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Final Project Report

Fingerprint Enhancement and Identification

by

Adaptive Directional Filtering

EE5359- Multimedia Processing

Spring 2015

Under the guidance of

Dr. K. R. Rao

Submitted by

Vishwak R Tadisina

[email protected]

ID: 1001051048

Fingerprint Enhancement and Identification by Adaptive Directional Filtering

V. R. Tadisina

2 EE-5359 Multimedia Processing- Spring 2015

List of Acronyms:

1D- One Dimension

2D- Two Dimension

AFIS – Automatic Fingerprint Identification System

DC- Direct Current

ECTI-CON - Electrical Engineering/Electronics, Computer, Telecommunications

and Information Technology Conference

FBI – Federal Bureau of Investigation

FFT- Fast Fourier Transform

ICBA- International Conference on Bioinformatics and its Applications

ICPR – International Conference on Pattern Recognition

IEE – Institution of Electrical Engineers

IEEE- Institute of Electrical and Electronics Engineers

ISCV – International symposium on Computer Vision

LCNS- Lecture Notes in Computer Science

LPF- Low Pass Filter

MATLAB – Matrix Laboratory

MTF – Modulation Transfer Function

WACV- Winter Conference on Applications of Computer Vision


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Index

S. No. Chapter Name Pg. No

1 Introduction 4

2 Structure of a fingerprint 5

3 Algorithm for Fingerprint Enhancement 7

3.1 Normalization 9

3.2 Ridge orientation and Frequency 9

3.3 Directional Filtering 12

3.3(a) Butterworth Filter 14

3.3(b) Gabor Filter 15

4 Fingerprint Identification 17

4.1 Reference Point Location 18

4.2 Feature vector 19

4.3 Fingerprint Matching 20

5 Implementation 22

6 Scope of the Project 27

7 References 27


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1. Introduction A person can be recognized using different means of identification, but identifying

a person based on the biometrics has become important in current diverse businesses

like law enforcement, information system security, finance physical access control

etc. [4]. Fingerprint based identification is one of the most important biometric

technologies which has drawn a substantial amount of attention recently [4]. It is one

of the most reliable mode of authentication. It has been extensively used by forensic

experts in criminal investigations for decades [2]. The best aspect of fingerprint-

based identification is that the fingerprints of a person are unique and does not alter

with aging of an individual [1]. Law enforcement agencies developed a method to

manually match fingerprint. But this method is tedious and time taking. So in early

1960s automatic fingerprint identification system (AFIS) [2] was started. There are

different ways for obtaining a fingerprint. It can be done either by digitalizing the

image taken by ink or by using inkless scanners. So from this it can be observed that

the reliability of a fingerprint identification method depends mainly on the quality

of the extracted features (minutiae) [1]. Various processing stages are included in an

AFIS as shown in Fig. 1 [11]. Representation of fingerprints plays a vital role for

automation in AFIS. This representation should have the following properties.

1. Keep back the uniqueness of each fingerprint in various levels of resolution.

2. Distinct characteristics of a fingerprint can be estimated easily.

3. Easy to apply automatic matching algorithms.

4. Immune to noise distortions.

5. Effective and simple representation [11].


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Fig. 1 Stages in an AFIS [11].

2. Structure of a fingerprint: An image of the surface of the skin of the fingertip is called a fingerprint. It consists

of ridges (black lines) separated by valleys as shown in Fig. 2 [2]. The design of the

ridge in a fingerprint can be depicted as an oriented texture pattern with constant

prevalent spatial frequency and orientation in a local neighbourhood. Orientation

depends on flow pattern of the ridges, and frequency on inter-ridge spacing [2].

Fig. 2 Ridges and valleys in a fingerprint image [2]


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The places which are visually striking on the ridge pattern of a fingerprint are called

singularities. There are two types of fingerprint singularities: core and delta. The

ridges of a fingerprint have irregularities, such as ridge endings, bifurcations,

crossovers, short ridges, etc. shown in Fig. 3 [11]. These anomalies can be used for

manual or automatic fingerprint identification and they are called minutiae. In a good

quality fingerprint, 60 to 140 minutiae can be found, but number of minutiae varies

from fingerprint to fingerprint [2]. The characteristics of fingerprint images are

shown in Fig. 4 [2].

Fig. 3 Bifurcations and short ridges [11]

Fig. 4 A fingerprint image with marked singularities, minutiae and the frequency spectra corresponding to the local regions [2].


