 2 2 1.6 2 0.8 1.2 1.6 1.2 1.6 2 1.2 1.6 1.6 4

1.2 0.8 1.6 2 0.4 1.6 0.8 1.2 1.6 1.2 2.4 1.6 1.6 1.6 1.6 1.6 1.2 1.6 2 2 5

1.6 0.8 0.8 0.8 1.2 0 2.4 1.6 1.6 0.8 2 1.2 1.6 1.6 1.6 1.6 1.6 1.6 2 1.6 6

0.8 1.6 2.4 2.8 1.2 2.4 0 1.6 2 1.6 3.2 2.4 2.4 2.4 2.4 2.4 1.6 2.4 2.8 2.8 7

1.6 1.2 2 2.4 0.8 1.6 1.6 0 0.8 1.6 2 2.4 2.4 2 1.6 1.2 1.6 1.6 2.8 1.6 8

1.6 1.6 2 2.4 1.2 1.6 2 0.8 0 1.6 2 2.4 2.8 2 2.4 2 2 2.4 2.8 2.4 9

0.8 0.8 1.6 1.6 0.8 0.8 1.6 1.6 1.6 0 2 1.2 2 2 2 2 1.6 2 2.4 2 10

2.8 2.4 2.4 2.4 2 2 3.2 2 2 2 0 2.4 2.4 1.6 1.6 1.2 2.4 2 2.8 1.6 11

2 1.6 0.8 1.2 1.2 1.2 2 2 2 1.2 2 0.4 0.8 1.6 1.6 2 1.6 1.2 2 2 12

2.8 1.6 1.2 1.6 1.6 1.6 2.4 2.4 2.8 2 2.4 1.2 0 1.2 1.6 1.6 1.6 1.2 1.6 1.6 13

2 1.2 1.6 2 0.8 1.6 2 1.6 2 1.6 1.6 1.6 1.2 0.4 2 1.2 2 2 1.6 1.6 14

2.8 1.6 1.6 1.6 1.6 1.6 2.4 1.6 2.4 2 1.6 2 1.6 2 0 0.8 2 0.4 2 0.8 15

2.8 1.6 1.2 2 1.6 2 2.4 1.6 2.4 2.4 1.6 2 1.2 1.6 0.8 0.4 2 0.8 2 1.2 16

1.6 1.6 2 2.4 1.2 1.6 1.6 1.6 2 1.6 2.4 2 1.6 2.4 2 2 0 1.6 3.2 2 17

2.4 2 2.4 2.8 1.6 2.4 2.4 1.6 2.4 2 1.6 2 1.2 1.6 2 1.6 1.6 1.6 2.8 1.6 18

2.8 1.6 1.6 1.6 1.6 1.6 2.8 2 2 2.4 2 2 1.6 0.8 1.6 1.2 2.4 1.6 0.8 1.2 19

2.8 1.6 2 2 1.6 1.6 2.8 1.6 2.4 2 1.6 2.4 1.6 1.6 0.8 0.8 2 0.8 2 0 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Transformation Parameter calculation

- On the basis of histogram differences, we can

make decision on local matching pairs. Then the

transformation parameter is calculated in the

following way by least squire method. Here r

represents the corresponding Transformation

Parameter.

Axial Representation of all Transformation

Parameters after Local match

- Three axes represent the translational (in both

x y direction), rotaional and scale changes. - The most dense part in graph represents the

correct transformation parameters only. We need

to conclude our results to that part.

Mean and Standard Deviation

- Mean and standard deviation is calculated with

the following mathematical equations.

Global Matching (Iteration Algorithm)

- Iteration method is used to converge the result

towards dense part of the graph. - For applying this method we need to calculate

mean and standard deviation of the distribution. - In the graph all transformation parameters are

present, calculated after local matching step. - The mean for this distribution is shown by the

triangle in centre.

Result after first iteration

- In this graph, black triangle is describing the

mean for the distribution. - After one iteration step some of the

transformation parameters, due to false local

match got removed.

Result after second iteration

- After second iteration, mean converges more

towards the dense area. - Black triangle is the mean point for this

distribution shown here.

After third iteration

- Performing iterations to converge the result,

gives the distribution having least standard

deviation. - Black star in this graph is the desired

transformation parameter i.e. r

Verification by transforming the template with

calculated parameters

Transformed With parameter r

Template Pattern in Database

Transformed version with Parameter r

Verification by Overlapping with original input

pattern

Matching Result for Ideal point sets

- No missing point
- N60
- Exactly matching

Random and Normalized Noise pattern

(a)

Results With Randomly Missing Points

- Missing points 20
- Total points60
- Matching points36
- Matching factor 0.76
- Noise factor0.031

Matching results after missing points

- Half no. of points (30) missing from pattern
- Missing points 30
- Total points60
- Matching points16
- Matching factor 0.91
- Noise factor0.021

Definitions

- t ? r/(2vn)
- t is distance of closeness which can be some

fraction of minimum pair-wise distance - ? is called matching factor, depends on point

pattern - rmaximum pair-wise distance/2
- N is no. of points in the pattern
- ? is noise factor shows the extent of noise

added to point pattern - ? added average error/mean pair-wise distance

Results for different ? and ?

