fingerprint

On the line width influence in directional field determination for fingerprint images
Flavio Maggessi Viola
Sanderson L. de Oliveira Gonzaga
Aura Conci*
Computer Institute, Federal Fluminense University, Niterói, RJ, Brazil
E-mail: {fviola,sgonzaga,aconci}@if.uff.br, *Corresponding author
Abstract: Determination of directional field is part of several image processes. In this work, this issue is related with automatic fingerprint identification systems especially in the initial steps. Definition of an accurate and concise model for directional fields improves the performance on estimating the fingerprint ridge and valley orientation. This work presents results of a current research in automatic fingerprint identification system. Text focuses the creation of directional field matrix from fingerprint images. The aim of the process is the location of singular points in fingerprint images with an original technique to smooth the directional image obtained. Experimental tests reveal that the line width is quite relevant in choosing which mask size should be used. Firstly, the system verifies the average width of ridges and valleys in fingerprints to consider whether the process use a mask with 9x9 or 17x17 pixels of size, identifying 8 possible angles for the directional field determination. In spite of the width ridge process evaluation, when creating the directional image, the technique is not time-consuming and tests perform very well both in terms of efficiency and robustness.
Keywords: biometrics, fingerprint, directional image, digital image processing, smoothing.
Biographical notes: F.M. Viola received his BSc in Computer Science in 1999. He is currently a MSc student in the Computer Institute of the Federal Fluminense University, Brazil. His current research interest includes biometrics and image processing (www.ic.uff.br/~fviola).
S.L.O. Gonzaga received his MSc in 2004 and a BSc in Computer Science in 1996. He is a DSc student in the Computer Institute of the Federal Fluminense University. His research interests include image processing and computational modeling (www.ic.uff.br/~sgonzaga).
A. Conci, Dr.Sc. is titular professor in the Department of Computer Science in Federal Fluminense University at Niterói (Brazil). Her research interests include Biomechanics, Applications of Computer Vision and Image Processing (www.ic.uff.br/~aconci).
1 INTRODUCTION
Identification based on fingerprints has been known and used for a long time. Even though researches in several other biometrics (as iris and retina), owing to their uniqueness and immutability, fingerprints are still today the most widely used biometric features (Gonzaga et al., 2005). Fingerprint matching is usually performed first at coarse level and after in fine level. An automatic fingerprint identification system usually depends on the correct localization of singular points (core and delta) for alignment before matching. Detection of those points is a non-trivial task (Gonzaga et al., 2005a). Poincare index, which is one of the methods used for such task (Gu et al., 2004; Gonzaga et al., 2005; Costa, 2001; Wang and Wang, 2004), uses orientation field. As a global feature, orientation field describes the basic structures of fingerprints. It is of low frequency, so that it must be robust with respect to abrupt variations and noises.
F. VIOLA, S.L.O. GONZAGA AND A. CONCI The influence of the average width of ridges and valleys in
fingerprint images is discussed in this work when carrying
directional image out. Next section presents the basic
definitions and sketch directional image technique. Section
3 comments the results obtained. Finally, in section
4 some
conclusions are drawn.
2 DIRECTIONAL
IMAGE
The ridge pattern in a fingerprint may be viewed as an
oriented texture having a fixed dominant spatial frequency
in a local neighborhood. The frequency is due to the inter-
ridge spacing present in the fingerprint, and the orientation
is due to the flow pattern exhibited by the ridges. By
capturing the frequency and orientation of ridges in non-
overlapping local regions in fingerprint images, a simpler
representation of the fingerprint is possible. However, to
match two fingerprints using such representation, a suitable
alignment of the underlying ridge structures is essential
(Ross et al., 2003). Such alignment can be obtained
considering the image orientation around the singular
points.
Topological analysis of fingerprint patterns is usually
performed considering a directional image in a form of
directional matrix. The directional matrix is a relatively
simple description of the ridge orientation. Each element of
that matrix is the average or dominant orientation in the
corresponding neighborhood (Vizcaya and Gerhardt, 1996).
Thus, each point in the directional matrix represents a block
of pixels in the original gray scale image. The goal of this
work is to identify the relation among the average line
width, the mask used on the computation of the directional
matrix and its adequate block size. In other words, it aims to
show the influence of the average line width on the initial
level of the automatic process.
2.1 Estimation
Let [i,j] be a generic pixel in a fingerprint image. The local
ridge orientation at [i,j] is the angle θij between the
fingerprint ridges and the horizontal axis. The approach
used in this work estimates the direction at each pixel from
the output of eight oriented filters. These filters calculate the
sum of the differences between the pixel [i,j] and eight or
sixteen neighbors along eight directions using a mask of
9x9, as proposed by Karu and Jain (1996) or 17x17 pixels,
as cited by Costa (2001), and here adapted. Such directions
can be seen in Figure 1.
To compute the direction in a block, a 9x9 or a 17x17
pixel mask is centered at middle pixel [i,j]. The gray values
of neighbor pixels in eight directions (positions marked by
numbers 0 to 7 in Figure 1) are added together to obtain the
sums S0 to S7. Both 9x9 and 17x17 pixel masks compute
the sums as (Gonzaga et al., 2005a):
∑
−=
−
′
+
−
=
n
n
K
j
i
I
K
m
j
mK
i
I
Sl)
,(
)
,
( (1) where m = |min (l , 2, 8 - l)|, m'=0 if l=4, m’=-2 if l=7, otherwise m' = |min (4-l , 2)| (4-l) /|4-l|.
