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CHAPTER 3

FINGERPRINT ENHANCEMENT

Fingerprint image quality plays an important factor in the

performance of any Automatic Fingerprint Identification System (AFIS).

Since the quality of the image is used to evaluate the system performance,

most of the fingerprint images taken with the use of fingerprint sensors are

subjected to enhancement process. Thus fingerprint image enhancement

forms the kernel problem of any fingerprint based recognition system. The

quality of the fingerprint image is degraded by skin conditions like wet or dry

skin, cuts and bruises, sensor noise, non-uniform contact with sensor surface

and inherently low quality fingerprint images like images of elder people,

laborers etc. The main aim of fingerprint image enhancement is to eliminate

noise, improve image quality, make feature extraction easy, increase the

recognition rate and ensure low error rate.

A significant percentage of fingerprints are of poor quality and

hence effective enhancement process must be applied on those images before

recognition. There are a number of fingerprint enhancement techniques

available in the literature for enhancing the low quality images but the

complexity and uncertainty found in those techniques leads us in to a difficult

situation while learning and teaching a system for appropriate recognition.

The proposed Improved Laplacian based Pyramidal Decomposition (ILPD)

method is an effective method for improving the quality of the images which

are of poor quality.

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3.1 IMPROVED LAPLACIAN BASED PYRAMIDAL

DECOMPOSITION (ILPD) FOR FINGERPRINT

ENHANCEMENT

Fingerprint recognition system depends on the quality of the input

image. To improve the quality of the image and to increase the recognition

rate and to ensure low error rate, the fingerprint is first subjected to

enhancement technique. The enhancement procedure involved in ILPD

method is based on local linear symmetry features which are sympathetic for

reliable minutiae extraction. The enhancement process is applied

progressively. This method avoids block-wise operations in the spatial

domain. Both absolute frequency and orientation information of the

fingerprint pattern are utilized to obtain the enhanced fingerprint image. The

former is implemented by exploiting several levels of band pass pyramid

independently. The typical ridge valley flow is enhanced using directional

averaging and the structure tensor directions (linear symmetry features) at

each level. The processing at lowest levels adds fidelity and details whereas

the rough ridge-valley flow is cleaned and gaps are closed at higher levels.

ILPD method is based on the concept image pyramiding or Multi-

Resolution Analysis (MRA) which is defined as the process of analyzing a

signal at multiple frequency levels. These methods are normally used for

image compression and medical image processing. Their significance to

fingerprint enhancement has not been quantified before in the survey. Since

the pertinent information in any image is concentrated within a few frequency

bands, the fingerprint image is decomposed to get different sub images in the

spatial domain.

The proposed ILPD method for enhancement is illustrated in Figure

3.1(the shaded blocks shows the additional process involved in the proposed

technique). The original image is subjected to pyramidal decomposition

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where the image gets divided in to three levels. Then each level separately

undergoes orientation estimation process using linear symmetry features

followed by directional filtering. The output is then reconstructed to produce

the enhanced image. Since this image has certain blurring effect, image

sharpening is applied to obtain the final enhanced version of the fingerprint

image.

Figure 3.1 Improved Laplacian based Pyramidal Decomposition (ILPD)

The exhaustive steps involved in the proposed enhancement

technique are shown in Figure 3.2 and are discussed in detail as follows:

Original Image

Pyramidal Decomposition

Orientation Estimation

Inverse Filtering

Wiener Filtering

Contrast Enhancement

Directional Filtering Pyramidal Reconstruction

Image Sharpening

Enhanced Image

Local Orientation Estimation

Linear Symmetry Features

Gabor Filters

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3.1.1 Pyramidal Decomposition (PD)

A pyramidal decomposition needs geometric transformation where

the image gets increased or decreased based on a particular scaling factor.

Thus the process consists of Gaussian like pyramids and Laplacian like

pyramids. Gaussian like pyramidal function decomposes the image into four

sub images. In Laplacian like pyramid the reduced images are expanded and

each of them is subtracted from the next lower level to yield the final three

sub images. To create the desirable Gaussian like and Laplacian like

pyramids, two functions namely reduce (I, k) and expand (I, k) are defined.

Here I is the image which decreases and increases by a factor k respectively.

The function reduce (I, k) will low pass the image using the Gaussian kernel,

where the original fingerprint image is reduced by a factor k, thereby reducing

the original image in to four sub images.

