Morphological Edge Detection Algorithm Based on Multi-Structure Elements of Different Directions

Abstract

Edge detection is one of the important pre-processing steps in image analysis. Edges characterize boundaries and edge detection is one of the most difficult tasks in image processing hence it is a problem of fundamental importance in image processing. Edges in images are areas with strong intensity contrasts and a jump in intensity from one pixel to the next can create major variation in the picture quality. Edge detection of an image significantly reduces the amount of data and filters out useless information, while preserving the important structural properties in an image. Conventionally, mathematical morphology edge detection methods use single and symmetrical structure elements. But they are difficult to detect complex edge feature, because they are only sensitive to image edge which has the same direction of structure elements. This paper proposed a novel edge detection algorithm based on multi-structure elements morphology of eight different directions. The eight different edge detection results are obtained by using morphological gradient algorithm respectively, and final edge results are obtained by using synthetic weighted method. The experimental results showed that the proposed algorithm is more efficient for edge detection than conventional mathematical morphological edge detection algorithms and differential edge detection operators.

Full text

Volume 1 No. 1, May 2011
International Journal of Information and Communication Technology Research
©2010-11 IJICT Journal. All rights reserved
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37
Morphological Edge Detection Algorithm Based on Multi-Structure
Elements of Different Directions
1 C.NagaRaju ,2 S.NagaMani, 3 G.rakesh Prasad, 4 S.Sunitha
1Professor and Head of IT, L.B.R.College of Engineering
2,3 Asst. professor L.B.R.College of Engineering- Mylavaram
4Asst. professor V.R.Sidhartha College of Engineering- Vijayawada
ABSTRACT
Edge detection is one of the important pre-processing steps in image analysis. Edges characterize boundaries and edge
detection is one of the most difficult tasks in image processing hence it is a problem of fundamental importance in image
processing. Edges in images are areas with strong intensity contrasts and a jump in intensity from one pixel to the next can
create major variation in the picture quality. Edge detection of an image significantly reduces the amount of data and filters
out useless information, while preserving the important structural properties in an image. Conventionally, mathematical
morphology edge detection methods use single and symmetrical structure elements. But they are difficult to detect
complex edge feature, because they are only sensitive to image edge which has the same direction of structure elements.
This paper proposed a novel edge detection algorithm based on multi-structure elements morphology of eight different
directions. The eight different edge detection results are obtained by using morphological gradient algorithm respectively,
and final edge results are obtained by using synthetic weighted method. The experimental results showed that the proposed
algorithm is more efficient for edge detection than conventional mathematical morphological edge detection algorithms
and differential edge detection operators.
Keywords: Fragmentation, edge detection, SE, catchment basins and MSE
1. INTRODUCTION
Image Segmentation is the process of partitioning
a digital image into multiple regions [6,7,8]. Actually,
partitions are different objects in image which have the
same features. The result of image segmentation is a set of
regions that collectively cover the entire image, or a set of
contours extracted from the image. All of the pixels in a
region are similar with respect to some characteristic or
computed property, such as color, intensity, or texture.
Adjacent regions are significantly different with respect to
the same characteristics. Edge detection is one of the most
frequently used techniques in digital image processing [8].
The boundaries of object surfaces in a scene often
lead to oriented localized changes in intensity of an image,
called edges. This observation combined with a commonly
held belief that edge detection is the first step in image
segmentation, has fueled a long search for a good edge
detection algorithm to use in image processing [11]. This
search has constituted a principal area of research in low
level vision and has led to a steady stream of edge
detection algorithms published in the image processing
journals over the last two decades. Even recently, new
edge detection algorithms are published each year. Edge
detection of an image reduces significantly the amount of
data and filters out information that may be regarded as
less relevant, preserving the important structural properties
of an image. Therefore, edges detected from its original
image contain major information, which only needs a
small amount of memory to store. The purpose of
detecting sharp changes in image brightness is to capture
important events and changes in properties of the world.
For an image formation model, discontinuities in
image brightness are likely to correspond to a)
Discontinuities in depth b) Discontinuities in surface
orientation c) Changes in material properties d) Variations
in scene illumination e) Grayness ambiguity f) Vague
knowledge. In the ideal case, the result of applying an
edge detector to an image may lead to a set of connected
curves that indicates the boundaries of objects, the
boundaries of surface marking as well curves that
correspond to discontinuities in surface orientation. If the
edge detection step is successful, the subsequent task of
interpreting the information contents in the original image
may therefore be substantially simplified. Unfortunately,
however, it is not always possible to obtain such ideal
edges from real life images of moderate complexity.
Edges extracted from non-trivial images are often
hampered by fragmentation i.e. the edge curves are not
connected, missing edge segments; false edges etc., which
complicate the subsequent task of interpreting the image
data. Mathematical Morphology is a powerful tool for
dealing with various problems in image processing and
computer vision [4,9].It was introduced in [9] as a
technique for analyzing geometric structure of metallic
and geologic samples. It was extended to image analysis in
[5, 10]. Mathematical morphology is a very important
theory, whose operation must be defined by set arithmetic.
Therefore, the image which will be processed by
mathematical morphology theory must been changed into
set. Mathematical morphology is composed by a series of
morphological algebraic arithmetic operators. The basic
morphological operations, namely erosion, dilation,
opening, closing etc. are used for detecting, modifying,

