Master Thesis Presentation, 14Dec07 Pair Wise Distance Histogram Based Fingerprint Minutiae Matching...

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Master Thesis Presentation, 14Dec07

Pair Wise Distance Histogram Based Fingerprint Minutiae Matching Algorithm

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

Master Thesis Presentation: 14DEC07Presented by:neeraj@dit.dongseo.ac.kr

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

Different fingerprints of two fingers

Different Features in a Fingerprint

Ridge Ending

Enclosure

Bifurcation

Island

Texture

Singular points

Feature points extracted

Extraction of minutiae

Image skeleton

Gray scale image

Minutia features

Feature Extraction with CUBS-2005 algorithm (Developed by SHARAT et al)

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 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 Input Pattern

cos sin( )

sin cosq x p

x t xs sq T p

y t ys s

Minutiae matching-Aligning two point sets

Template

Algorithm Steps The algorithm runs in two main steps:- (i) Local matching (ii) Global matchingIn local matching stepwise calculations are there:1. Calculate “k” nearest neighbors for each and

every point in both patterns.2. Calculate histogram of pair wise distances in

the neighborhood of every point.3. Find out the average histogram difference

between all the possible cases.4. Set the threshold level of average histogram

difference5. Compare the average histogram differences

with the threshold level.

Flow Chart

Point pattern “P” stored in database pattern “Q” is taken that is to be matched with “P”

Select a local point and it’s “k” nearest neighbors in patterns P

Select a local point and it’s “k” nearest neighbors in patterns Q

Make pair wise distance Histogram

Average histogram difference < Threshold level

Calculate and store transformation parameter

Iteration algorithm to calculate final Transformation Parameter

All point’s in pattern p is examined

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.

P1n4 P1n5

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.

H1=[4 2 0 0 2 0 1 2 3 1] H2=[1 3 2 5 0 0 2 3 0 1] H1 - H2 =[3 -1 -2 -5 2 0 -1 -1 3 0] Average histogram diff.(ΔH avg)=(1/10)*Σ(| 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 input0 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.

A xA yA xB

A yA xA yB

xA yA A B

yA xA A B

i i i i

A B a b a bi

l x x y y

i i i i

A B a b a bi

l x y y x

A a ai

2 2A xA yAD ll

cos sinT

x yr t t s s

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.

-100-50

all iterations together 5

rotangle

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.

-200-100

All transformation-parameters After Local Matching and Threshold Test

rotangle

High Density Area

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.

-200-100

Transformation Parameters After First Iteration Step

rotangle

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.

-200-100

Transformation Parameters After Second Iteration Step

rotangle

Mean converges to density

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”

cos sinT

x yr t t s s -200

100200

Transformation parameters after many iterations having minimum Std.Deviation

rotangle

Parameters and their mean final stage

Verification by transforming the template with calculated parameters

Template Pattern in Database Transformed version with Parameter ”r”

Verification by Overlapping with original input pattern

Transformed With parameter “r”

Matching Result for Ideal point sets No missing point N=60 Exactly matching

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

neighbours of point P

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

1.4neighbours of point q

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Random and Normalized Noise pattern

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

Magnitude of added noise in x & y direction

frequen

f part

magnitude t

Histogram pattern of Random noise

noise in x-dir

noise in y-dir

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.050

magnitude of noise added

frequen

r nois

agnitude

Histogram pattern of normalized external noise

noise in x-dir

noise in y-dir

0 5 10 15 20 25 30 35 40 45 50-0.05

Index of point

f nois

dded in x

direction f

each p

Plot for values of noise in each point

noise in x

noise in y

0 5 10 15 20 25 30 35 40 45 500

f nois

dded in x

direction f

each p

Index of particular point

Plot of random noise added in both direction

(c) (d)

Results With Randomly Missing Points

Missing points =20 Total points=60 Matching

points=36 Matching factor=

0.76 Noise factor=0.031

0 0.2 0.4 0.6 0.8 1 1.2 1.4

1.4neighbours of point P

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

neighbours of point q

Matching results after missing points

Half no. of points (30) missing from pattern

Missing points =30 Total points=60 Matching

points=16 Matching factor=

0.91 Noise factor=0.021

0 0.2 0.4 0.6 0.8 1 1.2 1.4

neighbours of point P

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

1.5neighbours of point q

Definitions t= λ *r/(2*√n) t is distance of closeness which can be some fraction

of minimum pair-wise distance λ is called “matching factor”, depends on point

pattern r=maximum pair-wise distance/2 N is no. of points in the pattern η is “noise factor” shows the extent of noise added to

point pattern η= added average error/mean pair-wise distance

Master Thesis Presentation, 14Dec07

Results for different λ and ηTotal points Matching

factor(λ)Noise factor(η)

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

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2original pointset "p"

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2pointset "q" after missing region and scaling, rotation changes

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1overlapping of P and Q pattern at 0.4 diff 3d ref

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2removed elliptical region from original pointset "p"

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1overlapping of P and Q pattern at 0.4 diff 4d ref

0 0.5 1 1.5 2 2.5 30

3neighbours of point q

0 0.5 1 1.5 2 2.5 30

3neighbours of point q

0 0.5 1 1.5 2 2.5 30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.9overlapping of P and Q pattern at 0.4 diff 4d ref

Performance with a real fingerprint

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Template Pattern "P"

0 0.5 1 1.5 2 2.5 3 3.5 40

4neighbours of point qInput realfingerprint "Q"

0.5 1 1.5 2 2.5 32

5Verfication of matching by overapping of P and Q pattern

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 wamelen’s 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

0 50 100 150 200 2500

no of total points for match

Comparision of performance

Wamelen's Algo

New Method

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:1. 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:1. Sharma Neeraj, Choi Nam Seok, Lee Joon Jae,

“Fingerprint Minutiae Matching Algorithm Using Distance Distribution Of Neighborhood”, MITA (2007), 21-24.

2. 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.

References1. 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.

3. 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.

4. Maltoni D., Maio D., Jain A.K., Prabhakar S. :”Handbook of Fingerprint Recognition”, Springer 2003.

5. 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.

6. 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.

7. 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.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

Magnitude of added noise in x & y direction

frequency o

f part

agnitude t

Histogram pattern of Random noise

noise in x-dir

noise in y-dir

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.050

magnitude of noise added

frequency o

r nois

agnitude

Histogram pattern of normalized external noise

noise in x-dir

noise in y-dir

0 5 10 15 20 25 30 35 40 45 50-0.05

Index of point

f nois

dded in x

direction f

each p

Plot for values of noise in each point

noise in x

noise in y

0 5 10 15 20 25 30 35 40 45 500

f nois

dded in x

direction f

each p

Index of particular point

Plot of random noise added in both direction

(c) (d)

Master Thesis Presentation, 14Dec07 Pair Wise Distance Histogram Based Fingerprint Minutiae Matching...

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