Coherence enhancement diffusion using robust orientation estimation

COHERENCE ENHANCEMENT
DIFFUSION USING ROBUST
ORIENTATION ESTIMATION
Mohammad A. U. Khan1, Tariq M. Khan2, Wadee Al-Halabi3, Hiba
Shahid4 and Yinan Kong5
1,4

Department of Electrical and Computer Engineering,
Effat University, Jeddah, Saudi Arabia.
mohammad_a_khan@yahoo.com

2,5

Department of Engineering, Macquarie University, Sydney, Australia
tariq045@gmail.com

3

Department of Computer Science, King Abdulaziz University, Saudi Arabia
wsalhalabi@kau.edu.sa

ABSTRACT
In this paper, a new robust orientation estimation for Coherence Enhancement Diffusion (CED)
is proposed. In CED, proper scale selection is very important as the gradient vector at that
scale reflects the orientation of local ridge. For this purpose, a new scheme is proposed in
which pre calculated orientation, by using orientation diffusion, is used to find the correct true
local scale. From the experiments it is found that the proposed scheme is working much better
in noisy environment as compared to the traditional Coherence Enhancement Diffusion.

KEYWORDS
Fingerprint Image Enhancement, Coherence Enhancement Diffusion Directional Filter Bank
(DFB), Decimation free Directional Filter Bank (DDFB).

1. INTRODUCTION
Biometric technology deals with identifying humans with their traits or characteristics. It deals
with measurable albeit distinctive characteristics which can be used to label and to a large extent
describe individuals [1]. Examples include, face recognition, DNA, palm print, hand geometry,
retina, iris recognition and fingerprint. Out of these many biometric techniques, fingerprint
identification is the most prevailing one which has been successfully used in numerical
applications in the past [2]. It has been observed that every human being has a unique and
immutable fingerprint [3]. Individually is hidden in the pattern of ridges and valleys on the
fingerprint surface. Ridges are found to terminate themselves at some locations and split at others.
These are referred to as ridge ending and bifurcation respectively. The locations corresponding to
these ridge endings and bifurcations are known as minutiae points. Identifying human fingerprint
means locating correctly these minutia points.
With the advancement in computer technology, need to automatic fingerprint identification of
fingerprint scans arises. Reliable extraction of minutiae is one of the critical step for an automatic
fingerprint identification system (AFIS). We can forsee the importance of the quality of input
David C. Wyld et al. (Eds) : CCSIT, SIPP, AISC, PDCTA, NLP - 2014
pp. 203–214, 2014. © CS & IT-CSCP 2014

DOI : 10.5121/csit.2014.4217

204

Computer Science & Information Technology (CS & IT)

fingerprint scan in determining the reliability of the overall automatic fingerprint identification
system (AFIS) [1]. The fingerprints are obtained with fingerprint scanners that may not provide a
perfect scan in all circumstances. The presence of dirt or oil on the surface of the finger may
result in blurred scan. Furthermore, due noise present in scanner electronics, the fingerprint scans
may not be of clear quality. Mostly, the noise in fingerprint image manifest itself in terms of cuts
or interpolated ridge lines. For automatic fingerprint identification system (AFIS) to work
reliability, these broken ridge lines need to be restored vis some enhancement process [4].
A fingerprint enhancement process generally consists of estimating local image parameters,
which in turn are used to tune a contextual filter that moves from one location to another on the
surface of fingerprint, smoothing noise on the way. Contextual filters can be conveniently defined
in the framework of partial differential equations [5]. A major development in PDE based image
diffusion was introduced earlier by Perona and Malik [6]. On the basis of their study, number of
diffusion filters have been proposed [7, 8, 9, 10, and 11]. Most of these techniques are based on a
scalar diffusivity parameter which guides the diffusion flux moving along the orthogonal to the
gradient direction. These techniques are linear and isotropic in nature, and have same common
disadvantages, like edge blurring. To improve the performance of these isotropic diffusion
Joachim Weickert [12] proposed a non-linear isotropic diffusion, which replaces scalar diffusivity
parameter with diffusion matrix to provide greater flexibility in dealing with oriented structure on
point to point basis. This technique is well known as Coherence Enhanced Diffusion (CED). The
analysis of the CED technique can be carried out by an eigen decomposition of the diffusion
matrix, which results in eigenvalues and eigenvectors. The eigenvalues dictates the amount of
smoothing, while the eigenvectors are responsible for steering these smoothing in proposer
directions. Though eigenvalues are essential part of coherence enhanced diffusion, a clean
computation of eigenvectors without noise may be ultimately responsible for evolving the whole
diffusion process. We believe that a CED in its current status lacks this clean steering process.
The impact of steering diffusion in wrong directions may distort some genuine minutia points
while creating fake ones as the same time. We propose to relieve the stress in providing clean
eigenvectors in the form of embedding an orientation diffusion block in the CED process. Thus
letting CED to worry only about proper diffusion speeds at each point. Thus CED will provide the
diffusion of noisy fingerprints with diffusivity parameters that align themselves with clean
directions at each diffusion step.
The research presented in this paper is concerned with finding reliable orientations and then
finding a way to embed them in the conventional CED algorithm. Orientation diffusions [13] has
been there for a while, that provides a framework for diffusing directions alone with noise
reduction at each step. We adapted the method to be used with the conventional CED scheme to
boost its performance in noisy images. The rest of the paper is organized as follow. Section II
details the Coherence Enhanced Diffusion. In section III a summary of orientation diffusion
method is discussed. Section IV describes how the pre-computed orientation is used in Coherence
Enhancement Diffusion. In Section V testing and validation is presented and finally the paper is
concluded in section VI.

