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A pitfall in fingerprint bio-cryptographic key generation5
Peng Zhang a, Jiankun Hu b,*, Cai Li c, Mohammed Bennamoun d,
Vijayakumar Bhagavatula e
a
School of Computer Science and Information Technology, Royal Melbourne Institute of Technology, Melbourne, Victoria 3001, Australia
School of Engineering and Information Technology, University of New South Wales at the Australian Defense Force Academy
(UNSW@ADFA), Room 202, Building 15, Northcott Drive, Canberra ACT 2600, Australia
c
School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, Melbourne, Victoria 3001, Australia
d
School of Computer Science and Software Engineering, The University of Western Australia, WA 6009, Australia
e
Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburg, PA 5213, USA
b
article info
abstract
Article history:
The core of bio-cryptography lies in the stability of cryptographic keys generated from
Received 17 December 2010
uncertain biometrics. It is essential to minimize every possible uncertainty during the
Received in revised form
biometric feature extraction process. In fingerprint feature extraction, it is perceived that
12 February 2011
pixel-level image rotation transformation is a lossless transformation process. In this
Accepted 16 February 2011
paper, an investigation has been conducted on analyzing the underlying mechanisms of
fingerprint image rotation processing and potential effect on the major features, mainly
Keywords:
minutiae and singular point, of the rotation transformed fingerprint. Qualitative and
Fingerprint features
quantitative analyses have been provided based on intensive experiments. It is observed
Minutiae
that the information integrity of the original fingerprint image can be significantly
Singular point
compromised by image rotation transformation process, which can cause noticeable
Rotation transformation
singular point change and produce a non-negligible number of fake minutiae. It is found
Bio-cryptography
that the quantization and interpolation process can change the fingerprint features
significantly without affecting the visual image. Experiments show that up to 7% biocryptographic key bits can be affected due to this rotation transformation.
ª 2011 Elsevier Ltd. All rights reserved.
1.
Introduction
With the development of information technology, it is more
likely and easier to attain and exchange information remotely.
The protection of personal information is a concern (Hoang
et al., 2009; Hu and Han, 2009; Hu et al., 2009; Hu et al.,
2010). The emergence of biometric security technology
resolved this problem to some extent. Among all biometric
security systems, fingerprint-based systems are definitely the
most popular. They also have been highly explored in
academic and research areas.
A fingerprint is the pattern of interleaving ridges and
furrows on the surface of a fingertip, where ridges refer to
a raised portion of the epidermis and furrows refer to valleys
5
Part of this work has been presented at the ICARCV 2010 (Zhang et al., 2010). A completely new section 4.2.3 on bio-cryptographic key
is added in this manuscript. In our previous work presented at the ICARCV 2010, the aim was to investigate the effects on features due to
image rotation. In this manuscript the whole theme of the work has been changed to investigate the effects on bio-cryptographic key
generation which is a very different and far more important aim. The feature-change part will serve as an intermediate result in this
process.
* Corresponding author. Tel.: þ61 2 62688186.
E-mail addresses: [email protected] (P. Zhang), [email protected] (J. Hu), [email protected] (M. Bennamoun), [email protected] (V. Bhagavatula).
0167-4048/$ e see front matter ª 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cose.2011.02.003
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
2
c o m p u t e r s & s e c u r i t y x x x ( 2 0 1 1 ) 1 e9
between ridges. Ridges in a fingerprint are highly structured,
and its whole configuration is determined in a fetal period and
remains unchanged in one’s lifetime (Moenssens, 1971).
In general, Fingerprint-based system can be categorized into
two types: fingerprint identification system (FISs) and fingerprint verification system (FVSs) (Hu et al., 2010). Normally, FIS is
applied to check whether the query fingerprint image can find
a match in the database while a FVS is used to determine
whether a query image can match a specific template.
In the identification and verification process, current
matching algorithms are almost exclusively based on critical
fingerprint features such as minutiae and singular points (SPs)
(Wang et al., 2007). Therefore, how to extract accurate minutiae
and singular point from the template and query image is
becoming a crucial problem. Also in bio-cryptography, extracting accurate fingerprint features is a major challenge due to
the uncertainty introduced at each impression (Hu, 2008).
In most fingerprint verification systems, the query fingerprint images may be rotated, translated or scaled with respect
to the template images. Therefore, registration algorithms are
needed to address this problem (Wang et al., 2007). Registration algorithms based on singular points tend to use singular
point as the reference point to establish a relative rotation and
transformation relationship between two fingerprint images.