Total points Matching factor(?) Noise factor(?) Time of match(sec) Accuracy()

50 0.508 0.024 1.97 99

60 1.12 0.016 2.53 98

70 4.73 0.019 3.12 94

70 1.23 0.0367 3.10 92

80 3.67 0.0198 4.01 93

80 2.78 0.0276 3.80 90

80 0.8954 0.0431 4.00 89

90 6.01 0.019 5.00 98

90 2.75 0.026 4.84 95

90 2.22 0.0398 4.93 90

90 0.8551 0.049 4.86 83

100 0.6159 0.018 6.063 97

100 2.2081 0.0226 6.00 93

100 3.2826 0.035 5.86 90

100 1.43 0.039 6.00 88

100 2.40 0.0435 6.016 85

Performance with missing points regionally

Performance with missing points regionally

Performance with missing points regionally

Performance with a real fingerprint

Results with real and random fingerprints

- The algorithm was tested on both randomly

generated point pattern and real data base. - The results shows correct identification in more

than 93.73 cases out of 500 tests, with randomly

generated data. - For real fingerprint data, method was tested on

some FVC (Fingerprint Verification Competition)

2004 samples. In most of the cases performance

was found satisfactory.

Comparative Performances of two methods over

randomly data

Total points to match Missing Points External noise added () Translation x y Time of match with wamelens method (sec.) Time of match with histogram method (sec.)

30 10 2.4 1.5 2.1 1.36 1.01

40 15 1.85 1.2 1.8 2.07 1.40

50 20 2.1 2.1 2.0 2.90 1.88

60 25 3.1 1.4 1.8 3.96 2.43

70 30 2.3 1.7 1.6 5.01 3.10

80 35 1.9 1.2 1.9 6.30 3.90

90 40 3.2 1.3 1.1 7.72 4.83

100 45 2.9 2.1 1.7 9.26 5.88

110 45 2.6 2.2 1.8 11.10 7.00

120 50 2.5 2.1 1.7 12.95 8.31

Comparison of performances

Advantages of the Method over others Proposed

earlier

- This algorithm undergoes two steps, so accuracy

is good and false acceptance rate is low. - Calculation is less complex with comparison to

other methods proposed yet. Here, histogram is a

basis to select the local matching pairs, while

in other randomize algorithms are lacking in any

basic attribute to compare. - Performance is better in case with missing points

from a specific region.

Limitations

- This algorithm is dependent on accuracy of

feature extraction method used for minutiae

extraction. - Method performs well if the number of missing

points in the pattern is less than 50 of total

minutiae points.

Future Work

- To enhance the performance of algorithm on real

fingerprint data is also a big challenge. - To calculate the computational complexity in big

O notation. - One important task is to develop an independent

method for feature points extraction from

fingerprints.

Publications

- Journal
- Sharma Neeraj, Lee Joon Jae Fingerprint Minutiae

Matching Algorithm Using Distance Histogram Of

Neighborhood, Journal of KMMS. (To be published

in Dec. 2007 edition) - International Conferences
- Sharma Neeraj, Choi Nam Seok, Lee Joon Jae,

Fingerprint Minutiae Matching Algorithm Using

Distance Distribution Of Neighborhood, MITA

(2007), 21-24. - Lye Wei Shi, Sharma Neeraj, Choi Nam Seok, Lee

Joon Jae, Lee Byung Gook, Matching Of Point

Patterns By Unit Circle, APIS(2007), 263-266.

References

- 1. Wamelen P. B. Van, Li Z., and Iyengar S.

S. A fast expected time algorithm for the 2-D

point pattern matching problem. Pattern

Recognition 37, Elsevier Ltd, (2004), 1699-1711. - 2. Park Chul-Hyun, Smith Mark J.T., Boutin

Mireille, Lee J.J. Fingerprint Matching Using

the Distribution of the Pairwise Distance Between

Minutiae, AVBPA (2005), LNCS 3546 (2005),

693-701. - Sakata Koji, Maeda Takuji, Matsushita Masahito,

Sasakawa Koichi, Tamaki Hishashi Fingerprint

Authentication based on matching scores with

other data, ICB, LNCS 3832, (2006), 280-286. - Maltoni D., Maio D., Jain A.K., Prabhakar S.

Handbook of Fingerprint Recognition, Springer

2003. - Chang S.H., Cheng F. H., Hsu Wen-Hsing, Wu

Guo-Zua Fast algorithm for point pattern

matching Invariant to translation, rotations and

scale changes. Pattern Recognition, Elsevier

Ltd., Vol-30, No.-2, (1997), 311-320. - Irani S., Raghavan P. Combinatorial and

Experimental Result on randomized point matching

algorithms, Proceeding of the 12th Annual ACM

symposium on computational geometry,

Philadelphia, PA, (1996), 68-77. - Adjeroh D.A., Nwosu K.C. Multimedia Database

Management Requirements and Issues, IEEE

Multimedia. Vol. 4, No. 3, 1997, pp 24-33.

- Thanks for your kind attention.

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