2. COHERENCE ENHANCED DIFFUSION
Weickert [14] considered a general class of anisotropic diffusion process. The process utilizes a
diffusion matrix depending on the local image structure via the so-called second-moment matrix
(or structure tensor). The second-moment matrix is a well-established tool for texture analysis
[15, 15, 17, and 18]. In [14], Weickert investigated the use of second-moment matrix information
to design anisotropic diffusion scale-space, which enhances the coherence of the ridge-like


205

texture in fingerprint. The method is generally referred to as Coherence Enhanced Diffusion
(CED), and is summarized in the following sections.
Consider an input fingerprint image L ( x, y ) . The anisotropic scale-space for the image

L ( x, y ) can be found by implementing the heat equation, given by:
∂ t L = div ( D∇L )

1

where D is the 2 × 2 diffusion matrix, adopted to the local image structure, via a structural
descriptor, called the second-moment matrix µ , defined as:

 Lx 2 Lx Ly 
 µ11 µ12 

µ =
=µ =
 Lx Ly Ly 2 
 µ12 µ 22 



2

where Lx 2 , Lx Ly and Ly 2 represents the Gaussian derivative filters, in x-and-y directions. The
matrix is a symmetric 2 × 2 matrix, with two dominant eigen values λmin and λmax , given by:

λmin = 1/ 2 ( s11 + s12 + α )

3

λmax = 1/ 2 ( s11 + s12 − α )
Where

α=

( s11 − s22 )

2

+ 4 s12 2

4

Let us now define the diffusion speeds cu and cv as

(

cu = max 0.01, 1 − e

− ( λmin − λmax )

2

/ k2

)

5

cv = 0.01
The diffusion matrix D with component is given by:


( c − c ) − ( s11 − s22 ) 
d11 = 1/ 2  ( cu − cv ) + u v

α


(c − c ) s
d12 = u v 12

α


( c − c ) − ( s11 − s22 ) 
d 22 = d11 = 1/ 2  ( cu − cv ) − u v

α



6

206


Once the diffusion matrix is constructed, we are set to start the evaluation process using Eq. 1
with input image L ( x, y ) as the starting point. In the process of evaluation, the image got
enhanced ridge pattern, as shown in Fig. 1

 d11 d12 
 can be decomposed using eigen decomposition, into eigenvalues
 d12 d 22 

The diffusion matric 

cu and cv along with eigen directions. By plotting these eigen directions on top of the enhanced
image it can be observed that these directions need to be corrected for better evolution. However,
their cleaning process for eigen directions need to be embedded in the CED process such that
each diffusion step is proceeded in the clean direction. For cleaning directions at each step, we
take the help of orientation diffusion process as suggested in [19].

Fig. 1. a) and b) are two noisy images from FVC database. c) and d) shows the results of CED enhancement
of a) and b) respectively.