After that, the query fingerprint image is transformed and the
transformed image is used to extract features which are
compared with the template.
In the evaluation of rotation processing algorithms,
a common perception is that pixel-level rotation transformation is almost information lossless (Wang and Hu, 2008).
In this paper, we perform qualitative and quantitative investigations on the effect of pixel-level fingerprint image rotation
transformation. The experimental results show that up to 7%
of the minutiae can be mis-matched. For the matched ones,
their positions deviate to up to 16 pixels. The position of the
singular point can change up to 55 pixels while the orientation
angle change can be up to 90 . This result demonstrates that
the distortion brought in by the image rotation transformation
process can have a non-negligible impact on fingerprint
features extraction. It is possible that the pixel-level image
rotation transformation process can produce a fingerprint
image that is very different from the original one as an input
to the subsequent feature extraction process. Care must be
taken when evaluating fingerprint feature extraction algorithms based on the pixel-level fingerprint image rotation
transformation.
The remainder of this paper is organized as follows: In
Section 2, we present the potential problem resulting from the
image rotation transformation process and discuss three
dominant interpolation algorithms used in the rotation
transformation process. An experimental evaluation scheme
is proposed in Section 3. Experimental results and analysis are
provided in Section 4. The Conclusion is given in Section 5.
2.
Problem description and analysis
In fingerprint image registration, a point with coordinate (x, y)
in the original image is mapped to point (x0 ,y0 ) in the resultant
image after rotation.
x0 x0 þ ðx x0 Þ cos4 y y0 sin4
(1)
y0 y0 þ y y0 cos4 þ ðx x0 Þ sin4
(2)
Here, (x0,y0) are the coordinates of the rotation center in the
original image, 4 is the rotation angle, if we assume the coordinates of rotation center to be (0,0), then (1), (2) will become:
x0 ¼ x cos4 y sin4
(3)
y0 ¼ y cos4 þ x sin4
(4)
In any area of the image, the coordinates of a pixel are
constantly an integer pair (x, y). After the rotation, (x0 ,y0 )
becomes a real number pair. However, a point with real
number coordinates cannot be displayed as a pixel in the
rotated image. In addition, after rotation, the pixels close to
each other might be separated. Gaps would emerge between
originally adjacent pixels. Therefore the region of interest
(RoI) is enlarged. For example: an original fingerprint image of
size 296 560 has 165760 pixels. After 45 rotation, the RoI has
166856 pixels. An extra 1096 blank pixels arise.
To make the rotated image visually look close to the original one, it is necessary to perform some interpolation algorithms and insert specific value to each blank pixel.
In practice, to each pixel with integer coordinate (x00 ,y00 ) in
the rotated image, its corresponding coordinates (x000 ,y000 ) in the
original image are calculated using the following equations:
000
x ¼ x00 cos4 þ y00 sin4
000
y ¼ x00 sin4 þ y00 cos4
(5)
(6)
Then, we use an interpolation method to estimate the value of
the point with coordinates (x000 ,y000 ) and assign that value to
a pixel with coordinates (x00 ,y00 ) in the rotated image.
At present, there are three basic interpolation algorithms:
nearest-neighbor, bilinear and bicubic interpolation (Arya
et al., 1998; Keys, 1981). The nearest-neighbor interpolation
assigns the value of pixel which is closest to (x000 ,y000 ) to it while
other two interpolation algorithms refer to multiple pixels
around (x000 ,y000 ). Undoubtedly, these interpolation algorithms
have a good performance in making the interpolated image
look smooth and visually similar to the original one. However,
the resultant image is in fact not exactly the same as the
original image. In fingerprint-based systems, all features
extraction techniques are based on image. Therefore, the
distortion of the image due to rotation may have an impact on
the accurate extraction of fingerprint features. It deserves
more attention from researchers.
3.
The proposed evaluation scheme
Before image rotation is performed, the theoretical positions
of minutiae and singular point in the rotated image can be
calculated using transformation equations. The theoretical
orientation of singular point can be calculated easily by
adding a rotation angle to the originally detected one.
Ideally, after image rotation the minutiae and singular
point should be rotated accordingly. In other words, their
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
c o m p u t e r s & s e c u r i t y x x x ( 2 0 1 1 ) 1 e9
Fig. 1 e Rotated image (blue) is aligned and superimposed
on the original one (red). (For interpretation of the
references to colour in this figure legend, the reader is
referred to the web version of this article).
detected positions and orientations in the rotated image
should be approximately the same as the theoretical ones.