Figure 3.2 Detailed Steps in ILPD

A two dimensional Gaussian function G(x, y) of an image f (x, y) is

defined as shown in Equation (3.1).

LPD

Original Fingerprint

l1

l2

LS3

LS

LS

l3

Enhanced Fingerprint

LS

LS2

LS1 OE

OE

OE

DF

Pyramidal Reconstruction DF

DF

Image Sharpening

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(3.1)

where the coefficient A is the amplitude at the coordinate points (x, y), (x0, y0)

is the center point of the image f (x, y) and are the x and y spreads of

the blob. The original image is convoluted with a Gaussian smoothing filter to

remove the white Gaussian noise. The idea behind Gaussian smoothing is to

use the two dimensional distribution as a point spread function and it is

commonly achieved using convolution. The two dimensional convolution is

performed by first convolving with a one dimensional Gaussian along x axis

and then convolving with another one dimensional Gaussian along y axis. The

Gaussian smoothed image is reduced based on the following Equation (3.2).

(3.2)

where, is the original fingerprint image , k is a constant reducing factor, say

0.5 and g1 is the reduced fingerprint. Similarly, Equations (3.3) (3.5) are

implemented for dividing the image in to several sub bands using pyramidal

decomposition method.

(3.3)

(3.4)

(3.5)

where g2, g3 and g4 are the decomposed low pass filtered sub images. To create

images containing only band limited signals of the original image, expand the

three images g2, g3 and g4 using Laplacian like pyramidal function which

acts as a band pass filter by a factor k and subtract each of them from the next

lower level yielding l1, l2 and l3 as shown in Equation (3.6)-(3.8).

(3.6)

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(3.7)

(3.8)

where l1, l2 and l3 are expanded images and g1, g2, g3 and g4 are images that

are obtained using Gaussian like formula, k is a constant factor. l1, l2 and l3

contain the low, medium and high frequencies (ridge-valley patterns) of the

original fingerprint. The above said process is shown in Figure 3.3.

Figure 3.3 Steps in Pyramidal Decomposition (PD)

3.1.2 Orientation Estimation (OE)

Before determining the orientation of the fingerprint, the three

bands of images (de-noised image bands) is subjected to inverse filtering and

wiener filtering. When convolution is applied, the image gets blurred or

Original fingerprint

image

g1

g2

g3

g4

expand

expand

expand

sub

sub

sub

l3

l2

l1

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corrupted. The quickest and easiest way to restore the image is by inverse

filtering. The inverse filtering is a restoration technique for de-convolution,

i.e., when the image is blurred by a known low pass filter, it is possible to

recover the image by using a form of high pass filter called as inverse filtering

or generalized inverse filtering. However, inverse filtering is very sensitive to

additive noise.

The wiener filtering is a linear estimation of the original image. The

wiener filtering executes an optimal tradeoff between inverse filtering and

noise smoothing. It removes the additive noise and inverts the blurring

simultaneously. The wiener filtering is most favorable in terms of the mean

square error. In other words, it minimizes the overall mean square error in the

process of inverse filtering and noise smoothing. These two levels of filtering

are added to improve the estimation process which uses the Linear Symmetry

(LS) features for extracting the local structure information

(Nilsson & Bigun, 2001). As shown in Figure 3.4, before orientation

estimation, the next step is Contrast Enhancement (CE). It is the process of

enhancing the contrast of the single band images using the formula given in

Equation (3.9).

(3.9)

Figure 3.4 Orientation Estimation (OE)

l1

l2

l3

CE OE

LS1

LS2

LS3

Denoising

Inverse filtering

Wiener filtering

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Using the above formula, the contrast of the decomposed single

band images l1, l2 and l3 are enhanced using the Equations (3.10) to (3.12).

(3.10)

(3.11)

(3.12)

is used to depreciate small vectors of size x in comparison

with those of large magnitudes. After obtaining the contrast enhanced output,

orientation estimation is applied to produce the linear symmetry outputs LS1,

LS2 and LS3. There are two types of local features available for extracting

the local structure in a fingerprint namely Linear Symmetry (LS) and

Parabolic Symmetry (PS) features. These features are helpful in various areas

of image processing such as image quality estimation, texture analysis, optical

flow estimation and recognition of crash test cross trackers. The local

neighborhood where the gray value changes only in one direction is said to

possess linear symmetry property. The LS property is obtained using the LS

tensor image which is a three dimensional image consisting of three real

numbers. The LS tensor image is described by the complex expression shown

in Equation (3.13).

