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CHAPTER 3
EFFICIENT MULTIMODAL BIOMETRIC
AUTHENTICATION USING FAST FINGERPRINT
VERIFICATION AND ENHANCED IRIS FEATURES
3.1 OVERVIEW
Due to sensitivity to noise, intra-class variability, data quality, non-
universality and other factors in many real world applications, unimodal
biometric systems often face significant limitations. It does not prove
effective in attempting to improve the performance of individual matchers in
such situations. By providing multiple pieces of evidence of the same identity,
multimodal biometric systems shown in Figure 3.1 seek to alleviate some of
these problems.
Figure 3.1 Overview of multimodal system using fingerprint and iris
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In this work, a multimodal biometric system to overcome the
limitations by using multiple pieces of evidence of the same identity is
implemented. However, due to its multiple processing stages the multimodal
biometric system is limited to the time constraints. To improve the speed of
authentication in the biometric system with acceptable accuracy, a dynamic
fingerprint verification technique fused with enhanced iris recognition using
the adaptive rank level fusion method is introduced. Various fusion
techniques including highest rank, borda count and logistic regression
methods were implemented. The system shows improvement in the False
Acceptance Rate (FAR) and Equal Error Rate (EER) curves when tested upon
the standard biometric dataset.
3.2 FINGERPRINT AUTHENTICATION SYSTEM
The two main topics of basic research under this solicitation
include: (i) measure the amount of detail in a single fingerprint that is
available for comparison, and (ii) measure the amount of detail in
correspondence between two fingerprints. The problem of finger print
individuality can be formulated in many different ways depending on which
one of the following aspects of the problem is under examination: (i) the
individuality problem may be cast as determining the probability that any two
individuals may have sufficiently similar fingerprints in a given target
population. (ii) Determine the probability of finding a sufficiently similar
fingerprint in a target population, when a sample fingerprint is given as input.
Figure 3.2 shows the sequential activities for a general fingerprint
identification system.
3.2.1 Segmentation
Figure 3.3 illustrates the results of segmenting a fingerprint image
based on variance threshold. The variance image in Figure 3.3(b) for the
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original image in Figure 3.3(a) shows that a very high variance value is
exhibited from the central fingerprint area, whereas a very low variance is
exhibited by the regions outside this area. Hence, to separate the fingerprint
foreground area from the background regions a variance threshold method is
used. As shown in Figure 3.3(c), the final segmented image is formed by
assigning the regions with a variance value below the threshold to a grey-level
value of zero. There is a trade-off involved when determining the threshold
value used to segment the image. If the threshold value is too large, results
have shown that foreground regions may be incorrectly assigned as
background regions. Conversely, if the threshold value is too small,
background regions may be mistakenly assigned as part of the fingerprint
foreground area. Hence, a variance threshold of 100 gives the optimal results
in terms of differentiating between the foreground and background regions.
Figure 3.2 Flowchart for fingerprint identification system
Figure 3.3 Segmentation using a variance threshold of 100
(a) Original Image (b) Variance Image (c) Segmented Image
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Hence, for discriminating the foreground area from the background
regions the variance threshold method is effective. There is a trade-off
involved when determining the threshold value used to segment the image.
Results have shown that foreground regions may be incorrectly assigned as
background regions, if the threshold value is too large. Conversely, if the
threshold value is too small, background regions may be mistakenly assigned
as part of the fingerprint foreground area. An optimal result in terms of
differentiating between the foreground and background regions is given by a
variance threshold of 100.
3.2.2 Fingerprint Image Enhancement
An important characteristic in a fingerprint image is the quality of
the ridge structures, as the ridges carry the information of characteristic
features required for minutiae extraction. Ideally, in a well-defined fingerprint
image, the ridges and valleys should alternate and flow in locally constant
direction. This regularity facilitates the detection of ridges and consequently,
allows minutiae to be precisely extracted from the thinned ridges. In this
work, the histogram equalization is applied for image enhancement.
3.2.2.1 Histogram equalization
The histogram of an image represents the relative frequency of
occurrence of the various gray levels in the image. Histogram modeling
techniques modify an image so that its histogram has a desired shape. This is
useful in stretching the low contrast levels of images with narrow histograms.
Histograms modeling have been found to be a powerful technique for image
enhancement.
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such t is uniform.
This mapping stretches the contrast (expands the range of gray levels) for
gray levels near the histogram maxima. The transformation improves the
detect ability of many image features by expanding the contrast for most of
the image pixels,. The probability density function of a pixel intensity level
is given by:
(3.1)
Where
0 <= rk<=1
- Number of pixels at intensity level k r
n - Total number of pixels.
