Area Based Novel Approach for Fuzzy Edge Detection

Abstract

This paper presents a novel approach for edge detection based on the univalue segment assimilating nucleus (USAN) area. The USAN area characterizes the structure of the edge present in the neighborhood of a pixel and can thus be considered as a unique feature of the pixel and is fuzzified. The Gaussian edge detector mask is then applied to the associated Gaussian membership function of the USAN area. A threshold is applied on the resultant gradient image to yield the binary image. The results of the proposed edge detector are compared with other well known edge detection techniques and it is found that the image obtained using the proposed approach is qualitatively the best

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AREA BASED NOVEL APPROACH FOR FUZZY EDGE DETECTION
M. Hanmandlu
Dept. of Electrical Engineering, I.I.T. Delhi, India.{mhmanduke.
Rohan Raj Kalra
Dept. ofComputer Science, S.I.T.M, Rewari, India. {___an______________
Vamsi Krishna Madasu
School ofEngineering Systems, Queensland University ofTechnology, Australia. {v da u
Shantaram Vasikarla
School of IT, American InterContinental University, U.S.A. {
.}
}
sv
ABSTRACT
This paper presents a novel approach for edge detection
based on
theUnivalue Segment Assimilating Nucleus
(USAN) area. The USAN area characterizes the structure of
the edgepresent in the neighborhood ofapixel and can thus
be considered as a unique feature of the pixel and is
fuzzified. The Gaussian edge detector mask is then applied
to the associated Gaussian membership function of the
USAN area. A threshold is applied on the resultant gradient
image to yield the binary image. The results oftheproposed
edge detector are compared with other well known edge
detection techniques and it isfound that the image obtained
using theproposed approach is qualitatively the best.
Index Terms: Edge detection, USAN area
1. Introduction
Edge detection is extensively used in image processing
applications to separate the object from the background in
images. Using edges, significant amount of data can be
reduced by filtering out the useless information while
preserving the structural properties ofan image.
A lot of research has been done in the field of image
segmentation using edge detection. Some of the earliest
operators to detect edges in an image were proposed by
Sobel, Prewitt, Roberts, etc. These operators used local
gradient methods to detect edges along a specified direction.
The lack of noise control in these operators results in their
poor performance on blurred or noisy images. Canny [1]
proposed a method to counter noise problems, wherein the
image is convolved with the first order derivative of the
Gaussian filter for smoothing in the local gradient direction
followed by thresholding to yield edges. Marr and Hildreth
[2] proposed an algorithm that finds edges at the zero-
crossings of the imageLaplacian.
techniques for edge detection also saw much advancement
through the SUSAN method [3], which works by associating
a small area of neighboring pixels with similar brightness to
Non-linear
filtering
each center pixel. More recent techniques pose the edge
detection as a fuzzy reasoning problem. Fuzzy logic used in
[4] employs morphological edge extraction method. Ho et
al. [5] have used both global and local image information
for fuzzy categorization and classification based on edges.
Tizhoosh in [9] has developed an approach for fast fuzzy
edge detection. In
detection uses both global and local image information. This
work was based on our earlier work reported in [8]. We
extend the approach in [6] by using the concept of SUSAN
edge detector. Now as in [3] we calculate the USAN or
similar brightness area around each pixel because area
conveys more efficient information about the structure of
the image. We use the Gaussian membership function to
represent the USAN area of [3] in the fuzzy domain. Then
these fuzzified values are in the range [0, 1] corresponding
to the gray map in the range (0-255). Then we apply a local
edge detector mask over the fuzzified values to get the
gradient values which depict a thick edge map of the image.
The next step is a simple thresholding on the gradient values
to yield fine edges.
[6] a fuzzy-based approach to edge
2. FUZZIFICATION
In this section, we will show the computation ofUSAN area
so that it can be fuzzified for further processing to obtain the
binary image.
2.1. Univalue Area Calculation
In this approach, a local region is defined around each pixel
as this local area contains information about the structure of
the image. Following SUSAN[3], we define a circular mask
ofradius 3.4 which leads to an area of37 pixels on the basis
of experiments. Here the central pixel is known as nucleus.
The brightness of each pixel is compared with that of the
nucleus of the mask. The area of the mask is constituted by
the pixels having same brightness as the nucleus. This area
of mask
as
the USAN (univalue
assimilating
is known
nucleus). The most important property of
segment
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USAN area is that it falls to half as the edge is approached.
The area around each pixel is computed from:
(I(r ) -I(ro ))8
Cm ne
t()
where, t is the threshold of the brightness gradient and is set
to 20. In (1) r is the intensity value ranging from 1 to 256,
and ro is the intensity value at the nucleus. The value ofCm,n
is the area ofthe mask at location (m, n) in the image X. The
Eqn. (1) is adapted from [3] where the power is 6. But this
value is found not suitable for fuzzification; hence we have
arrived at 8.
2.2. Histogram based Fuzzy Membership
Function
The membership function gives the degree by which a
particular property, for e.g., intensity is associated with a
pixel. Here, we use a Gaussian membership function that
contains only one parameter fuzzifierfh, given by:
1u(m, n)=G(cm )=e (Cmax-C),n 12
where, m = 1,2...M; n = 1,2...N, Cmax is the maximum area
around any pixel. Here cmax= 37; (because we are using a
circular mask of 37 pixels), Cm n is the area value at (m,n)th
location.
A fuzzy histogram is used to obtain the frequency of
occurrence of membership function of the area in the fuzzy
image X. Thus we get
X = U{A (k), p(k)}
where, pu(k)
associated USAN
area and p(k)
occurrence of this area in an image X.
Thus a normalized probability function is derived so as to
satisfy the condition:
37
L
p(k)=I
k =
Use of kth area in(2) leads to
Au(k)= e
where, k varies between 1 and 37 (cmax), and fuzzifierfh can
be determined from [8]:
Cmx
E, (Cmax
2
kO
fh
-1
Z (Cmax
k =O
The entropy function using (5) is given by
E(p)=-{,(k)lnp(k)+ (1-p(k))ln(1-p(k))}
(2)
(3)
is the membership of each pixel with an
isthefrequency of
(4)
I
-(Cm ax
k)
212
(5)
1
- k) 4p(k)
6
=
- k) 2p (k)
(7)
3. LOCAL EDGE DETECTOR
An area based edge detector is defined in [6] as:
y[ [p(m+i,n+j)-p(m,n)]°
q(m,n)= e 2i
where i
detector mask is wxw.
The two parameters, a and P are the design parameters.
The mask is a generalized Gaussian function. For example a
=p= 2 would yield a normal Gaussian mask. The use of
USAN area membership function helps find edge pixels that
can be easily localized. These are further accentuated by
applying the edge operator in (8) as gives the edge map of
the image.
This is not the case with the most of primitive
edge operators like Sobel, Prewit etc. except the Canny edge
detector that has been constructed imposing the localization
constraint.
2(fh)8
(8)
, j = [-(w-l)/2
, (w-1)/2]
, and size of the edge
3.1 Entropy Optimization ofparameters a and ,B
As the final edge output depends heavily on two parameters,
cc and P;
Taking into consideration that the edge mask is applied
locally and doesn't involve the entire image the entropy
function is computed from
E(q (m,n))
the optimization of these parameters is required.
[(m,n)lnq(m,n) +
(m,n))ln(I-q(m,n))]
(9)
The derivatives ofE w.r.t. a andP are obtained as:
8E
OE
aa
aq(m,n)
17yKaInKInK-
2(fh)/
8OE
8E
8/3
a(m, n)
aa
-1-7}
i(m,n)
8/3
Oi1(m,n)
2(fh )8
{I
77}
(10)
(11)
where, K =[u(m + i, n + j)-u(m, n)]
The above derivatives are used in the learning of the
parameters, a and P recursively by the gradient descent
technique. The learning laws are as follows:
aE
anewaold
a ea0 OC
(12)
(13)
fi old
8
a p
We can optimize E with respect to
image before attempting edge detection.
fh
for an improved
where, Ea and
range [0, 1] corresponding to a and D respectively. If a and
p are the learning factors chosen in the
Pi new