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3. Algorithm for Fingerprint Enhancement:

There are numerous algorithms for fingerprint enhancement [4]. An ideal algorithm

must increase the contrast between the ridges and valleys of a fingerprint for visual

examination or automatic feature extraction. In this algorithm during the processing

of each pixel, a local neighbourhood of that pixel is considered. Directional filters

are used as the ridges and valleys have well-defined frequency and orientation in the

local area. Here the filtering process is adaptive as the parameters of these directional

filters depend on the local ridge frequency and orientation. So in frequency domain,

directional filters are used for fingerprint enhancement [2].

The flowchart of the fingerprint enhancement algorithm is shown in Fig. 5 [4]. The

main steps of the algorithm include:

1. Normalization: To obtain a pre-specified mean and variance, an input

fingerprint image is normalized [2].

2. Local orientation and Frequency estimation: The normalized input fingerprint

image is used for computing orientation and frequency images [2].

3. Region mask estimation: Each block in the normalized input fingerprint image

are sorted out into a recoverable or an unrecoverable block to find a region

mask estimate [2].

4. Filtering: An enhanced image is obtained from the ridge-and-valley pixels in

the normalized input fingerprint image by using a bank of Gabor filters or

Butterworth filters that are tuned to local ridge orientation and ridge frequency

[2].

Fig. 5 A flowchart of fingerprint enhancement algorithm [4]


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Fig. 6 Various stages in a fingerprint enhancement and identification algorithm [15]

Fig. 7 In (a) the pixel with three neighbours is a ridge bifurcation and in (b), pixel with only one neighbour is a ridge ending [15].


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3.1 Normalization:

Normalization is a process that is pixel wise. The clarity of the ridge and valley

structures are not affected by normalization. It inhibits the variations in grey-level

values along ridges and valleys [2].

Let, I(x, y) denote the grey-level value at pixel (x, y), Mi and Vi denote the estimated

mean and variance of I, respectively, and Ni(x, y) denote the normalized grey-level

value at pixel (x, y). The normalized image is defined as follows [2]:

Ni(x, y) =

{

M0 +√

V0(I(x, y) − Mi)2

Vi, if I(x, y) > Mi

M0 −√V0(I(x, y) − Mi)

2

Vi, Otherwise

(1)

M0 and V0 are the desired mean and variance values, respectively [2].

3.2 Ridge orientation and Frequency:

The orientation field O is defined as a P×Q image (called orientation or directional

image), where O (i, j) represents the local ridge orientation at pixel (i, j). It is used

for fingerprint enhancement, classification and ridge detection [4]. Block wise

representation is used for local ridge orientation. There are a number of techniques

that can be used to calculate orientation fields [4]. Least mean square orientation

estimation based on gradient is used [12]

At first, the input fingerprint image is arranged into non-overlapping blocks

of size W × W.

The gradients gx(i, j) and gy(i, j) for each pixel (i, j) of the block, are calculated.

Simple Sobel operator [4] is used for calculating the gradient.

The average squared gradient [g̅sx, g̅sy ] [12] in a block specified by window

size W is given by:


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[g̅sxg̅sy

] =

[ ∑ ∑ [gx

2(u,v)−gy2(u,v)]

j+W2

v=j−W2

i+W2

u=i−W2

∑ ∑ 2 gx(u,v)gy(u, v)j+W2

v=j−W2

i+W2

u=i−W2 ]

(2)

The average gradient ϕ direction and dominant local orientation for the block are

given by:

Φ(i, j) = 1

2 tan−1

(

∑ ∑ 2 gx(u, v) gy(u, v)

j+W2

v=j−W2

i+W2

u=i−W2

∑ ∑ [gx2(u, v) − gy

2(u, v)]j+W2

v=j−W2

i+W2

u=i−W2 )

(3)

O(i, j) = Φ(i, j) +

π

2 (4)

as the angle of gradient is perpendicular to the ridge orientation a correction of 90

degrees is essential. Here blocks of size W × W for orientation estimation and

gradients gx and gy are used and calculated using Sobel operator [2].

To remove faulty ridge orientation values at the distorted and noisy regions

further smoothing is required on orientation values. It is done by converting

orientation image into a continuous vector field as shown in the Fig. 8, defined

as follows:

Ψx(i, j) = cos[2 O(i, j)] (5)

Ψ𝑦(𝑖, 𝑗) = sin[2 𝑂(𝑖, 𝑗)] (6)

where Ψx(i, j) and Ψy(i, j) are the x and y components of the continuous vector field

respectively.