The following experiment is conducted to evaluate the
impact of image rotation process on fingerprint feature
extraction:
1) Rotation angle is set to 5, 10, 15.90 respectively.
2) For any given rotation angle, the original image is subsequently rotated using three different interpolation algorithms: nearest-neighbor, bilinear and bicubic.
3) Minutiae and singular point are extracted from both
original and rotated image. Their positions and orientations are recorded.
4) The theoretical positions and orientations of minutiae and
singular point in the rotated images are calculated based
Fig. 2 e Minutiae surrounded by bounding boxes.
3
Fig. 3 e Change of ridge pattern in the singular point area.
Up: original image. Down: rotated image. The rotated
images are aligned from left to right in this order: D30,
D15, L15, L30 where “D” indicates counterclockwise
rotation and “L” indicates clockwise rotation.
on those detected from the original images using transformation equations.
5) The practically detected positions and orientations of
minutiae and singular point in the rotated images are
compared with those calculated in step 4.
6) The rotated fingerprint image is matched and overlapped
with the original one. The matched pair of minutiae are
recorded.
Fig. 4 e Change of ridge pattern in boundary area. Up:
original image. Down: rotated image. The rotated images
are aligned from left to right in this order: D30, D15, L15,
L30 where “D” indicates counterclockwise rotation and
“L” indicates clockwise rotation.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
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c o m p u t e r s & s e c u r i t y x x x ( 2 0 1 1 ) 1 e9
8) All the bounding boxes are selected and lined up in such
order: from top left corner to bottom right corner.
9) Keys for the original fingerprint and the rotated one are
generated respectively in the following manner:
a) Each bounding box will sequentially generate one digit
of the key.
b) If the candidate image has detected minutiae in
a specific bounding box, the corresponding digit is set
to 1. Otherwise, that digit is set to 0.
10) Keys generated from the original image and the rotated
one are compared with each other.
Fig. 5 e Illustration of rotated image. Left: original image.
Right: image rotated by 45 counterclockwise.
7) The rotated fingerprint image is aligned with the original
one. The expected effect is as demonstrated in Fig. 1. For
each minutia presented in the overlapped image, detected
either in the original image or the rotated one, a bounding
box is applied with the minutia point in the center (Fig. 2).
The side length of the bounding box is the same as the one
in what has been used in the step 7.
4.
Experimental results and analysis
Our experiments are conducted on a public-domain database FVC2002-DB2, which contains 800 live-scanned grayscale fingerprints in total. All images are in the size of
296 560 pixels. The commercial fingerprint recognition
software Verifinger 5.0 SDK is used for fingerprint feature
extraction. It is full NIST MINEX certified and commonly used
by 1000þ end-user product brands in 98 countries over the
past 12 years. Matlab 7.6.0 is employed to perform image
rotation, data analyses, visualization and statistics.
4.1.
Change of ridge pattern
As aforementioned, the pixel values in the rotated image are
calculated based on the original image using an interpolation
algorithm. No matter how complex and well designed the
interpolation algorithm is, and no matter how clear and
smooth the resultant fingerprint ridges appear to the human
eye, the pixel values in the rotated images are still somewhat
different from their counterparts. From the perspective of
fingerprint recognition, the integrity of the ridge pattern is
compromised. Fig. 3 and Fig. 4 present the change of the ridge
pattern under rotation.
Fig. 3 demonstrates how ridges change in singular point
area during rotation. In the singular point area, one originally
continuous ridge with high curvature breaks and forms a ridge
ending in the þ30 rotated image. Two parallel ridges in the
original image meet each other in the 15 rotated image.
Another example is given by Fig. 4, which depicts the
rotation effect in the boundary area. The ridge topology in the
squared area of the original area is very complex. However,
after rotation none of the rotated image exactly retains the
Fig. 6 e Minutiae records and matched minutiae pair. Left:
detected minutiae in the original fingerprint. Middle:
detected minutiae in the rotated fingerprint. Right:
matched minutiae pair denoted by indexes.
Fig. 7 e Maximum minutiae positional deviation.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
c o m p u t e r s & s e c u r i t y x x x ( 2 0 1 1 ) 1 e9
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Fig. 8 e Illustration of ridge deformation. Left: original image. Right: rotated image.
original ridge pattern. It is difficult to recognize the similarity
between them. Another issue worth noticing is that when the
original image is rotated by the same angle in two opposite
directions (clockwise and counterclockwise). The changes of
ridge pattern are noticeably different.
4.2.
Change of fingerprint features
As the ridge pattern changes during image rotation, the
extracted minutiae and singular point change accordingly.