(3.13)

Here i= and are the derivatives of the image f in x and y directions.

The tensor image consists of one complex number called as I20 and one real

number I11. I20 is a vector image where each pixel is represented by a vector

and the length of the vector is a measure of the local LS strength and the

argument is the estimated local orientation as shown in Equation (3.14).

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(3.14)

w

convolution operator and is the scalar product having the Gaussian kernel.

The real number is represented as shown in Equation (3.15).

(3.15)

I11 is a scalar image and it measures the amount of local gray value change

and is always less than or equal to . The ridge-valley orientation of

the contrast enhanced levels l1, l2 and l3 are estimated using the

Equation (3.16).

; for each level i (3.16)

In the above equation, acts as an upper boundary for the linear

symmetry certainty, and by dividing through , unreliable orientations

are attenuated, whereas the strong ones are promoted. is a complex valued

image with being the magnitude estimation and angle of gives the

local orientation of the image. contains the most localized orientation

information and the higher pyramid levels and contains a coarse

orientations of a

band-pass filter/Laplacian pyramid are found more robust than the

orientations estimated by a low-pass pyramid/Gaussian pyramid.

3.1.3 Directional Filtering (DF)

Pyramidal directional filtering method is an effective method to

enhance the images by improving the PSNR (Peak Signal-to-Noise) value and

also it removes the sweat pores. Gabor filter is used for achieving the above

said purpose. Normally, Gabor filters are characterized by orientation,

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frequency and sensitivity. In general, Gabor filters are supported by a set of

band pass filters for its complete operation. This type of filtering is performed

to preserve the ridge structures. This band pass filter bank is tuned to the

corresponding local frequency and orientation for each neighborhood and

they are used to obtain the first order and second order derivative patterns

which are used for further processing. The general form of Gabor filter is

given in Equations (3.17) (3.19).

(3.17)

here, and (3.18)

(3.19)

where and are the standard deviations of the Gaussian envelope along

the x and y axes respectively, is the orientation of the filter and f is the frequency of the sinusoidal wave. The orientations that are considered in Gabor filters are 0, 45, 90, 135, 180, 225, 270, 315 and 360. The output form Gabor filtering consists of real part and imaginary part and these features cannot be stored directly and hence statistical measures are taken for storage purpose. Gaussian filters are used to obtain the first order and second order derivative patterns which are used for further processing. Directional averaging is applied to all levels independently. The local filtering

direction within follows the ridges/valleys of the fingerprint and it is given

by the Equation (3.20).

(3.20)

Pixels with less than (a pre-determined threshold) are

assigned a value zero, thus achieving segmentation of the fingerprint from the background (having more noisy regions). If is greater than (another

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pre-determined threshold, greater than ), a reasonable quality with the

presence of ridge-valley pattern at level i is ensured and the above said filtering is done. In general, and are set below 0.5. This type of

directional filtering adaptively increases the smoothing amount and direction along the ridge-valley structures. Fine minutiae points are preserved in the lowest pyramidal level l1 because filtering directions are sensitive to

them. At the higher pyramidal levels l2 and l3, the rough ridge-valley flow is

smoothed and gaps that are caused by scars are closed because and contain the global orientation.

3.1.4 Pyramidal Reconstruction (PR)

After obtaining the directional filtering output of the image, the

image is reconstructed as shown in Figure 3.5 and it follows Equation (3.21).

From the Figure 3.5, it can be seen that is expanded and added with the DF

of LS2 to get the reconstructed image L3. Similarly, the obtained L3 is

expanded and added with the DF of LS1 to get the reconstructed image L2.

To conclude, the obtained L2 is lengthened to produce the reconstructed image L1.

Figure 3.5 Steps in Pyramidal Reconstruction (PR)

LS1

LS2

LS3

Expand

L3 Reconstructed

Expand

L2

Reconstructed

DF

DF

Expand

L1

Reconstructed

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fp =

l1;

expand (l3, k) + l2 (3.21)

3.1.5 Image Sharpening (IS)

The final enhanced version of the original fingerprint is generated

using a contrast enhancement process called as image sharpening which improves the PSNR image. After the reduction and reconstruction of image

bands, there is a possibility that some unwanted data can get in to the enhanced fingerprint image. In addition to this, while reconstructing the

decomposed pyramid levels, the image gets blurred. To recuperate the

original image, image sharpening (un-sharp filter) is applied after reconstruction to produce the final enhanced output. An un-sharp filter is an

operator that is used to sharpen images thereby enhancing the contrast of the

image. The input-output relation for the un-sharp masking filter is shown in Equation (3.22).