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Fig.8 A continuous vector field formed by a local orientation image with a block of size W x W and center O (i, j).

Then the filter implementation [1] is given by,

Ψx′(i, j) = ∑ ∑ L(u, v)

WΨ/2

v=−WΨ/2

Ψx(i − uW, j − vW)

WΨ/2

u=−WΨ/2

(7)

Ψy′(i, j) = ∑ ∑ L(u, v)

WΨ/2

v=−WΨ/2

Ψy(i − uW, j − vW)

WΨ/2

u=−WΨ/2

(8)

O′(i, j) =

1

2 tan−1 (

Ψy′(i, j)

Ψx′(i, j)

) (9)

where L is a 2D LPF, W is the block size and WΨ × WΨ specifies the size of the

filter, Ψx′(i, j) and Ψy

′(i, j) are the x and y components of the continuous vector field

respectively after smoothing.

Local ridge frequency can be estimated by:

The grey values of all the pixels situated in each block are projected along a

direction perpendicular to the local orientation and computed. This projection

forms a 1D wave with the local extrema relevant to the ridges and valleys of

the fingerprint [2];


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The average number of pixels between two consecutive peaks in the 1D wave

generated above is denoted by K (i, j). The frequency ω(i, j) is computed as,

𝜔(i, j) =

1

K (i, j) (10)

in order to explain the above estimation a modeled fingerprint image instead

of the original raw fingerprint images can be used. A one dimensional (1D)

modeled fingerprint image is used. A finite rectangular wave (as seen in

Fig. 9) which is regarded as the simplification of the projection of all grey

values of the pixels in a direction, normal to the local orientation of the block

with local extrema corresponding to the ridges and valleys of the fingerprint.

Fig. 9 Finite rectangular wave as a modeled fingerprint [15].

3.3 Directional filtering:

In frequency domain local ridge spacing (ρ) gives radial component and local ridge

orientation (ϕ) gives angular component of a filter.

An ideal model of band pass directional filter in Fourier domain [1] can be expressed

using polar coordinates (ρ, ϕ) as


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H(ρ, ϕ) = Hr(ρ)Ha(ϕ) (11)

Hr(ρ) and Ha(ϕ) depend on local ridge spacing and local ridge orientation

respectively [12].

Fig. 10 Filter in Fourier domain (a) band pass (radial) component, (b) directional (angular) component, (c) combination of previous two [1].

Instead of applying appropriate filter for each pixel, a finite number of predefined

filters (regarding to finite number of discrete orientations, and fixed frequency) are

applied. The degradation of the filter image and number of filters must be small and

it can be obtained in following way:

1. Either an average ridge frequency or a constant is set empirically for entire

database set to eliminate filter dependence on local ridge frequency. So that the

context of the filter is determined only by the orientation

2. A fixed number (8 or 16) of orientation values by discretization is formed from

which a small number of directional filter components can be obtained.

The Fourier transform Pi, i = 1, 2, . . . , n of the filters is pre-computed and stored.

Filtering an input fingerprint image q(x, y) with dimensions C × D is performed as

follows [3]:

The 2D-FFT F(u, v) of input fingerprint q(x, y) image is computed,

𝐹(𝑢, 𝑣) =1

𝐶 . 𝐷 ∑∑𝑞(𝑥, 𝑦) 𝑒𝑥𝑝 [−𝑗2𝜋 (

𝑢𝑥

𝐶+𝑣𝑦

𝐷)]

𝐷−1

𝑦=0

𝐶−1

𝑥=0

(12)

here u= 0, 1, 2,…, 31 and v = 0, 1, 2,…, 31.

Each directional filter Pi is point-by-point multiplied by F(u, v), obtaining n

filtered image transforms PFi(u, v), i = 1, 2, . . . , n.

Inverse 2D-FFT is computed for each PFi(u, v) resulting in ‘n’ filtered images

pfi(x, y), i = 1, 2, . . . , n (spatial domain) [3]. For x = 0, 1, 2 …31 and y = 0, 1, 2 ...31.


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𝑝𝑓𝑖(𝑥, 𝑦) = ∑∑𝑃𝐹𝑖(𝑢, 𝑣) 𝑒𝑥𝑝 [𝑗2𝜋 (𝑢𝑥

𝐶+𝑣𝑦

𝐷)]

𝐷−1

𝑣=0

𝐶−1

𝑢=0

(13)

All the value of pixels in one block of enhanced image take on the same position

from the filtered image which emphasizes determined orientation for corresponding

block. So enhanced image can be obtained from the filtered image [3] as seen in

Fig. 11.