3. ORIENTATION DIFFUSION
Orientation filed estimation is considered as first step moving towards enhancement process as
suggested in [1]. But in noisy environment, this provide a challenge. In research literature,
different techniques have been in use for orientation estimation in noise-degraded images. The
notable examples can be cited in [20], where a filter bank based approach is used, and [21], where
waveform projection, and [22] with spectral estimation. To increase the degree of accuracy for the
initial coarse estimation, mathematical modelling using Bayesain network [23] and complex
polynomial can be proposed. Later, [24] introduces an enhanced gradient-based approach for
reliable orientation estimation. In this scheme, dominant orientation of a base block from its four
overlapping neighbourhoods is estimated and finally a best estimate is selected from least noise-


207

affected neighbourhood. However, gradients are un-reliable and error-prone on fingerprint
images affected by noise like scares, smudges, dryness or wetness of finger [25]. Recently, DFB
has [26] also been used to provide reliable orientation. However, we feel that orientation diffusion
provide a natural coupling for our purpose. The reason for this natural coupling stems from the
fact that orientation diffusion provides a gradually decrease in noise levels present in orientations
as opposed to a step process adopted by DFB based orientations.
According to [19], the correct way of diffusing orientation is to adopt a non-linear diffusion
function in the form as given below:

θ ( x, t + 1) = θ ( x, t ) + λ

∑
n∈N ( x )

sin (θ ( n, t ) − θ ( x, t ) )

7

where N ( x ) is the set of all 8 neighbours around x location. Also θ has to be in the range
of [ −π , π ] .
The discrete implementation of orientation diffusion, as described by Eq. 7 on a cropped noisy
pattern of the fingerprint image shown in Fig. 4. The initial condition of diffusion process was

 gy  π
 + . The boundary
 gx  2

calculated from the gradient of the image intensities, i.e, θ initial = tan −1 
condition are set to zero gradients.

The results of running the diffusion may be seen in Fig. 2. We notice the desirable effect of
smoothing orientations on the way. The two singularities of orientations that ate present in the
fingerprint would be difficult to detect in the original image using a local gradient operator. We
found that this orientation diffusion inspired by simple physical systems, can de-noise an
orientations data effectively, by eating out already existing print-singularities with new generation
of singularities, Thus, it does support the casuality property of diffusion.

Fig. 2. a) sample noisy image, b) CED Orientation, and c) Orientation enhanced by orientation diffusion

208


Fig. 3. Orientation Fed CED block diagram

4. ORIENTATION FED COHERENCE ENHANCED DIFFUSION
As we discussed in section II, the CED process starts by taking an input image, then calculate its
gradients g x and g y respectively. From g x and g y , it computes the second moments matrix

 s11 s12 

 to depict the rotation in local structure. The second moment matrix can be
 s12 s22 
decomposed to provide us with eigen values λ1 & λ2 and also the eigen directions e1 & e2 . In the
conventional design, these lambdas and eigenvectors can be used in the construction of diffusion
matrix used in diffusion process.
However, in our proposed scheme, we keep intact the lambdas, but take e1 & e2 direction for
further cleaning. For this purpose, we feed e1 & e2 into our orientation diffusion module for
further de-noising. Once cleaned, we feed this cleaned e1 & e2 back to our module of computing
diffusion matrix. And thus the process continues.

Fig. 4. a) sample noisy image, b) CED enhanced image, and c) Orientation Fed CED


209

5. TESTING AND VALIDATION
Statistically, the set of minutiae denoted by symbol M were algorithmically obtained and
evaluated against the set of minutiae marked by an expert denoted by symbol F and the minutiae
are classified into two types: termination and bifurcation. Each minutiae point m
compartmentalized into one of the following classes:
•

Correct: The correlation between minutiae points generated through the algorithm and
those
obtained
from
the
expert
is
perfect
position,
i.e

( m ∈ F ∩ M and type ( m ) = type ( m ) )
F

M

•

False: The expert did not mark the location corresponding to the one obtained through the
algorithm, i.e ( m ∈ M , m ∉ F )

•

Missing: The minutiae location has been marked by the expert but couldn't be seen within
the algorithmically generated image, i.e ( m ∉ M , m ∈ F )

•

Misclassified: The minutiae location marked by the expert could be is also the one found
by the method with the exception that one has been classified as bifurcation and other has
been classified as termination, i.e m ∈ F ∩ M and type F ( m ) ≠ type M ( m )

(

)

Compartmentalization of all the minutiae set is followed by the performance measurement which
is computed statistically. This is done on minutiae obtained from the algorithm as well as
minutiae marked by the experts which makes the performance measurement relative to either total
number of minutiae found algorithmically or the total number of minutiae found by the expert
markings. The measures relative to minutiae marked by the expert which detects the aptitude of
the technique to detect correct minutiae are as follows:
• Missing minutiae is defined as

