Image restoration based on morphological operations

International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.3, June 2014
DOI : 10.5121/ijcseit.2014.4302 9
IMAGE RESTORATION BASED ON MORPHOLOGICAL
OPERATIONS
A.M.Raid1
, W.M.Khedr2
, M.A.El-dosuky1
and Mona Aoud1
1
Mansoura University, Faculty of Computer Science and Information System
2 Zagazig University, Faculty of Science
ABSTRACT
Image processing including noise suppression, feature extraction, edge detection, image segmentation,
shape recognition, texture analysis, image restoration and reconstruction, image compression etc uses
mathematical morphology which is a method of nonlinear filters.
It is modulated from traditional morphology to order morphology, soft mathematical morphology and fuzzy
soft mathematical morphology. This paper is covers 6 morphological operations which are implemented in
the matlab program, including erosion, dilation, opening, closing, boundary extraction and region filling.
KEYWORDS
Image Restoration, Structure Elements (SE), and Morphological operations.
1. INTRODUCTION
Image restoration provides a means to reconstruct damaged regions of an image. Image
components for representation and description of region shape, such as boundaries, skeletons, and
the convex hull are extracted by Morphological image processing [1]. It can be used for filtering,
thinning and pruning. It is constructed with operations on sets of pixels. More sophisticated
mathematical development are been required to Morphological processing for gray scale images
[2,3].
Dilation and erosion are the main morphological operations [4]. The objects are expanded in
dilation operation, thus small holes probably are filled and disjoint objects are connected. The
objects are diminished in erosion operation with etching away (eroding) their boundaries. An
application with the ability to select the proper structuring element and how erode or dilate the
objects is proposed. These operations can be customized for an application by the proper selection
of the structuring element, which determines exactly how the objects will be dilated or eroded [5].
The state of any given pixel in the output image is determined by applying a rule to the
corresponding pixel and its neighbors in the input image in the morphological dilation and
erosion operations [6]. The operation as dilation or erosion can be defined by the rule used to
process the pixels. In this paper will mainly concentrate on 4 morphological operations and 2
basic morphological algorithms which are implemented in the program, including erosion,

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dilation, opening, closing, boundary extraction and region filling, Users can arbitrarily choose one
of the morphological operations through the six radio buttons, Change dynamically the SE size
through moving the slider and there are 3 types of SE which are implemented in the program,
including diamond, square and octagon. The pop-up menu change se type dynamically.
The rest of this paper organize in three sections, The next section introduces morphological
operations and its steps, section three explains Some basic morphological algorithms and section
four shows the results of each operation and 2 basic algorithms.
2. Morphological Operations
2.1 The operation of dilation
The process of the structuring element B on the image A and moving it across the image in a way
like convolution is defined as dilation operation. The two main inputs for the dilation operator [7]
are the image which is to be dilated and a set of coordinate points known as a structuring element
which define also as a kernel. The exact effect of the dilation on the input image is determined by
this structuring element [8]. The following steps are the mathematical definition of dilation for
binary images:
1. Suppose that is the set of Euclidean coordinates corresponding to the input binary
image, and that is the set of coordinates for the structuring element.
2. Let denote the translation of so that its origin is at .
3. Then the dilation of by is simply the set of all points such that the intersection of
with is non-empty.
It dilation is defined as set operation. is dilated by , written as , is defined as (1):
} (1)
Among them, is for the empty set, is for the structure element, and is for the reflection of
collection .
An example is shown in Figure (2.1), Note that with a dilation operation, all the 'black' pixels in
the original image will be retained, any boundaries will be expanded, and small holes will be
filled.
The some Characteristics of Binary dilation operator are:
• It is translation invariant.
• It is increasing, that is, if then .

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• It is commutative.
• It is associative, i.e. .
• It is distributive over set union
Figure (2.2) Effect of dilation using a 3×3 square structuring element on binary image
2.2 The operation of erosion
The erosion process is as same as dilation, but the pixels are converted to 'white', not 'black'. The
two main inputs for the erosion operator [9] are the image which is to be eroded and a set of
coordinate points known as a structuring element which define also as a kernel. The exact effect
of the erosion on the input image is determined by this structuring element. The following steps
are the mathematical definition of erosion for binary images:
1. Suppose that is the set of Euclidean coordinates corresponding to the input binary
image, and that is the set of coordinates for the structuring element.
2. Let denote the translation of so that its origin is at .

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3. Then the erosion of by is simply the set of all points such that is a subset of .
is eroded by , recorded as , and defined as (2)
Among them, is for the empty set, is for the structure element, and is for the supplement
of collection .
In Figure (2.3), the only remaining pixels are those that coincide to the origin of the structuring
element where the entire structuring element was contained in the existing object. Because the
structuring element is 3 pixels wide, the 2-pixel-wide right leg of the image.
Figure (2.4) Effect of erosion using a 3×3 square structuring element on binary image
2.3 The operation of opening and closing
The combination of the two main operations, dilation and erosion, can produce more complex
sequences. Opening and closing are the most useful of these for morphological filtering [10]. An
opening operation is defined as erosion followed by a dilation using the same structuring element

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for both operations. The basic two inputs for opening operator are an image to be opened, and a
structuring element. Graylevel opening consists simply of graylevel erosion followed by
graylevel dilation. See Figure (2.5) for the illustration of the opening process.
Using the structure element to do the open operation on the set , expressed as , definite
as
Figure (2.5) Representation of the opening process
Figure (2.6) Effect of opening using a 3×3 square structuring element on binary image
Closing is opening performed in reverse. Simply it is defined as dilation then erosion using the
same structuring element for both operations. The main inputs of the closing operator are an
image to be closed and a structuring element. The process of a graylevel dilation followed by
graylevel erosion is defined as Graylevel closing. Figure (2.7) shows the effects of filling in holes
and closing gaps which define as closing operation.