Volume 1 No. 1, May 2011
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©2010-11 IJICT Journal. All rights reserved
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manipulating the features present in the image based on
their shapes. The shape and the size of SE play crucial
roles in such type of processing and are therefore chosen
according to the need and purpose of the associated
application. Usually, people use single and symmetrical
structure elements morphology to detect image edge. But
they are difficult to detect complex edge feature, because
they are only sensitive to image edge which has the same
direction of structure elements and are not so effective to
the edge which has the direction other than the structure
elements in [1, 2, 3].In this paper, a novel multi-structure
elements (MSE) morphology algorithm is proposed to
detect the edge of image.
2. WATERSHED METHOD
The watershed transform [12, 13] is a popular
segmentation method coming from the field of
mathematical morphology. The intuitive description of
this transform is quite simple: if we consider the image as
a topographic relief, where the height of each point is
directly related to its gray level, and consider rain
gradually falling on the terrain, then the watersheds are the
lines that separate the lakes called catchment basins that
form.
Generally, the watershed transform is computed
on the gradient of the original image, so that the catchment
basin boundaries are located at high gradient points. The
watershed transform has been widely used in many fields
of image processing, including medical image
segmentation, due to the number of advantages that it
possesses: it is a simple, intuitive method, it is fast and can
be parallelized [14, 15] and almost linear speedup was
reported for a number of processors up to 64 and it
produces a complete division of the image in separated
regions even if the contrast is poor, thus avoiding the need
for any kind of contour joining. Furthermore, several
researchers have proposed techniques to embed the
watershed transform in a multiscale framework, thus
providing the advantages of these representations [16, 17].
A simplest morphological water shed method is gradient
method.
2.1 Morphological Gradient
The morphological gradient m of a function f is
defined by:
)]()[()( SpSppm  (1)
Step2: Compute Morphological Gradient hi
Where is the dilation of
f at the point x and is the
erosion of f and S would be the detection of obstacles but
the main problem is structuring element applied on image.
Some important drawbacks have been exist, some most
important are as follows.
))(())(( jpSupiSp 
))(( InfiSp  ))(( jp
First is Over segmentation, when the watershed
transform infers catchments basins from the gradient of
the image, the result of the watershed transform contains a
myriad of small regions, which makes this result hardly
useful. The use of a marker image [18] to reduce the
number of minima of the image and thus the number of
regions is the most commonly used solution. Also
interesting is the utilization of a scale space approach to
select the interesting regions using different filters
(morphological operations [19], or nonlinear diffusion
[20]).
Second is Sensitivity to noise, the Local
variations of the image can change the result dramatically,
this effect is worsened by the use of high pass filters to
estimate the gradient which amplify the noise. Third is
Poor detection of significant areas with low contrast
boundaries if the signal to noise ratio is not high enough at
the contour of interest the watershed transform will be
unable to detect it accurately.
Furthermore the watershed transform naturally
detects the contours with higher value between markers
which are not always the contours of interest and fourth is
Poor detection of thin structures, When the watershed
transform is applied on the gradient image the smoothing
associated with gradient estimation together with usual
approach of storing gradient values only at the image pixel
positions rather than with sub-pixel accuracy make it
difficult to detect thin catchments basin areas. Often this is
critical for successful segmentation of images.
2.2. Marker Algorithm
The procedure can be enhanced by defining
markers for the objects to be extracted. These markers are
obtained by various means which is described as follows,
Let R be the set of markers Where R is a
connected components
ii RR 
,) i ).( jRjRi 
Consider the function g defined by g = (1-km )
Where u is the upper limit of the gradient m and KM
indicator function of R and the contours of the marked
objects are watershed lines. This marking technique is
Nonparametric and is simply based on the difference of
Contrast between the object and its border. The
Regularized gradient of size s of the function p is the
transform defined by the following procedure
2.2.1. Algorithm
Step1: Read gray level Image size of N XM.
Step3: Erode hi with structuring element
Si- 1. (Ei-1)
Step 4: Dilate Ei-1 with Structuring element Si+1. (Di+1)
Step5: Compute Difference of Morphologic al gradient, hi
and Di+1 (hi+1)
Step 6: Erode hi+1(ui )
This operation depends on size parameter. The
main advantage of this method is its ability to take into
38