The histogram is derived by plotting kr rp against kr . A new
intensity ks of level k is defined as:
(3.2)
The histogram equalization is applied locally by using a local
window of 11x11 pixels. This results in expanding the contrast locally, and
changing the intensity of each pixel according to its local
neighborhood. Figure 3.4 presents the improvement in the image contrast
obtained by applying the local histogram equalization. Figure 3.5 represents
the quality improvement after applying histogram equalization.
3.2.3 Fingerprint Enrolment
As the ridges carry the information of characteristic features
required for minutiae extraction, the quality of the ridge structures in a
fingerprint image is an important characteristic. Ideally, in a well-defined
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fingerprint image, the ridges and valleys should alternate and flow in the
locally constant direction. This regularity facilitates the detection of ridges
and consequently, allows minutiae to be precisely extracted from the thinned
ridges.
Figure 3.4 Histogram equalization
Figure 3.5 Output of histogram equalization
Inte
nsity
Fre
quen
cy
Probability Probability
Inte
nsity
Fre
quen
cy
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3.2.4 Reference Point Location
For establishing a reference point, since fingerprints have many
conspicuous landmarks, any combination of them could be used for
establishing a reference point. The point of maximum curvature of the ridges
in the fingerprint image is defined as the reference point of a fingerprint.
To align two fingerprint images, a reference point as well as the
orientation of each image must be located. The most commonly used
reference point is the core point. A core point is defined as the point at which
a maximum direction change is detected in the orientation field of a
fingerprint image or the point at which the directional field becomes
discontinuous. Several methods have been proposed for core point detection.
3.2.4.1 Orientation estimation
The orientation field of a fingerprint image defines the local
orientation of the ridges contained in the fingerprint as in Figure 3.7 and Figure
3.8 shows the orientation estimation for a fingerprint image. The least mean
square estimation method employed by Hong et al (1999) is used to compute
the orientation image. This is a gradient based method which proves to be
simple and most accurate with high quality images. However, instead of
estimating the orientation block-wise, their method has been extended into a
pixel-wise scheme, which produces a finer and more accurate estimation of the
orientation field.
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Figure 3.6 Regions for integrating pixel intensities in for computing
A(i; j)
Figure 3.7 The orientation of a ridge pixel in a fingerprint.
Figure 3.8 Orientation estimation of fingerprint image
1. A block of size W x W is centered at pixel (i; j) in the
normalized fingerprint image.
2. For each pixel in the block, compute the gradients (i; j) and
(i; j), which are the gradient magnitudes in the x and y
directions, respectively. The horizontal Sobel operator is used
to compute (i; j):
(a) Original Image (b) Orientation Image
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The vertical Sobel operator is used to compute (i; j)
3. The local orientation at pixel (i; j) can then be estimated using
the equations 3.3 to 3.5 as;
(3.3)
(3.4)
(3.5)
where
(i; j) - Least square estimate of the local orientation at
the block centered at pixel (i; j).
4. Smooth the orientation field in a local neighborhood using a
Gaussian filter. The orientation image is firstly converted into
a continuous vector field, which is defined as:
(3.6)
(3.7)
where and - x and y components of the vector field,
respectively.
After the vector field has been computed, Gaussian smoothing
is then performed as follows:
(3.8)
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(3.9)
where
G -- Gaussian low-pass filter of size
5. The final smoothed orientation field O at pixel (i; j)
is defined as:
(3.10)
Reference Point Detection: The reference point or the core point
of the fingerprint image is obtained using the following algorithm.
Compute the sine component (i, j) of the smoothed orientation
field becomes a reference point:
(3.11)
The sine component possesses an attractive characteristic in that it
reflects the local ridge direction. The sine component of a perfectly horizontal
orientates vertically. Due to the discontinuity property, the sine component
value always changes abruptly in areas near a reference point. Because of such
findings, the following procedure is added.
Initialize a two-dimensional (2-D) array and set all its entries to 0.
Scan the sine component map in a top-to-bottom, left-to-right manner. For
each sine component, (i, j)
threshold,
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(a) (b) (c) (d)
Compute the difference D
Compute the Ci(i,j)value
Figure 3.9 Examples of the results of reference point location algorithm
The result of the reference points found in the arch-type fingers is
shown in Figure 3.9 (a), (b), (c) and (d) . It can be observed that the locations
of the reference points are consistent in different impressions of the same
finger.