Z (3.22)

In the above equation X and are the input and output images

and is a positive constant which controls the fraction of the high pass

filtered image Z to be added to the input image. The value of must be in

the range 0.0 to 1.0 and the default value for is 0.2.

3.2 RESULTS AND DISCUSSION

Fingerprint images are taken from the FVC 2004 database. Using

MATLAB Version 7.9 on Windows 7 Operating System the work is

implemented. To enumerate the capability of the proposed enhancement method, it is required to test them on very low quality fingerprint data, where

consistent enhancement and minutiae extraction becomes indispensible.

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Hence FVC 2004 database is used, which was collected to provide a more

challenging bench mark for the state-of-the-art recognition systems. Also in

terms of impression quality, the FVC 2004 database is regarded as more

challenging than the entire earlier collected fingerprint databases. FVC 2004

databases are difficult than FVC 2002 and FVC 2000 due to the various

perturbations that are intentionally introduced. FVC 2004 database consists of

four different databases DB1, DB2, DB3 and DB4 which were collected by

(DB1), optical

on (DB4).

While collecting the fingerprint data in FVC 2004 database using

optical sensors, the perturbations that are added consists of the following: the

individuals were asked to place the finger in different positions, to exaggerate

skin distortion and rotation, to diverge the contact pressure applied to the

sensor surface and their fingers are additionally dried /moistened to impose

challenging the image quality conditions. FVC 2004 database contains 110

different fingers and eight different impressions of each finger yielding a total

of 880 fingerprints. Each database has two different sets A and B. Set A

contains the fingerprint images from the first 100 fingers and set B contains

the fingerprint image from the next 10 fingerprints. The size of DB1

fingerprint images is 640 x 480 (307Kpixels) taken at 500 dpi. Similarly, the

size of DB2 fingerprint images is 328 x 364 (19Kpixels) taken at 500 dpi, the

size of DB1 fingerprint images is 300 x 480 (144Kpixels) taken at 512 dpi

and the size of DB4 fingerprint images is 288 x 384 (108Kpixels) taken at 500

dpi.

In FVC 2004 database, for each person, eight representative

fingerprints are presented. These impressions are classified as good, medium

and bad quality images depending on eye perception. i.e., it is purely a subjective process. The images having visually high clarity with un-

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interrupted ridge flow and minimum scares are classified as good quality

images. The images with middle level of interruptions and scares are

classified as medium quality images. Visually poor quality images with high

impairments are classified as bad quality images. By considering the above

said factors, the quality of the image is decided. The original and the

enhanced fingerprint images before and after applying the proposed ILPD

model are shown in Figure 3.6.

Figure 3.6 Original and Enhanced Fingerprint Images

The histograms of the original and the enhanced fingerprints are

shown in Figure 3.7. It is clear from the histogram that the intensities are

uniformly distributed between the dark and the light pixels for the enhanced

image whereas the intensities are concentrated towards one end of the image

before enhancement.

Two metrics are used to measure the superiority of the enhanced

fingerprint image after applying the pyramidal decomposition model. They

are Peak Signal-to- Noise Ratio (PSNR) and Mean Square Error (MSE).

MSE represents the cumulative squared error between the reconstructed and

the original image. The low value of MSE represents the lower error in the

reconstruction of the image. The MSE value is computed as given by

Equation (3.23).

(3.23)

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(a) (b)

Figure 3.7 (a) Histogram of Original Fingerprint Image (b) Histogram of Enhanced Fingerprint Image

In Equation (3.23), M and N are the number of rows and

columns in the input images. The PSNR is a measure of the peak error

between two images in decibels. It is computed as shown in Equation (3.24).

(3.24)

Figure 3.8 Performance Analysis in terms of MSE Values

Here, R = 255. Thus PSNR compares how far the original image

and the reconstructed image are equal. Higher the value of the PSNR and

lower the value of the MSE represents the better quality of the enhanced

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image. Figure 3.8 plots the MSE values for LPD method and the proposed

ILPD method for 100 samples of FVC 2004 DB1-a database, where x axis

represents the number of samples and y axis represents the MSE values. It is

pragmatic from Figure 3.9, that the MSE values are reduced considerably for

ILPD method than the existing LPD method.