4.2.1.
Change of minutiae
Ideally, two sets of extracted minutiae from the rotated
fingerprint image and the original image respectively should
have a one-to-one mapping relationship. However that was
not the case as in our experiments. Actually, new minutiae
arose and some originally detected minutiae disappeared in
the rotated image. Some minutiae were detected in both the
original and the rotated fingerprint. They were matched by
visual examination. However, they were considered as two
different minutiae by the machine due to positional deviation.
All these contribute to the loss of matched minutiae. An
example is given in Figs. 5 and 6.
In Fig. 5, a fingerprint image is rotated by 45 counterclockwise. The detected minutiae records from the original
one are listed in the left table in Fig. 6. The minutiae records
detected from the rotated one are listed in the middle table in
Fig. 6. The matching result of the two images is listed in the
Fig. 9 e Illustration of ridge stretching. Left: original image. Middle: image rotated using bilinear interpolation. Right: image
rotated using bicubic interpolation.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
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Fig. 10 e Illustration of ridge merging. Left: original image. Middle: rotated image using the nearest-neighbor interpolation.
Right: rotated image using the bicubic interpolation.
right table in Fig. 6. As we can observe from Fig. 6, there are 36
detected minutiae from the original image while 47 detected
minutiae from the rotated one. 33 min pairs are matched,
which means that 3 min in the original image and 14 min in
the rotated one cannot find their counterparts due to the
reasons mentioned above.
The maximum positional deviation between matched
minutiae is depicted in Fig. 7. The highest number is 16. This is
high enough to exceed the size of pixel blocks used to estimate
the orientation field in some algorithms. Different interpolation algorithms are designed based on different mathematics
foundations. They have different applications and can be
adopted to handle a specific issue. During fingerprint image
rotation, the algorithm should be able to recover as much
information as possible. However, the interpolation algorithm
used in fingerprint image processing is not specifically
designed for its application. The peculiarity of fingerprint is
not taken into consideration. Fingerprint images are just
treated as nothing but ordinary images. Therefore, the interpolation itself could behave in an unsuitable way and deform
the ridges which it is supposed to recover. In Fig. 8 the
deformation of ridge pattern in a rotated image is presented.
Former continuous ridge breaks and separate ridges are
merged into one.
Fig. 11 e Example of mis-detected singular point.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
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Fig. 12 e Example of positional and orientational change of singular point.
Fig. 13 e Example of orientational change of singular point.
Fig. 9 demonstrates how two algorithms behave in
different way. The bilinear interpolation algorithm stretches
the vertical ridge so that the ridge meets the ridge above it.
Although there is no minutia lost, the type of that minutiae
changes and the minutia direction becomes different from its
counterpart in the original one. Another example is given in
Fig. 10. Two parallel ridges in the square are merged into one
using the nearest-neighbor interpolation while the bicubic
Fig. 14 e Maximum positional deviation of singular point.
Fig. 15 e Maximum orientational deviation of singular
point.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
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Fig. 16 e The number of fingerprint images with mis-detected singular point in 100 images.
algorithm keeps them separate. Regarding minutiae, two ridge
endings are lost in the middle image.
4.2.2.
Singular point displacement
Theoretically, after rotation the singular point in the rotated
image should change accordingly. Unfortunately, this is not
the case. The direction of the singular point is very sensitive to
image rotation transformation. Both the location and the
direction of singular point could change unpredictably. In
Fig. 11, after rotation the core point near the left boundary is
mis-detected due to the change of the ridge pattern: the two
originally broken ridges meet in the rotated image.
Even if the global ridge pattern around SP is generally
preserved, a slight change will still affect the SP detection. In
Fig. 12, the ridge pattern seems intact while the curvatures of
ridges actually change. These changes lead to the change of
the detected SP position and orientation. Even if the position
of SP is correctly detected, its orientation could still change.
An example is given in Fig. 13. The detected positions of the
bottom SP in the both images are almost the same. However,
the orientation is rotated counterclockwise by nearly 30
difference.
Fig. 14 shows statistics for the maximum positional deviation of singular points when the original images are rotated
by different degrees. The positional deviation can be up to
55 pixels.
Fig. 15 depicts the maximum orientational deviation of
singular point when the original image is rotated by 5, 10,
15.90 respectively. It is up to around 90 and no less than 60 .
Due to the change of ridge pattern, the detected singular
points in the original images might be mis-detected in the
rotated image. Fig. 16 shows the statistics of the number of
mis-detected singular points in 100 fingerprint images when
the original images are rotated by 5, 10, 15.90 .