For each pixel (i, j) in E, integrate pixel intensities (sine component
of the orientation field) in regions RI and RII shown in Figure 3.6 and assign
the corresponding pixels in A the value of their difference:
(3.12)
By applying the reference point location algorithm over a large
database the regions RI and RII were determined empirically. The radius of
the semi-circular region was set equal to the window size w. The geometry of
regions RI and RII is designed to capture the maximum curvature in concave
ridges. Although this approach successfully detects the reference point in
most of the cases, including double loops, the present implementation is not
very precise and consistent for the arch type fingerprints because it is difficult
to localize points of high curvature in arch type fingerprint images.
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The entry Ci(i,j) is used to compute the continuity of a possible
reference point candidate and is defined as shown below:
(3.13)
The difference D in the circular mask indicates the extent of the
change of direction for the concave ridges. The position with the maximum
value is obtained after all the sine components have been scanned. In other
words, the location with the sharpest change in the orientation of the ridge
direction becomes a reference point.
Due to the presence of noises in a fingerprint image, it is not
uncommon that the location with an abrupt change in the orientation field is
mistaken as a false reference point. To alleviate the problem, the following
conditions must be checked to verify the genuineness of a reference point:
With the convergence property of the ridges curvature near the
reference point, a reference point should be located in the block
(i,j) at which the corresponding Ci(i,j)value > Ci threshold.
In general, if two reference point candidates have the same D
value, the one located at the bottom should be taken as the true
reference point
The above procedure is applied using a larger grid size (w=8) first
and then refine the grid size (w=3) to restrict the search in a localized
fingerprint image. The method not only increases the processing speed, but
also reduces the possible error due to scars or noises in the fingerprint image.
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3.2.5 Minutiae Extraction
The endings and bifurcations of the fingerprint images are known
as the minutiae which are shown in the Figure 3.10
Figure 3.10 Example of a ridge ending and a bifurcation
The most commonly employed method of minutiae extraction is the
CN concept. This method involves the use of the skeleton image where the
ridge flow pattern is eight-connected. The minutiae are extracted by scanning
the local neighborhood of each ridge pixel in the image using a 3 x 3window.
Figure 3.11 shows the result of performing minutiae extraction on a
fingerprint image and various process involved to achieve the goal.
3.2.5.1 Binarization
Most minutiae extraction algorithms operate on binary images
where there are only two levels of interest: the black pixels that represent
ridges, and the white pixels that represent valleys. The conversion of a grey
level image into a binary image is called Binarization. This improves the
contrast between the ridges and valleys in a fingerprint image, and
consequently facilitates the extraction of minutiae. The output of the binarized
image from the enhanced image (Figure 3.12 (a)) is shown in Figure 3.12 (c).
(a) (b)
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Figure 3.11 Results of performing minutiae extraction on a fingerprint
image
The binarization process involves examining the grey-level value of each pixel in the enhanced image, and, if the value is greater than the global threshold, then the pixel value is set to a binary value one; otherwise, it is set to zero. The outcome is a binary image containing two levels of information, the foreground ridges and the background valleys.
3.2.5.2 Thinning
The final image enhancement step typically performed prior to minutiae extraction is thinning. The morphological operation that successively erodes away the foreground pixels until they are one pixel wide is called thinning. A standard thinning algorithm is employed, which performs the thinning operation using two sub-iterations.
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(a) Enhanced Image (b) Binary Image (c) Thinned Image
The application of the thinning algorithm to a fingerprint image
preserves the connectivity of the ridge structures while forming a skeletonized
version of the binary image. This skeleton image is then used in the
subsequent extraction of minutiae.
Figure 3.12 demonstrates that the global thresholding technique is
effective in separating the ridges (black pixels) from the valleys (white
pixels). The results of thinning show that the connectivity of the ridge
structures is well preserved, and that the skeleton is eight-connected
throughout the image. In particular, Figure 3.12 (c) shows that the thinning
algorithm is able to accurately extract the skeleton of minutia points without
disrupting the continuity of the ridge flow pattern. Figure 3.13 shows the
output after applying binarization and thinning over the given input.
The CN value is then computed. Half the sum of the differences
between pairs of adjacent pixels in the eight-neighborhood is defined as the
CN value. Using the properties of the CN, the ridge pixel can then be
classified as a ridge ending, bifurcation or non-minutiae point. For example, a
ridge pixel with a CN of one corresponds to a ridge ending, and a CN of three
corresponds to a bifurcation.