Figure 3.9 Performance Analysis in terms of PSNR Values

Figure 3.9 plots the PSNR values for LPD method and the proposed

ILPD method for 100 samples from FVC 2004 DB1-a database, where x axis

represents the number of samples and y axis represents the PSNR values. It is

observed from Figure 3.10, that the PSNR values are amplified considerably

for the proposed ILPD method than the existing LPD method.

Figure 3.10 (a) (l) shows the step by step procedure of a sample fingerprint

image from the FVC 2004 DB1-a database using the proposed ILPD method.

Pyramidal decomposition is done with the help of Laplacian like and

Gaussian like pyramidal fuctions. Gaussian like pyramidal function is

implemented using a function called fpecial in MATLAB which accepts

. This operation produces four sub images which are

then expanded to produce the three sub images with band pass effect as

shown in Figure 3.10 (b) - (d).

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(a) Input Image

(b)Decomposed Image -1

(c)Decomposed Image-2

(d)Decomposed Image-3

(e)Inverse Filtered image

(f)Wiener Filter Image

(g)DF-Image 1

(h) DF-Image 2

(i)Reconstructed Image-1

(j)Reconstructed Image-2

(k)Reconstructed Image-3 (l) Sharpened Image

Figure 3.10 Fingerprint Images showing the Step by Step Process of a Sample Fingerprint Image from FVC 2004 DB1- a Database using the proposed ILPD Method

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The ouput of inverse filtering and wiener filtering are shown in

Figure 3.10 (e) and (f) respectively. The directional filter outputs are shown

in Figure 3.10 (g) and (h). The next step is to get the reconstructed images and

are shown in Figure 3.10 (i) (k). The final enhanced version of the

fingerprint image is shown in Figure 3.10 (l).

Table 3.1 Comparative Analysis of various Image Enhancement Methods based on PSNR and MSE Values

Enhancement Technique PSNR MSE

Histogram Equalization 31.036 543.5

Gabor Filters (Hong et al 1998) 41.02 363.4

Directional Median Filters (Wu et al 2004) 38.24 302.9

LPD (Fronthaler et al 2008) 41.01 23.78

Proposed Method (ILPD) 41.75 4.34

Table 3.1 gives a comparative study on the proposed ILPD with the

various enhancement techniques based on its PSNR and MSE values. It is

sensible that the PSNR for the proposed ILPD is augmented and the MSE is

decreased than the other enhancement techniques. Table 3.2 shows the CPU

time needed for each and every step in the proposed ILPD model on Intel

Pentium-4 system with 1.82 GHZ processor.

The time needed for completing each and every step is calculated

by using the function cputime () in MATLAB. This function returns the total

CPU time in seconds from the time it was started. The total time needed for

completing the entire enhancement process is 0.356 seconds.

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Table 3.2 CPU Time for the Proposed ILPD Method on Intel Pentium-4 System with 1.82 GHZ processor.

Stages in ILPD method Time in Seconds

Pyramidal Decomposition (PD) 0.120

Orientation Estimation (OE) 0.075

Directional Filtering (PDF) 0.083

Pyramidal Reconstruction (PR) 0.031

Image Sharpening (IS) 0.048

Total Time 0.356

Figure 3.11 shows the CPU time needed for computation in terms

of seconds. From this graph it is comprehensible that the computation time is

low for the proposed fingerprint image enhancement method when compared

to the other methods.

Figure 3.11 Performance Analysis in terms of CPU Time

Interpreting Figure 3.12, it is concluded that the proposed method

has led to favorable performance among the given enhancement methods,

resulting in the lowest equal error rate on all the four FVC 2004 datasets.

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Figure 3.12 Performance Analysis in terms of EER

From all the above comparisons, it is observed that the proposed

ILPD method for fingerprint image enhancement produces healthier

performance both quantitatively and qualitatively when compared with other

enhancement methods. The proposed method takes less time taken for the

entire enhancement process completion with no blocking artifacts and also

this method produces low false minutiae recognition and the matching error is

reduced significantly by the usage of LS property. The usage of image scale

pyramid and directional filtering in spatial domain improves the

computational efficiency. A benefit of the proposed technique is that it is

possible to implement through fast signal processing techniques like 1D

filtering, pyramidal processing etc., that are applied directly to the original

gray scale images, thus avoiding morphological operations. Another

importance with the proposed method is that the local linear symmetry

features could provide added value in non-minutiae based fingerprint

recognition sytems also. The use of an image-scale pyramid and directional

filtering in the spatial domain for fingerpint enhancement process improves

the matching performance as well as the computational efficiency.