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P diverge or converge too quickly the value ofcaand£8
have to be altered respectively to ensure convergence.
3.3. Image thresholding
After edge image based on USAN areas is generated, the
next task is to binarize the image according to a certain
threshold.
An
optimum
experimentally as:
thresholdis determined
I{ A> 0.911
lo
< 0.911
Cth(m'n)
O
(14)
4. PROPOSED ALGORITHM
The steps of the area based fuzzy edge detector algorithm
are as follows:
1.
2.
3.
4.
5.
6.
Calculate the area (c) around each pixel in the image.
Calculate the value ofparameterfh.
Fuzzify the area using Gaussian membership function.
Optimize a and P iteratively until they converge.
Apply the local fuzzy edge detector function f(m, n).
Apply
from Step 5.
Stop
the selected threshold on the thick edge map
7.
almost one pixel-thick edges. The result of thresholding is
shown in Fig. 2.
In all the test images, the original shape is retained with a
good balance of detail and speckle-textured edges. For
comparison purposes, we have applied the Canny edge
detectorand
space
operator [7] on the test images. Results are as shown in Fig.
3 whereas in Fig. 4 we have applied the SUSAN method on
test images. It appears that Fig. 3 and Fig. 4 have much
difference in the appearance ofthe Lena image.
Canny yields unnecessary edges thus cluttering the
main shape details whereas the proposed area based edge
detector drops some edges and enhances the important edges
that contribute to the main shape. The Gaussian gradient
diffusion
operator
causes
blurred
accentuates only the strong edges but most valuable details
of the face are lost. SUSAN edge detector causes the
problem of step edges. This distinctive
proposed
area based edge
recognition applications.
scaleGaussian gradientdiffusion
edges,
and
mainly
feature of the
ideal detectorisfor face
5. RESULTS AND DISCUSSIONS
(a) Original image
II
..i
i..
(b) Gradientimage
The fuzzy edge detector is implemented on the standard
256x256 pixel gray level test images, i.e., Lena, Barbara
and Cameraman images. Prior to the application of this
algorithm no preprocessing was done on these images. As
this algorithm has three phases: fuzzification using the
Gaussian function, local edge detection using the proposed
Gaussian type edge masks and thresholding, we will present
results at each of these three phases.
edge mask, we will get an edge map of the image which is
then refined by the thresholding operation. Here the Lena
image is used for visual analysis. We haven't attempted
quantitative analysis as it requires an additional processing
such as edge linking and edge sorting as per their lengths.
The technique yielding the large number of longest edge
segments is considered the best. However, this criterion
doesn't work
quantitative analysis is not explored here.
After applying the
for textured image
such
asLena. The
5.1 Experimental Results
The original and gradient images of Lena are shown in
Fig.l. As can be seen in the gradient image the structure of
the image is retained but the edges are very thick. Then
thresholding is done to binarize the image and to obtain
Fig.1 Edge Detection using fuzzification
Fig. 2 Thresholded Image
I-
I SA.../v.
I
'Cf
ZI.F.- I.P
%
I-4:- F -4
;-
.:,
'
I
L;
11i'
I
1B:
i1'
4*
I"
1i
n
(aCanEdge9m operator
Fig. 3 Comparative Output