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account the variations of the initial function. The
watershed of the supmax of ui (w) is less over segmented
than the watershed of h. This segmentation can now be
used for extracting a coarse marker of the image. This
marker is obtained by selecting the catchments basin of w
located at the other end of the Image. This marker is
smoothed and an outer marker is built in order to mark the
region of the image which does not belong to the image.
These Two markers are used to modify the gradient h. The
divide lines of the modified gradient are the contours of
the object. Marker is a connected component in the image
region and used in watersheds for edge detection. Image
markers are obtained for image simplification. A
simplified image S is built starting from the image F and
its gradient G(F).
Let’s consider the minima M of G and let’s
define a function h as follows:
h=F.PM where PM is the indicator function of M. Now
compute the reconstruction of h by dilation inside the
catchment basins. This operation produces an image where
each basin of gradient is valued. This valuation leads to a
simplified image s made of tiles of constant grey values.
This gradient will be null everywhere except on the divide
lines of g where it is equal to the absolute difference
between the grey-tone values of catchment basins CBi and
CBj separated by Gij.
Grad jiij FFG )( (2)
This gradient image is then used to define a new function
V.

ixVxvXi )(:)( (3)
jji CBUvX )( (4)
Where, CBj are the catchment basins adjacent to
any arc with a watershed of the gradient less or equal to i.
The watershed functions point-out the regions of the
image surrounded by brighter contrast edges. In this
approach, image segmentation is composed of two
independent steps .The first and most critical step consists
in finding markers for the objects to be extracted. The
second one Consists of modifying the gradient function
and computing the watersheds. The main drawback of this
technique is identification of markers and SE is very
difficult.
3. NOVEL METHOD
The selection of structure element is a key factor
in morphological image processing. The size and shape of
SE decide the final result of detected edges. The basic
theory of multi-structure elements morphology is to
construct different structure elements in the same square
window and these structures elements comprise almost all
the line extending directions in the square window.
Let {F(m, n)} (m, n є Z) is a digital image, and
(m,n) is its centre, then structure elements in (2N+1) ×
(2N+1) square window can be denoted by:


NnmNinnmmFA ii 




1,1,*),1,1(


(5)
Where i=1, 2, ----4N-1, α=180/4N, øi is the direction angle
of SE
In this paper, we choose N=2, then in the 5×5
square window, the direction angles of all structure
elements are ø= 00, 22.50,450, 67.50, 900, 112.50, 1350and
157.50 And these structure elements are shown in Fig.1,
where “1” denotes the components of SE. In fact, structure
elements Ai can be got by decomposing 5×5 square SE A
as shown in Fig.2. Therefore, Ai and A satisfies:
i
UAA

(6)
Fig.1a Fig.1b Fig.1c
Fig.1d Fig.1e Fig.1f
Fig.1g Fig.1h
Fig1
Fig2
Step1: pre process the Image to eliminate misclassified
regions in the image
cbA


*2 (7)
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Where b and c are

MFHXb ii )(
))(),(max( minmax xbabsxbabsbc 
Where Xmax and Xmin are the maximum and minimum gray
values of mask and Hi (F) is the frequency of occurrence
of Xi.
Step2: Construct structure elements Ai of different
directions according to the method presented above.
Step3: By taking the structure elements got in step2
respectively to detect the edges Ei (F) of original image by
morphological gradient edge detector.
Step4: Based on every detected edge Ei (F) in step3, use
synthetic weighted method to calculate final detected edge
by

M
iii FEWFE 1)()( (8)
Where E(F) is the possible detected edge of original
image, M is the number of structure elements and wi is
the weight of different detected edge information. It can be
calculated by Wi = 1/M.
Step 5: To find fine edges divide original image by edge
image and multiply by its average in accordance with
equation

),(*),(),(),( 1yxEyxEyxfyxD  (9)
Where
x, y – pixel coordinates
D-resultant edge image
E-edge image from step3
E1- average of edge Image E
The division of the original images by its average
reveals the differences between these two images. Due to
image borders blur while average filtration the differences
are especially visible in case of edge whilst fire images
areas they are almost unrecognizable and which makes
image intensity equals original image average intensity so
the result of the division is regarded to be images of edges.
4. EXPERIMENTAL RESULTS
The experiments are carried out to evaluate the
performance of proposed method with existing methods.
The proposed method has also been tested on a wide
range of natural and synthetic 512X512 pixel 8-bit
gray-scale images with increasing complexity levels. The
given images are containing intensity, texture and illusory
boundaries respectively. This section constructed the
edges for these different image attributes. The final
segmentation results are illustrated. As can be seen, these
images, which traditionally require different algorithms to
segment, can now be processed using the multi-structure
elements morphology of eight different directions. In these
images, the average gray scale of eight directions was
equalized to prevent biased segmentation results due to
leakage of the component through the filters. This method
produced better results compared to traditional methods
like watershed, Sobel and canny edge detecting
techniques. As per visual perception analysis the pixels
misclassified as a third region at the image boundary are
removed by the proposed method. According to results
watershed, Sobel operators produced week edges for all
images and eliminated some important features in the
images and discontinuity in the edge gray level intensities.
Canny edge operator is more efficient for edge detection
even though it produced poor edges for low contrast
images and unimodel histogram images such as rose, eye
and forest images which have been shown in the results.
Canny is high sensitive to noise compare to other methods.
The performance of novel method is almost all
same as on all test images. This method depends on
suitable selection of SE. The global threshold values of
various images according to the watershed method, Sobel
operator, Canny operator and novel method are shown in
table1 and drawn the graph1. The values and graph
explains that the novel method works better for noise and
complex images with optimal values for edge detection.
The novel method produced good and brighter edges by
retaining important features in the images. This method
works smoothly even in complex structure, noise and
uneven illumination. Based on the results conclusions are
made.
1. Anshu a) Watershed b) Sobel
c) Canny d) Novel
2. Rose a) Watershed b) Sobel
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c) Canny d) Novel
3.Eye a) Watershed b) Sobel
c) Canny d) Novel
4.Lena a)Watershed b)Sobel
c) Canny d) Novel
5.Forest a)Watershed c)Sobel
c) Canny d) Novel
6.Pra a)Watershed c)Sobel
c) Canny d) Novel
7.Nani a)Watershed b)Sobel
c) Canny d) Novel
1.Anshu Histogram b.Rose Histogram
41
3.Eye Histogram 4.Lena Histogram