Figure 3.12 Results of applying binarization and thinning to the
enhanced image
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(a) Ridge Ending (b) Bifurcation
Figure 3.13 Results of applying binarization and thinning
The CN method is used to perform minutiae extraction. This
method extracts the ridge endings and bifurcations from the skeleton image
by examining the local neighbourhood of each ridge pixel using a 3X3
window. The CN for a ridge pixel P is given by
(3.14)
where Pi is the pixel value in the neighborhood of P. For a pixel P, its eight
neighboring pixels are scanned in an anti-clockwise direction as follows:
The pixel can then be classified according to the property of its CN
value after the CN for a ridge pixel has been computed. A ridge pixel with a
CN of one corresponds to a ridge ending, and a CN of three corresponds to a
bifurcation. For each extracted minutiae point, the following information is
recorded:
x and y coordinates,
orientation of the associated ridge segment, and
type of minutiae (ridge ending or bifurcation).
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The extracted minutiae points are superimposed on the original
image. Visual inspection of the image indicates that the majority of the
marked minutiae points from the skeleton image correspond to valid minutiae
points in the original image.
3.2.6 Fingerprint Verification
Once the reference point is located, all minutiae extracted from a
master fingerprint image can be aligned with the reference point to generate a
circular sub region in the original image. This sub region contains a fixed
number of minutiae to be matched with similar minutiae contained in a live
template during an authentication process.
First, the Cartesian coordinates of the extracted minutiae in a
master fingerprint image are converted into Polar coordinates using the
following equations:
Figure 3.14 The first N minutiae and their reference point formed
(3.15)
(3.16)
(3.17)
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Where: (xi,yi) - Cartesian coordinates of minutia i
i - Minutia orientation
(ri - Polar coordinates of minutia i
- Normalized minutia orientation
(corex, corey) - Cartesian coordinates of the reference point
Core orient - Reference point orientation
Figure 3.14 shows the minutiae and their reference point formed by applying the minutiae algorithm on a fingerprint image.
The minutiae are rotational and transitional invariant with respect to their reference point, in polar coordinate representation. Aftransformation, the minutiae are sorted in ascending order according to their distances from the reference point. To compute a minimum area that covers a predetermined number of minutiae points, the first minutiae from the list to form a master feature template is selected (Maio et al 2002). Especially in the Arch fingerprints, that some reference points are located near the boundaries of the images. Such cases can lead to large bounding circle size as shown in Figure 3.15. As a remedy, an average center (Xcenter, Ycenter) is constructed.
(3.18)
where, (Xi, Yi) - Cartesian coordinates of minutia in the feature template (Xcenter, Ycenter) - New centre of the feature template.
It should be noted that, to tolerate elastic distortion errors during an image capture process a pre-defined constant Rd is added. Subsequently,
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minutiae points only in the bounding circle centered at the average center is found out.
Figure 3.15 Size of a bounding circle is large if the reference point is
near boundary (b) Size of the bounding circle decreases
3.3 IRIS RECOGNITION
The iris is the plainly visible, colored ring that surrounds the pupil.
It is a muscular structure that controls the amount of light entering the eye,
with intricate details that can be measured, such as striations, pits, and
furrows. The iris is not to be confused with the retina, which lines the inside
of the back of the eye as in Figure 3.16. No two irises are alike. There is no
detailed correlation between the iris patterns of even identical twins, or the
right and left eye of an individual. The amount of information that can be
measured in a single iris is much greater than fingerprints. An iris recognition
camera takes a black and white picture from 5 to 24 inches away, depending
on the type of camera. The camera uses non-invasive, near-infrared
illumination (similar to a TV remote control) that is barely visible and very
safe.
Unlike other biometric technologies that can be used in surveillance
mode, iris recognition is an opt-in technology. In order to use the technology,
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one must first glance at a camera. Iris recognition cannot take place without
permission. The picture of an eye is first processed by software that
localizes the inner and outer boundaries of the iris, and the eyelid contours, in
order to extract just the iris portion. Eyelashes and reflections that may cover
parts of the iris are detected and discounted.
Being the first step in iris recognition, iris segmentation defines the
image contents used for feature extraction and matching, which is directly
related to the recognition accuracy. Speed is often a bottleneck in practical
applications, and iris segmentation is often found to be the most time-
consuming module in an iris recognition system. It is reported that most
failures to match in iris recognition result from inaccurate iris segmentation.
Figure 3.16 Eye Structure and Iris features
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Iris segmentation is to locate the valid part of the iris for iris
biometrics, including finding the pupillary and limbic boundaries of the iris,
localizing its upper and lower eyelids if they occlude, and detecting and
excluding any superimposed occlusions of eyelashes, shadows, or reflections.