Fig. 11 Block diagram of a fingerprint enhancement algorithm [3]

3.3(a) Butterworth filter:

The band pass Butterworth filter [14] for radial component Hr(ρ) of order k, having

center frequency ρ0 and bandwidth ρBW [14] is given as:

Hr(ρ) = √(ρρBW)

2k

(ρρBW)2k + (ρ2 − ρ0

2)2k (14)

Then (15) gives the directional component


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Ha(ϕ) = {cos2

π(ϕ − ϕ𝑐)

2ϕBw if ϕ < ϕBw

0 Otherwise

(15)

where ϕBW is the angular bandwidth, and ϕc is the orientation of the filter [14].

Fig. 12 Butterworth bandpass frequency response

3.3(b) Gabor Filter:

Frequency-selective and orientation-selective properties of Gabor filters [6] make

them significant both in frequency and spatial domain. By simple adjustment of

mutually independent parameters, configuration of Gabor filters can be varied based

on different shapes, orientations, width of band pass and central frequencies. The

significant characteristic of a Gabor filter is, if properly tuned it can perform

frequency selective filtering on an image maintaining only regions of a given

frequency and orientation. This fundamental implications are used for research in

fingerprint image analysis and enhancement using this filter [4, 6].

An even symmetric Gabor filter general form [4] in the spatial domain is given by


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h(x, y, ϕ, Ω) = exp [−0.5 {(x

σx


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Fig. 13 An even-symmetric Gabor filter. (a) The Gabor filter with f = 10 and ϕ = 0. (b) The corresponding MTF [4].

4. Fingerprint Identification For fingerprint identification it is ideal to get representations of fingerprints which

are invariant with reference to scale, translation and rotation [22]. The scale variance

difficulty can be eliminated easily since most fingerprint images could be scaled as

per the dpi specification of the sensors. To remove the other two variance problems

a reference frame can be formed which is rotation and translation invariant [22]. The

translation invariance is handled by establishing a single reference point (core point).

This reference point is obtained based on the assumption that all the fingerprints are

vertically oriented. But practically the fingerprint images may be oriented up to

± 45º away from actual assumed vertical orientation. Cyclic rotation of the feature

values in the Fingercode in the matching stage handles this image rotation partially

[22].

4.1 Reference Point Location

Fingerprints have many perceptible landmark structures which can be used

collectively for finding a reference point [22]. The reference point or core point of a

https://www.google.com/search?es_sm=122&q=define+perceptible&sa=X&ei=SwM2VZz6D8r3sAXKtIGACw&ved=0CCQQ_SowAA


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fingerprint is the point at which the curvature of the concave ridges is maximum as

shown in Fig.14.

Fig. 14 Concave and convex ridges in a fingerprint image when the finger is positioned upright [22].

After finding the smoothened orientation image in section 3.2. From equation (9)

compute E, an image containing only the sine component of O′ [22]

𝐸𝑝(𝑖, 𝑗) = sin(O′(𝑖, 𝑗)). (24)

A label image A(i, j) which indicates the reference point is initialized. Integrate pixel

intensities R1 and R2 for each pixel (i, j) in Ep(i, j) as shown in Fig. 15. Assign the

value of their difference in corresponding pixels to A(i, j) [22]

𝐴(𝑖, 𝑗) = ∑𝐸𝑝(𝑖, 𝑗) −∑𝐸𝑝(𝑖, 𝑗).

𝑅2

𝑝=0

𝑅1

𝑝=0

(25)

On a large database a reference point algorithm is used to empirically determine the

regions R1 and R2 [22]. The maximum curvature in concave ridges can be captured

making use of the geometry of regions R1 and R2. Find the maximum value in

A(i, j) [22] and assign its coordinate to the core, i.e., the reference point.


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Fig. 15 Regions for integrating E pixel intensities for A (i, j) [22].

After finding the core point the fingerprint image undergoes directional filtering in

eight different directions.

4.2 Feature vector

From [22] it is clear that a fingerprint image can be sectored into a total of 16 × 5 =

80 sectors (S0 through S79) whose core point [22] is the center of these sectors as

shown in Fig. 16.

Fig. 16 Reference point (x), the region of interest, and 80 sectors [22].