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6. Conclusions
(b) SUSAN Edge Detection
Fig.4 SUSAN Output
(a) Original image (b) Fuzzified image
< ,~~~~1
(c) Thresholded Image(d) SUSAN Edge Detection
Fig. 5 Results on Cameraman
(b) Fuzzified Image
L,L
'I"
(c) Thresholded Image
(d) SUSAN Edge Detection
Fig. 6 Results on Barbara
The area based fuzzy edge detector presented in this paper
uses the area concept in [3]. The area is fuzzified using the
Gaussian membership function. The local edge detection
operator is applied using parameters a and P which are
optimized using the entropy optimization method to obtain
the gradient image which is the edge map of the image.
Then, a thresholding level is selected to obtain the fine edge
image. Results show that this edge detector is immensely
suitable
fingerprint identification as it does not distort the shape of
the image and is able to retain all the important edges unlike
other edge detectors.
However, in this work it remains to
undertake quantitative analysis to judge the performance of
various edge detectors. Appropriate fuzzification function
and thresholding selection are important for the success of
the proposed edge detection algorithm.
for applications such as face recognition and
Acknowledgement
The
LASTEC, Defense Research and Development Organization
Delhi (DRDO) under the Contract number: 5/ST/04-051.
authors
gratefully
acknowledgethe
support
of
7. References
[1]
J.F.
detection", IEEE Transactions on Pattern Analysis and
Machine Intelligence, 8(6), 1986, 679-698.
[2] D. Marr, and E.C. Hildreth, "Theory of edge detection",
Proc. ofthe Royal Society ofLondon, b207, 1980, 187-
217.
[3] S.M.
Smith, and J.M. Brady, "SUSAN
approach to low level image processing", International
Journal ofComputer Vision, 23(1), 1997, 45-78.
[4]
Symposium on Allied Computing, 1994.
[5] K.H.L. Ho, and N. Ohnishi, "FEDGE - Fuzzy edge
detection by fuzzy categorization and classification of
edges", Fuzzy Logic in Artificial Intelligence, Springer,
IJCAI'95 Workshop, Montreal, Canada, 1188:182-196.
[6] M. Hanmandlu, J. See, and S. Vasikarla, "Fuzzy edge
detector
using
entropy
International Conference on Information Technology:
Coding and Computing, 2004, 665-670.
[7] B.M. ter Haar Romeny, Front-End Vision and Multi-
Scale Image Analysis, Kluwer Academic Publishers,
2002.
[8] M. Hanmandlu, M., D. Jha, M., and R. Sharma, "Color
image
enhancement
using
Recognition Letters 24(1-3), 2003, 81-87.
[9] H.R.Tizhoosh,
"Fast
fuzzy edge
Annual
Meeting
of
Information Processing Society, 2002, 231-242.
Canny,
"A
computationalapproach
to
edge
- A new
I. Bloch, "Fuzzy sets in image processing", ACM
opimization",
Proc.
fuzzification",
Pattern
detection",
American
Proc.
Fuzzy
theNorth
(a) Original image
taJ uriginai1 ima1ge