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Like binary image, at opening operation, Use b to erode f plainly first, then on the results
obtained, use b to do dilate operation. Also, using b to do closing operation on , expressed as
, definite as
Figure (2.7) Representation of the closing process
Figure (2.8) Effect of closing using a 3×3 square structuring element on binary image
3. Some Basic Morphological Algorithms
3.1 Boundary extraction
The boundary of a set A, denoted by , can be obtained by first eroding by and then
performing the set differences between and its erosion. That is,
(5)

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Where B is a suitable structuring element.
‘–‘ is the difference operation on sets (illustrated in Figure (3.1)).
Figure (3.1) Representation of the boundary extraction algorithm
Figure (3.2) Representation of the main operations on sets
3.2 Region Filling
The algorithm for region filling based on set dilations, complementation, and intersections. The
main idea is filling the entire region with ‘black’ starting from a point inside the boundary. If
we adopt the convention, first step all non-boundary (background) points are labeled ‘white’ and
then we assign a value of ‘black’ to p to. Filling the region with ‘black’ by the following
procedure:
(6)

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where
,
is the symmetric structuring element
is the intersection operator (see Figure (3.3))
is the complement of set (see Figure (3.3))
The algorithm terminates at iteration step if . The filled set and its boundary is
contained by the set union of and .
Figure (3.3) Representation of the region filling algorithm
4. SIMULATED RESULTS
At matlab program we applied the 4 morphological operations and 2 basic algorithms using six
radio buttons, so users can determine any of the morphological operations needed, we added 3
types of SE (diamond, square and octagon ) and a slider to modify dynamically the SE size,.
Dynamically change SE type through the pop-up menu, the experimental results for each
operation and algorithms show in the following figure.

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Figure (4.1) Effect of dilation on grayscale image with SE type = square
Figure (4.2) Effect of erosion on grayscale image with SE type = diamond

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Figure (4.3) Effect of opening on grayscale image with SE type = octagon
Figure (4.4) Effect of closing on grayscale image with SE type = diamond

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Figure (4.5) Apply boundary extraction algorithm on grayscale image with SE type = diamond
Figure (4.6) Apply boundary extraction algorithm on grayscale image with SE type = diamond
Figure (4.7) Apply region filling algorithm on grayscale image

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5. IMAGE RESTORATION USING MORPHOLOGICAL OPERATIONS, A
CASE STUDY
The general idea behind using Morphological operations in image restoration is to apply dilation
& erosion with the same factor.
Example:
In matlab program:
The disadvantages of this method is if the objects near with the distance (2*SE_size) then stuck
together so in future work we will consider separating objects in the image.

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6. CONCLUSION
Image processing techniques which deal with the shape (or morphology) of features in an image
is described by Morphological image processing (or morphology). In this paper 4 morphological
operations (dilation, erosion, opening and closing) and 2 basic algorithms (boundary extraction
and region filling) are implemented in matlab program with user interface in which changing the
parameters of SE such as its size or type are simple.
7. REFERENCES
[1] R.C.Gonzales, R.E.Woods, “Digital Image Processing”, 2-nd Edition, Prentice Hall, 2002.
[2] J. Gil and R. Kimmel, “Efficient dilation, erosion, opening and closing algorithms in Mathematical
Morphology and its Applications to Image and Signal Processing” V, J. Goutsias, L. Vincent, and D.
Bloomberg, Eds. Palo-Alto, USA, June 2000, pp. 301.310, Kluwer Academic Publishers.
[3] Z.Fang, M.Yulei, Z.Junpeng, “Medical Image Processing Based on Mathematical Morphology”, The
2nd International Conference on Computer Application and System Modeling (2012).
[4] U.Scot.E, ”Computer Vision and Image Processing”, Prentice Hall, NJ, 1998, ISBN 0-13-264599-8
[5] J. Gil and R. Kimmel, “Efficient dilation, erosion, opening, and closing algorithms”, IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1606.1617, December
2002.
[6] G.V.Tcheslavski, “Morphological Image Processing: Grayscale morphology”, ELEN 4304/5365 DIP,
Spring 2010.
[7] H.Heijmans, “Morphological image operators”, Advances in Electronics and Electron Physics.
Academic Press, 1994.
[8] R. Haralick, S. Sternberg, and X. Zhuang, “Image analysis using mathematical morphology”, IEEE
Transactions on Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 532.550, July 1987.
[9] Serra.J, “Mathematical Morphology and Its Applications to Image Processing”, Kluwer Academic
Publishers, Boston (1994)
[10] L.Vincent, “Morphological area openings and closings for greyscale images”, in Proc. Shape in
Picture '92, NATO Workshop, Driebergen, The Netherlands, September 1992, Springer-Verlag.

Image restoration based on morphological operations

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