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5.Forest Histogram 6.Novel Histogram
7.Nani Histogram
Table 1
Graph1
5. CONCLUSIONS
The present study on Image processing is a
collection of techniques that can be applied to the given
images. In this paper, a novel multi-structure elements
morphological edge detection algorithm is proposed to
detect image edge. The technique developed is very useful
for Image segmentation and classification. The selection
of structure element is a key factor in morphological
image processing. The size and shape of SE decide the
final result of detected edges. The basic theory of multi-
structure elements morphology is to construct different
structure elements in the same square window. And these
structures elements comprise almost all the line extending
directions in the square window. The given experimental
results show that the algorithm is more efficient than the
usually used single and symmetrical SE morphological
edge detection operator and differential edge detection
operators such as watershed method , Sobel operator and
canny operator,. The detected edge is more pinpointed,
integral and continual, and the edge information is more
abundant. Moreover, the novel proposed algorithm can
filer the noise more successfully than other operators by
high lighting brighter edges. Even though this method
produces better results, it fails to shadow elimination of
Images see in 7d. The eight different edge detection results
are obtained by using morphological gradient algorithm
are better edges over traditional methods.
REFERENCES
[1] T. Chen, and Q. Wu, R. Rahmani-Torkaman, and J.
Hughes, “A pseudo top-hat mathematical
morphological approach to edge detection in dark
regions,” Pattern Recognition, vol. 35, no. 1, pp. 199-
210, January 2009.
[2] J. Rivest, “Morphological operators on complex
signals,” Signal Processing, vol. 84, no. 1, pp. 133–
139, January 2007.
[3] H. Park and RT Chin, “Decomposition of arbitrarily
shaped morphological structuring elements,” IEEE
Trans. Pattern Analysis and Machine Intelligence,
1995, vol. 17, no.1, pp. 2-15, January 2005.
[4] E. Bataillou, “Weighted averaging using adaptive
estimation of the eights,” Signal Processing, vol. 44,
no.1, pp. 51-66, January 2009.
[5] Y. Ma, M. Yang, and L. Li, “A kind of omni-
directional multi-angle structuring elements adaptive
morphological filters,” Journal of China Institute of
Communications, vol. 25, no. 9, pp. 86-92, September
2002.
[6] Orlando J. Tobias and Rui Seara, ”Image
Segmentation by Histogram Thresholding Using
Fuzzy Sets”, IEEE Transactions on Image
Processing, Vol.11, No.12, 2004, pp. 1457-1465.
[7] M. Abdulghafour, ”Image segmentation using Fuzzy
logic and genetic algorithms”, Journal of WSCG, vol.
11, no.1, 2003.
[8] N. Senthilkumaran and R. Rajesh, “Edge Detection
Techniques for Image Segmentation-A Survey”,
Proceedings of the International Conference on
Managing Next Generation
SoftwareApplications(MNGSA-08),2008,pp.749-760.
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©2010-11 IJICT Journal. All rights reserved
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[9] Daniel L. Schmoldt, Pei Li and A. Lynn Abbott,
”Machine vision using artificial neural networks with
local 3D neighborhoods”, Computers and Electronics
in Agriculture, vol.16, 1997, pp.255-271.
43
[10] N. Senthilkumaran and R. Rajesh, “A Study on Split
and Merge for Region based Image Segmentation”,
Proceedings of UGC Sponsored National Conference
Network Security (NCNS-08) , 2008, pp.57-61.
[20] Clark, A.A.; Thomas, B.T., “Evolving image
segmentations for the analysis of video sequences,
Computer Vision and Pattern Recognition”, CVPR
2001. Proceedings of the 2001 IEEE Computer
Society Conference on, Volume: 2, 8-14 Dec. 2001.