• False minutiae is defined as

Mis sin g
F

False
F

• Misclassified minutiae is defined as

• Correct minutiae is defined as

Missclassified
F

Correct
F

• Total error which is the summation of false positive, false negative and misclassified
errors is defined as

Mis sin g ∪ False ∪ Missclassified
F

• Classification rate for the purpose of enhancing the graphical visualization is defined as

Correct
Missclassified

210


Large number of missing minutiae could be tolerated to certain extent but the large number of
false minutiae would lead to larger noise rate within the mapping stage. On the other hand,
prominence of classification error is based on the manner in which the mapping algorithm deals
with the types of minutiae. Using the techniques described above, the database of true minutiae
was generated, by using the sample images given in Fig. 6 which is used to evaluate the
orientation and scale-matched filters to produce improved input image along with the techniques
described above.

Fig. 5. Sample images used for evaluation measure

The table compares the result obtained using the above method.
Table1. This table shows the evaluation measure comparing minutiae of proposed algorithm
Proposed

Correct

False

Missing

Misclassified

Image1

21

4

6

4

Image2

18

8

8

5

Image3

21

19

9

1

Image4

31

5

5

1

Image5

20

12

20

3

Image6

10

15

20

1

Image7

16

11

27

4

Image8

6

2

30

1

Mean

17.875

9.5

15.625

2.5


211

Table2. This table shows the evaluation measure comparing minutiae of [12] CED Enhancement algorithm
[12]CED

Correct

False

Missing

Misclassified

Image1

19

8

6

6

Image2

17

9

7

5

Image3

20

21

6

3

Image4

24

5

10

4

Image5

21

17

19

5

Image6

8

16

22

2

Image7

15

10

26

3

Image8

5

3

30

2

Mean

16.125

13.25

15.75

3.75

The average number of minutiae points present in the image marked by the expert and the ones
marked by the algorithm for all the eight images was taken, which represented $F$. This was
computed to be 15 using which some performance measures were computed. For the proposed
method, classification error which is calculated as misclassified over correctly detected minutiae
was found to be

Missclassified / F ∩ M
*100 = 0.89%
F

8

For the CED method, classification error which is calculated as misclassified over correctly
detected minutiae was found to be

Missclassified / F ∩ M
*100 = 1.45%
F

9

In Fig7, the bar chart shows the performance evaluation measure of both schemes.

6. CONCLUSIONS
Coherence enhancement diffusion filters are the one which have control on the size/shape of the
filter but, these use derivative for rotation matrix which is not considered as a reliable method.
Therefore, in this work presents a new and a reliable method for orientation estimation is
proposed to explicitly calculate the orientation field of a fingerprint image. By using this
orientation new local scales for Diffusion matrix are adaptively calculated. The experiments
conducted on the noisy images showed promising results of the proposed scheme.

212


Fig. 6. Sample images used for evaluation measure


213

Fig. 7. Performance Evaluation Measure of both schemes

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AUTHORS
Dr Yinan Kong
Dr Kong leads the VLSI Research Group at Macquarie. He is also currently the Director
of Higher Degree Research, Department of Engineering, Macquarie University, Sydney,
Australia. Dr Kong obtained his PhD from the University of Adelaide, Australia.
During his research at the VLSI Research Group at Macquarie University and Centre for
High Performance Integrated Technologies and Systems (CHiPTec) at the University of
Adelaide, Dr Kong focused on digital VLSI design at an arithmetic level for specific
applications like cryptography and DSP. He achieved the hardware construction of a
1024-bit RSA cryptosystem at only 0.4 ms per decryption, the fastest ever FPGA implementation of RSA.
In the meantime, he developed Bachelor Degree of Computer Engineering at Macquarie Engineering as
well as postgraduate teaching in embedded computer system design and computer arithmetic with hardware
focused.
Tariq Mahmood Khan
Tariq Mahmmod Khan is interested in both Digital Image Processing (with an emphasis
on biometrics) and VLSI. He is currently involved in the hardware implementation of
multi-modal biometrics project, led by Yinan Kong. The main goal of this project is to
develop a fast processor for different design approaches. The aim is to test these
approaches on a multi-modal biometric system consisting fingerprint, iris and face. Prior
to starting his PhD in Engineering at Macquarie University, he received a degree in BS
Computer Engineering from COMSATS Institute of Information & Technology,
Islamabad Pakistan and MSc in Computer Engineering from University of Engineering
& Technology, Taxila Pakistan.

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