Let Fiϕ (x, y) be the ϕ - direction filtered image for sector Si. Now i ϵ {1, 2, 3,…79}

and ϕ ϵ {0º, 22.5º, 45º, 67.5º, 90º, 112.5º, 135º, 157.5º}. The feature value Viϕ [22]

is the average absolute deviation from mean defined as

𝑉𝑖𝜙 = 1

𝑛𝑖 (∑|𝐹𝑙𝑖𝜙(𝑥, 𝑦) − 𝑃𝑙𝑖𝜙 |

𝑛𝑖

𝑙=0

) (26)


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where ni is the number of pixels in Si and Pi ϕ is the mean of pixel values in a sector.

The average absolute deviation of each sector in each of the eight filtered images

defines the components of the feature vector.

4.3 Fingerprint matching

Based on the Euclidean distance between the corresponding Fingercode, fingerprint

matching is done. A Fingercode is a compact length code obtained by the filter-based

bank algorithm in [22] which uses a bank of Gabor filters to capture both local and

global details in a fingerprint. Reference point removes the translation variance

problem. To eliminate rotational variance the Fingercode is rotated cyclically [22].

The steps corresponding to single step cyclic rotation [22] of the features of the

Fingercode are described by (27)-(29). This corresponds to a feature vector which

would be obtained if the image were rotated by 22.5º. A rotation by R steps

corresponds to a rotation R × 22.5º of the image. A positive and negative rotation

implies clockwise and counterclockwise rotation respectively. The Fingercode [22]

obtained after R steps of rotation is given by

𝑉𝑖𝜙

𝑅 = 𝑉𝑖´𝜙´ (27)

𝑖´ = (𝑖 + 𝑚 + 𝑅)|𝑚| + (𝑖

𝑚) ×𝑚 (28)

𝜙´ = (𝜙 + 180º + 22.5º × 𝑅)|180º| (29)

where m is the number of sectors in a band, i ϵ {0,1 , 2,…79} and ϕ ϵ {0º, 22.5º, 45º,

67.5º, 90º, 112.5º, 135º, 157.5º}. Five templates are stored corresponding to the

following five rotations of the Fingercode: 𝑉𝑖𝜙−2, 𝑉𝑖𝜙

−1, 𝑉𝑖𝜙0 , 𝑉𝑖𝜙

1 𝑎𝑛𝑑 𝑉𝑖𝜙2 . To obtain

five different matching scores, input Fingercode is matched with these five

templates. The Fingercode corresponds to a rotation of 22.5º. But the fingerprints

are rotation invariant to small rotation within ± 11.25º. So another feature vector for

each fingerprint is generated which corresponds to a rotation of 11.25º. To generate

this, the original fingerprint is rotated by 11.25º. From the above rotated fingerprint

image five more templates are formed. So a total of ten templates for each fingerprint

[22] are formed as shown in Fig. 17. Fingercodes are generated for every 11.25º of

rotation of the fingerprint image this takes care of rotation invariance [21]. The

matching is done by taking into account the minimum matching distance score of

the ten stored templates [22]. Matching can be done with this minimum score which


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gives the best alignment of the two fingerprints. So the fingerprints are matched

using this minimum score.

Fig. 17 Examples of 640-dimensional feature vectors: (a) First impression of finger 1, (b) second impression of finger 1, (c) Fingercode of (a), (d) Fingercode of (b), (e) first impression of finger 2, (f) second impression of finger 2, and (g) Fingercode of (e), and (h) Fingercode of (f) [22].


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5. Implementation The performance of the proposed algorithm is tested using the fingerprint database

in [24]. The fingerprint images in this database are greyscale images. They have a

spatial resolution of 96 dpi and an amplitude resolution of 8 bits per pixel.

Dimension of each image is 640 x 480 pixels.

Normalization

Parameters for normalization are set to 100 for both M0 and V0. The ridge

orientations were discretized to 8 values (step 22.5◦). The original fingerprint

images and their normalized images are shown in the Fig. 18.

Fig. 18 a, b, c and d: Original fingerprint images; i, ii, iii and iv: Corresponding normalized images.

Ridge orientation and frequency

To determine ridge orientation, the input fingerprint images are divided into non-

overlapping blocks of size 8 × 8. Then the gradients gx(i, j) and gy(i, j) for each pixel

(i, j) of the block, are calculated by Sobel edge-emphasizing filter. The gradient and

edge detected images are shown in Fig. 19. Then all these gradient values are used

to compute average squared gradient and the average gradient ϕ direction. This

image is smoothened further using a 2D LPF to remove noise. Original fingerprint


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images and their orientation images are shown as quiver plots in the Fig. 20. A quiver

plot is vector plot which displays the direction of the ridges in the fingerprint as

arrows with components (u, v) at the points (x, y).