AUTHORS
[11] N. Senthilkumaran and R. Rajesh, “A Study on Edge
Detection Methods for Image Segmentation”,
Proceedings of the International Conference on
Mathematics and Computer Science (ICMCS-2009),
2009,Vol.I, pp.255-259.
[12] A.N. Moga and M. Gabbouj,“ Parallel image
component labeling with watershed transformation,”
IEEE Trans., Pattern Anal Machine Intel., vol. 19, pp.
441-450, May 1997.
[13] J.M. Gauch, “Image segmentation and analysis via
multiscale gradient watershed hierarchies,” IEEE
Trans, Image Processing, vol. 8, pp. 69-79, 1999.
Dr C. NagaRaju received his B.Tech degree
in Computer Science from J.N.T.University
Anantapur, M.Tech degree in Computer
Science from J.N.T.University Hyderabad
and PhD in digital Image processing from
J.N.T.University Hyderabad. Currently, he is working as a
professor & Head of IT in LakiReddy Bali reddy College
of Engineering, Vijayawada. He is professor incharge for
systems department. He has got 15 years of teaching
experience. He has published twenty six research papers in
various national and international journals and about
twenty eight research papers in various national and
international conferences. He has attended twenty
seminars and workshops.He is member of various
professional societies like IEEE, ISTE and CSI.
[14] O.F. Olsen and M. Nielsen, “ Multi-scale gradient
magnitude watershed segmentation,” in ICIAP ’97-9th
Int. Conf. on Image Analysis and Processing, ser.
Lecture Notes In Computer Science. Berlin,
Germany: Springer-Verlag, 1997, vol. 1310, pp. 6-13.
[15] E. Dam and M. Nielsen, “Non-linear diffusion for
interactive multiscale watershed segmentation,” in
MICCAI 2000: Fourth International Conference on
Medical Image Computing and Computer-Assisted
Intervention, ser. Lecture Notes in Computer Science.
Berlin, Germany: Springer-Verlag 2000, vol. 1935,
pp. 216-225.
Sikhinam Nagamani received her B.Tech
Degree in Information Technology from
R.V.R& J.C College of engineering
Nagarjuna University, Guntur.M.Tech in
Software Engineering from Godavari Institute of
Engineering and Technology. She is working as assistant
professor in the department of IT, LBRCollege of
Engineering, Mylavaram. She has three years of
experience. She attended two conferences and five work
shops
[16] J.L. Vincent, “Morphological grayscale reconstruction
in image analysis: Applications and efficient
algorithms,” IEEE Trans. Image Processing, vol. 2,
pp. 176-201, 1993.
[17] S.Beucher,“Watershed, hierarchical segmentation and
waterfall algorithm,” in Mathematical Morphology
and Its Applications to Image Processing, Dordrecht,
The Netherlands: Kluwer, 1994. pp. 69-76.
G. Rakesh Prasad received his B.Tech Degree
in Information Technology from
LBRCollege of Engineering, Mylavaram.
M.Tech in Software Engineering from
LBRCollege of Engineering, Mylavaram. He is working
as assistant professor in the department of IT, LBRCollege
of Engineering, Mylavaram. He has one year of
experience. He attended two conferences and five work
shops
[18] J.Weickert,“Fast Segmentation methods based on
partial differential equations and the watershed
transform,”in Proc.DAGM Symp,1998,pp.93-100.
[19] J. Sijbers, P.Scheunders, M. Verhoye, A. Van der
Linden, D.Van Dyck, and E. Raman, “ Watershed-
based segmentation of 3D MR data for volume
quantization,” Magn. Reson. Image. ,vol. 15, pp. 679-
688, 1997.
S.Sunitha received her B.Tech Degree in
Information Technology from V.R.
Siddhartha College of engineering,
Vijayawada.M.Tech in Software Engineering
from LBRCollege of Engineering, Mylavaram. She is
working as assistant professor in the department of IT,
V.R. Siddhartha College of engineering,Vijayawada. She
has five years of teaching experience. She attended two
conferences and four workshops.