Figure 1 Mask with 17x17 pixels to compute the directional
image
On Equation (1), the difference between the 9x9 and 17x17 pixel mask is the use of n as 2 or 4 and the use of unitary or double increment in K, respectively on sums. If the pixel [i,j] has a value C, then its angle is given by:
d=p if∑
=
<
+
+
7
8
3
)
2(
i
Sl
Sq
Sp
nC; otherwise d=q (2)
Being p and q integers in [0,7], such that Sp = minimum S l (l=0...7), Sq = maximum S l (l=0...7) and S l is each one of S0 to S7 on Equation (1). In other words p is the index of the minimum S l and q is the index of maximum S l. Equation (2) gives an average direction of each block of 9x9 or 17x17 pixel, quantified to eight possible angles: l= lπ/8 radians.
Each block represents a cell of the directional matrix, which is a directional image representation of the considered neighborhood. The directional image, whether directly computed by the directional matrix, may contain several unreliable elements due to the local process characteristics. In this situation, regularization or a smoothing step is very useful in enhancing the directional images, as shown in the next section.
2.2 Smoothing
After computing the directional matrix, this work smoothes it to reduce noise and increase the precision of the correct angle localization. This work uses the more frequently angle in a 3x3 blocks. That is, such 3x3 angle block filter scans the image setting its central angle with the more frequently angle found. Figure 2 shows a 3x3 filter scanning the first block, which occurs 7 times the angle π/4 radians, once π/2, and once with 0 radian angles. The central angle of such
O N THE LINE WIDTH INFLUENCE IN DIRECTIONAL FIELD DETERMINATION FOR FINGERPRINT IMAGES
block is set with the more frequently angle, that is, the π/4 radians.
Figure 2 Directional image with a 3x3 filter (in red) scanning the first block and the central angle set(in black)
When two or more frequencies have the same number of elements in the 3x3 angle block, the number of angles in the block filter, is increased and the process is repeated, this time with a block of 4x4 (5x5 and so on) angles, until the most frequent direction is found. Figure 3 illustrates the method developed, where from the original fingerprint image the algorithm evaluates its medium width ridge, such as the work presented by Kovács-Vajna et al. (2000). If it has a medium width ridge bigger than 6 pixels, the computational routine uses a 17x17 pixel block; otherwise, it calculates the directional image with a 9x9 pixel block. The process smoothes the directional image obtaining good results as shown in next section.
Figure 3 Algorithm scheme 3 EXPERIMENTAL
RESULTS
This section presents examples that illustrate the relation among line width and the number of pixels in the block and the directional image obtained by the developed application. The selected fingerprint images have their directional image computed by the approach presented in section 2.1 and 2.2. Synthetic (from Sfinge, http://bias.csr.unibo.it) and natural images have being used, all in the BMP format, with 256x256 gray level pixels.
Figure 4 shows one of the synthetic images used in different resolutions considering its line average width. Obtaining the directional image, when the original image is scanned by the 9x9 mask, each block of the directional matrix represent a region of 9x9 pixels and for each block an average direction is calculated. Therefore, for each image of 256x256 pixels, a 28x28 directional matrix is generated.
Figure 4 Synthetic images with average ridge width with a) 6,
b) 8 and c) 9 pixels
Figure 5 present the processing of fingerprints with a 9x9 mask: directional image (top left), original and directional images overlapped (top right), directional image smoothed (bottom left) and overlapping original and directional images smoothed (bottom right). In Figure 6 it uses a 17x17 pixel mask and as a result, a 15x15 directional image is obtained. Tests were done in several images with ridge average width among 3 and 10 pixels. Using a 9x9 pixel mask for directional image generation, good results were obtained with average width minor than 7 pixels, because the mask size is big enough to verify the line orientation (Gonzaga et al., 2005a). Applying the 9x9 pixel mask in images where ridge and valley present an average of 7 and 8 pixels, the obtained results were inferior to those obtained in images with lines of 6 pixels on average width. However, the orientation can be still estimated, as shown in Figure 5. When using fingerprint images with average ridge bigger than 8 pixels, as the 9x9 pixel mask can lay exact in the middle of a ridge or valley, the mask is not big enough to distinguish the orientation, as illustrated in Figure 5. It does not obtain good results when generating directional images. So an evaluation of the average line width is important for defining the mask used on directional field estimation process. If the ridge width is smaller than 7 pixels, a 9x9 pixel mask can be used. Otherwise, a 17x17 pixel mask is more appropriated to obtain good results (Figure 6).
F. VIOLA, S.L.O. GONZAGA AND A. CONCI Figure 5 Results of processing image in Figure 4b by a 9x9 mask
Figure 6 Results of processing image in Figure 4c by 17x17 mask
Figure 7 shows the core (in white) and delta (in black)
points identification by using Poincare index for real image
and that in Figure 4.
Figure 7 Singular points localized for the synthetic (left) and
natural (right) images
4 CONCLUSIONS
Methods that use a similar process to this work are quite
used for defining directional image. Experimental tests
shown in this work, using synthetic and real images,
evidence that such methods suffer great influence of the
average width of fingerprint ridges and valleys. When
creating directional image of fingerprints, the mask size
depends on the average width of fingerprint lines. If the
image has lines with average width bigger than 6 pixels,
either the image should be resized or a 17x17 pixel mask
must be used.
The process used in this work for directional images sums
the differences between the pixel and their neighbors in the
block along eight directions. The directional image
computed from fingerprint may contain several unreliable
elements (due to local scratches or cluttered noise).
Therefore, regularization or smoothing step is necessary. A
novel scheme for this smoothing is presented in this work
with good results.
ACKNOWLEDGEMENT
The second author acknowledges Capes and the third one is
grateful to CNPq for financial support.
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