Daugman(2007) used the following integro differential operator to find the
circular boundaries of an iris:
(3.19)
This operator serves as a circle finder which searches the maximum
angular integral of radial derivative over the k-means clustering algorithm on
the position and intensity feature vector of the iris image.
3.3.1 Iris Detection After Reflection Removal
The objective of iris detection is not only to identify the presence of
an iris in input image but also to determine its position and scale as shown in
Figure 3.17 (a), (b), (c) and (d) with steps involved in this process.
Figure 3.17 Flowchart of iris segmentation algorithm.
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An adaptive threshold Tref
R(x,y) of image I(x,y) is used.
3.3.2 Pupillary and Limbic Boundary Localization
A novel iterative Pulling and Pushing (PP) method has been used
here. In this method, several important considerations involved in its effective
implementation are presented after a brief introduction.
Figure 3.18 PP method
3.3.2.1 The pulling and pushing method
(2006) and young et al(2003). Its mechanics are illustrated in Figures. 3.18(a)
and 3.18(b), where denotes N identical mass less springs with the
equilibrium length R and spring constant k. One end of the springs is attached
to a circle whose radius is R and the other end joins at point O.
At the beginning, all the springs are relaxed, and O is the
equilibrium position, as shown in Figure 3.18(a). Then, an appended force is
a restoring force to resist the introduced deformation:
(a) (b) (c) (d)
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(3.20)
Where
- Current length of is
ie - Direction radiating from ' .
As illustrated in Figure 3.18(b), the composition of will
push ' back to its equilibrium position after the appended force is
removed. Here, the composition force is obtained by equation 3.21
(3.21)
Figure 3.19 Flowchart of the PP method with an illustration. (a) The
result of iris detection (b) Edge detection in polar
coordinates. (c) The PP forces in cartesian coordinates
(d) The new estimation driven by the forces in (c)
Based on such mechanics, the PP method is developed as illustrated
in Figure 3.19 (a), (b), (c) and (d). Let the localization of the pupillary
boundary taken as an example (the limbic boundary can be similarly located).
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Suppose O0P is the rough position of the pupil center obtained by iris
detection, the PP method then works as follows:
1. Perform vertical edge detection on the image after
transforming the original iris image into polar coordinates
(centered by O0P). Only one edge point along each column is
preserved to avoid most of the noisy edge points, as shown in
Figure 3.20 (b). In addition, only the [ ] sector is used to
avoid the influence of the upper eyelid occlusion.
2. Join each resulted edge point
(3.22)
and the center point O0P with an imaginary spring-like line in
attached to a circle and meeting at O0P, as shown in Figure
3.20(c) is got.
(3.23)
(3.24)
3.3.3 Eyelid Localization
Locating the upper and lower eyelids is an even harder problem
involved in iris segmentation. It is impossible to fit them with simple shape
assumptions since, the shape of eyelids is so irregular. In addition to this, the
upper eyelid tends to be partially covered with eyelashes, making the
localization more difficult. Fortunately, these problems can be solved by an
1D rank filter and a histogram filter. The 1D rank filter removes the
eyelashes, while the histogram filter addresses the shape irregularity.
112
3.3.4 Eyelid Models
To tackle the shape irregularity of eyelids, three typical models of
upper eyelid as shown in Figure 3.20 are statistically established by clustering
the manually labeled eyelids in a training set. The idea is that, given a probe
upper eyelid, its shape similarity with the images is calculated and the model
with the highest similarity score is taken as an initial guess of its shape.
Although it is inaccurate, this initial guess provides cues for noise
elimination.
Figure 3.20 Examples of upper eyelid models
The flowchart of the proposed Eyelid Localization (EL) method is
depicted in Figure 3.21. Let us take the localization of upper eyelid as an
example, the method works as follows:
Figure 3.21 Flowchart of eyelid localization
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Crop the image Region of Interest (ROI), the ROI Iroi of the
iris image is cropped based on the localization results (Figure
3.21 (a)).
Filter Iris Region of Interest (IROI) with a 1D horizontal rank
filter (Figure 3.21 (b). With the observation that the eyelashes
are mostly vertical thin and dark lines, IROI is horizontally
filtered with a 1D rank filter.
Calculate a raw eyelid edge map. Edge detection is then
performed on the upper region of Iranked along the vertical
direction as shown in Figure 3.21 (c), resulting in a raw eyelid
edge map Erow.