Fig. 19 (a), (b), (c) and (d) are original fingerprint images; (i), (ii), (iii) and (iv) are their respective Edge detected images; (1), (2), (3) and (4) are their respective Gradient images.


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Fig. 20 (a), (b) and (c) are original fingerprint images; (1), (2) and (3) are their respective orientation image quiver plots.


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Directional filtering

Bank of Gabor filters:

The inter-ridge distance in the fingerprint image is the main factor in determining

the parameters Ω, σx and σy, for optimal Gabor filter operation. The filter frequency

is the average ridge frequency Ω = 1/B where B is the average inter-ridge distance.

If Ω is too large spurious ridges are created in the filtered image, whereas if Ω is too

small nearby ridges are merged into one. The parameters are set to be Ω = 1/5, and

σx = σy = 4.0 [21]. Trade-off in selection of σx and σy is done based on empirical data

[5], so that the filter is robust to noise, but still can capture ridge information at fine

level. Eight different values for ϕ = iπ/8, i= 1, 2, …, 7 (0º, 22.5º, 45º, 67.5º, 90º,

112.5º, 135º, 157.5º) with respect to the x-axis are used. A 0º oriented filter

accentuates those ridges which are parallel to the x-axis and smoothens the ridges in

the other directions [21]. Filters tuned to other directions work in a similar way.

These eight directional-sensitive filters capture most of the global ridge

directionality information as well as the local ridge characteristics present in a

fingerprint [22]. Original fingerprint images and enhanced images obtained by

filtering with eight Gabor filter are shown in Fig. 21. To seize the whole global ridge

information in a fingerprint at least four directional filters are necessary [22], but in

order to capture local characteristics eight directional filters are required. So, four

directions are required for classification and eight directions for matching. Although

there is some redundancy among the eight filtered images, the verification accuracy

is improved by capturing both the global and local information [22].


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Fig. 21 (a), (b) and (c) are original fingerprint images; (1), (2) and (3) are the enhanced images obtained by directional filtering using a series of Gabor filters.


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6. Scope of the Project: The objective of this project is to apply the algorithm proposed in section 3 to

smudged and corrupted fingerprints to obtain enhanced images. This is done by

adaptive directional filtering in the frequency domain by using Butterworth [2] and

Gabor filters [1] for fingerprint image enhancement and also for removing noise.

MATLAB is used to normalize the corrupted fingerprints. Then the frequency and

ridge orientation are computed for each fingerprint image. After that the image is

filtered using directional filters. Here Butterworth and Gabor filters are used to

obtain an enhanced image. The quality of the images obtained from both filters is

compared visually. Fingerprint identification is done using MATLAB coding on the

filtered enhanced image by detecting reference point and storing a feature vector in

the form of a Fingercode in a data file. This data file is used as a database for

fingerprint matching [21].

7. References:

[1] A. M. Raiˇcevi´c and B. M. Popovi´c, “An Effective and Robust Fingerprint Enhancement by

Adaptive Filtering in Frequency Domain”, Facta Universitatis (NIS) Ser.: Elec. Energ.,

vol. 22, no. 1, pp.91-104, April 2009.

[2] J. E. Hoover, “The Science of Fingerprints: Classification and Uses”, Federal Bureau of

Investigation, Washington, D.C., Aug. 2006.

[3] B. G. Sherlock, D. M. Monro and K. Millard, “Fingerprint enhancement by directional

Fourier filtering,” IEE Proc. Vision Image Signal Process., vol. 141, no. 2, pp.87–94,

April 1994.

[4] L. Hong, Y. Wan and A. K. Jain, “Fingerprint image enhancement: Algorithm and

performance evaluation,” IEEE Trans. Pattern Anal. Machine Intell. vol. 20, no. 8,

pp. 777–789, Aug. 1998.

[5] A. Willis and L. Myers, “A cost-effective fingerprint recognition system for use with low-

quality prints and damaged fingertips,” Pattern Recognition, vol. 34, pp. 255–270,

Jan. 2001.

[6] J. Yang, L. Lin, T. Jiang and Y. Fan, “A modified Gabor filter design method for fingerprint

image enhancement,” Pattern Recognition Letters, vol. 24, pp. 1805–1817, Jan. 2003.

[7] L. Hong, A.K. Jain, S. Pankanti and R. Bolle, “Fingerprint Enhancement,” Proc. First

IEEE- WACV, pp. 202-207, Sarasota, Fla., Dec. 1996.

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