It has been assumed that when an image is rotated by 90 ,
the integrity of the image should be best preserved because
Fig. 17 e Generated keys from original and rotated images.
the pixel value matrix of the rotated image is a transposition
of the original image’s pixel value matrix. However, from
Fig. 16, it can be observed that even when the image is rotated
by 90 there are still 6 mis-detected SPs.
4.2.3.
The effect on the generated keys
From the key generation method described in Section 3, it can
easily be deduced that if the rotated image carries lossless
information, the two keys generated from original image and
rotated image should be identical. Actually, the keys should
consist of consecutive 1’s. However, this is not the case. An
example is given in Fig. 17, which clearly illustrate the difference in the keys generated from the original and the rotated
images. The keys generated from the original image and the
rotated image are different. This can easily be explained. The
key generation is based on the fingerprint feature, specifically
minutiae information. Since the minutiae change during
image rotation, the generated keys will inevitably be different.
A pair of 1’s at the same digit position indicates a matched pair
of minutiae while a difference in value implies mismatching.
We can even gain some insight on how the ridge pattern has
been changed by examining the keys. For instance: two
consecutive 0s in the ‘original’ key might imply that a continuous ridge broke in the rotated fingerprint.
The 0s appeared in the key can be considered as error
digits. Therefore, we can use digit error rate as a measure of
the image rotation’s negative impact. The digit error rate is
Fig. 18 e Bit error rate distribution.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003
c o m p u t e r s & s e c u r i t y x x x ( 2 0 1 1 ) 1 e9
shown in Fig. 18. We can observe that up to 7% of the digits in
the key are error bits when the rotation angle is set to 30 or 40 .
5.
Conclusion
In this paper, we investigated the effect on the generated keys
when an original fingerprint image is rotated. Our extensive
quantitative and qualitative analyses on experimental data
have revealed out that the positions of minutiae and singular
point in rotated image can change significantly away from
their theoretical values. Up to 7% of the minutiae are mismatched. The position of the singular point can change up to
55 pixels while the orientation angle can change up to 90 . It is
found that the quantization and interpolation process can
change the fingerprint features significantly without
affecting the visual appearance of the image. Care must be
taken when evaluating fingerprint feature extraction algorithms based on the pixel-level fingerprint image rotation
transformation. For the evaluation of algorithms on rotation
transformation, it is suggested to use feature rotation instead
of image rotation.
Acknowledgment
This work is supported by ARC Discovery Project DP0985838
and ARC Linkage Project LP100200538.
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Dr. Hu, J. is a full professor of cyber security at the School of
Engineering and Information technology, The University of new
South Wales at the Australian
Defense Force Academ (UNSW@ADFA) since February 2011. Before
he moved to the UNSW@ADFA, he
was an associate professor at the
School of Computer Science and
Information Technology, RMIT
University, Australia. His major
research interest is in computer
networking and computer security, especially biometric security.
He has been awarded six Australia
Research Council grants. He served as Security Symposium CoChair for IEEE GLOBECOM 08 and IEEE ICC09. He was Program CoChair of the 2008 International Symposium on Computer Science
and Is Applications. He has been on editorial board for following
journals: Journal of Network and Computer Applications, Elsevier;
Journal of Security and Communication Networks, Wiley; and
Journal of Wireless Communication and Mobile Computing,
Wiley. He is the lead Guest Editor of a 2009 special issue on
biometric security for mobile computing, Journal of Security and
Communication Networks, Wiley. He received a Bachelors degree
in industrial automation in 1983 from Hunan University, P.R.
China, a Ph.D. degree in engineering in 1993 from the Harbin
Institute of Technology, P.R. China, and a Masters degree for
research in computer science and software engineering from
Monash University, Australia, in 2000. In 1995 he completed his
postdoctoral fellow work in the Department of Electrical and
Electronic Engineering, Harbin Shipbuilding College, P.R. China.
He was a research fellow of the Alexander von Humboldt Foundation in the Department of Electrical and Electronic Engineering,
Ruhr University, Germany, during 19951997. He worked as
a research fellow in the Department of Electrical and Electronic
Engineering, Delft University of Technology, the Netherlands, in
1997. Before he moved to RMIT University Australia, he was
a research fellow in the Department of Electrical and Electronic
Engineering, University of Melbourne, Australia.
Please cite this article in press as: Zhang P, et al., A pitfall in fingerprint bio-cryptographic key generation, Computers & Security
(2011), doi:10.1016/j.cose.2011.02.003