Eliminate noisy edge points through shape similarity
Calculation as shown in Figure 3.21 (d).
Fit the eyelid with a parabola curve. The exact shape of the
eyelid is obtained by parabolic curve fitting as shown in
Figure 3.21 (e).
3.3.5 Eyelash and Shadow Detection
Eyelashes and Shadows (ES) (Figure 3.22) are another source of
occlusion that challenges iris segmentation method. The basic idea of the
solution proposed is to extract an appropriate threshold for ES detection via a
statistically established prediction model.
2 distance is adopted to measure the dissimilarity between two
considered histograms h1 and h2 as follows
2= (3.25)
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Finally, the detection result is refined by checking the connectivity
of the candidate points to the upper eyelid. The idea is that most eyelashes
and shadows appear near the upper eyelid. This refinement is necessary
because it relaxes the burden of selecting the detection threshold. It allows us
to not spend too much effort trying to find an optimal threshold but just a
moderately good and loose one.
Figure 3.22 Eyelash detection
3.4 MULTIMODAL BIOMETRIC AUTHENTICATION
It is often not possible to achieve a higher recognition rate and
attempt to improve the performance of single matchers. In such situations,
single recognizer may not prove to be effective due to inherent problems. By
utilizing a multi biometric system, these problems can easily be alleviated by
providing multiple pieces of evidence of the same human subject, thus
achieving higher and more reliable recognition.
In this work, the results of fingerprint and iris authentication are
combined to improve system performance. The raw-scores of fingerprint and
iris have different distributions, the sigmoid function to normalize these raw-
scores are applied from 0 to 1. Finally, the multimodal biometric
authentication system by fusing these normalized-scores using an adaptive
rank level fusion method is proposed. The fused-score is used to classify the
unknown user into the acceptance or rejection.
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3.4.1 Score Normalization
Transforming the raw-scores obtained using different modalities to
a common domain using a mapping function is called Normalization.
Normalization generally has various methods such as z-score, min-max,
decimal change, and sigmoid function. The sigmoid function is used in this
work to normalize the raw-scores of fingerprint and iris. The sigmoid function
is used in this work, since it is useful to include the outlier data while still
preserving the significance of data within the standard deviation of the mean.
The normalization method using the sigmoid function maps the raw-scores to
the [0, 1] interval, and is defined by
(3.26)
Where - Defined the
raw-score of i - th modality
- Normalized-score.
and - Mean and standard deviation of raw scores.
3.4.2 Adaptive Rank Level Fusion
Fusion can be done at the rank level when the output of each
biometric matcher is a subset of possible matches sorted in decreasing order
of confidence. The goal of rank-level fusion is to consolidate the rank output
by individual biometric subsystems (matchers) in order to derive a consensus
rank for each identity. An effective adaptive rank level fusion scheme
(Monwar and Gavrilova 2009) shown in the Figure 3.23 below that combines
information presented by multiple domain experts based on the rank-level
fusion integration method is implemented.
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3.4.2.1 Highest rank fusion
In the highest rank method, the fused rank of a user is computed as
the lowest rank generated by different classifiers is given by
Rj = (3.27)
This rank fusion technique is similar to applying the max rule for
fusion at the score level. As a consequence of applying this fusion rule, ties
between users may be randomly broken.
Figure 3.23 Schematic representation of adaptive rank level fusion
3.4.2.2 Borda count fusion
In the Borda count method, the fused rank is estimated as the sum
of the ranks of individual classifiers:
(3.28)
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The advantage of the Borda count method over the highest rank is
its ability to account for the variability in ranks due to the use of a large
number of classifiers.
3.4.2.3 Logistic regression method
In the logistic regression method a weighted sum of the individual
ranks is calculated. When different matching modules have significant
differences in their accuracies this method is very efficient, but this method
requires a training phase to determine the weights.
The logistic response function is given by
(3.29)
(3.30)
Where
and - parameters of the logistic regression
model
To evaluate the multimodal results of fingerprint and iris, the
various rank level fusion techniques such as highest rank, borda count and
logistic regression methods are compared in terms of Genuine Acceptance
Rate (GAR). It is evident from the results that the multimodal authentication
system with logistic regression fusion techniques has better error rates when
compared with highest rank and borda count methods. Further, the training
and recognition time of various rank level fusion approaches is compared. It
could be inferred that higest rank method shows 10% improvement in the
recognition time comparative to other methods. The detailed procedure for the
experimentation and the result comparisons are given in section 6.2.