PROJECT TITLE: Boundary Extraction By Dilation and Erosion (With MatLab)
Write a computer program to
implement morphological boundary extraction capable of performing binary
dilation and erosion with an arbitrary structuring element of size 3 x 3 that
can be specified by the user.
ABSTRACT:
Mathematical morphology is one of
the data processing methods that is extremely useful for image processing and
has many applications, such as, boundary extraction ,noise elimination, shape
description, texture analysis, and so on. The mathematical base of
morphological processing is dilation and erosion which are described by set
analysis and can be expressed in logical AND, OR notation .The
objective of this project is to write a program capable of performing binary
dilation and erosion with an arbitrary structuring element of size 3 x 3 that
can be extracted the boundary or edge of an image. To simulate these two
operations, image processing toolbox functions of MATLAB programming language
is used.
Morphology, Dilation and Erosion:
¨ Morphology:
The word morphology signifies the study of form or structure. In image
processing we use mathematical morphology as a means to identify and extract
meaningful image descriptors based on properties of form or shape within the
image.
¨ Dilation:
Dilation is an operation that ‘grows’ or ‘thickense’ objects in a binary
image. Mathematically, dilation is
defined in terms of set operations. The dilation of A and B is defined as
¨ Erosion:
Erosion is an operation that ‘Shrinks’ or ‘thins’ objects in a binary image.
The mathematical definition of erosion of A by B is defined as
¨ Structuring Element:
A structuring element is a rectangular array of pixels containing the values
either 1 or 0 (akin to a small binary image). Structuring elements have a
designated center pixel. An example of Structuring element
Fig 1: The local neighborhood
defined by a structuring element. This is given by those shaded pixels in the
image which lie beneath the pixels of value 1 in the structuring element
In Matlab, to
construct the structuring element array by using ‘strel’ function. The example below illustrates how Matlab displays
when a strel object is created:
>> se3 = strel (‘disk ’, 3); % A disk
of radius 3
Which displays the matrix as
follows:
Algorithm for Boundary
Extraction:
¨ Erosion
Algorithm: The boundary of a set A, denoted
by β(A), can be obtained by first eroding A by B and then
performing the set differences between A and its erosion. That is,
β(A)=A – (AΘB)
where
B is a suitable structuring element. ‘–‘ is the difference
operation on sets.
¨ Dilation
Algorithm: The boundary of a set A, denoted
by β(A), can be obtained by first dilating A by B and then
performing the set differences between A and its erosion. That is,
β(A)=
(A B) – A
where
B is a suitable structuring element. ‘–‘ is the difference
operation on sets.
Dilation Operation: Three pixel-long diagonal line with the origin at the center
When the
structuring element overlaps 1-valued pixels, the pixel at the origin is marked
1. In Matlab, we can carry out image dilation using the Image Processing Toolbox
functions imdilate.
>>imdilate_image
= imdilate(Orginal_binary_image,structuring_element_array);
Erosion
Operation: a three-pixel-long vertical line with the origin at
the center
In Matlab, we
can carry out image erosion using the Image Processing Toolbox functions “imerode”.
>>imerode_image
= imerode(Orginal_binary_image , structuring_element_array);
Results
of Dilation:
Results
of Erosion:
Discussion:
In the above result, it
is shown that the two morphological operations of Dilation and Erosion is
applied for our selected black and white image. To simulate these two operations, image processing toolbox
functions of MATLAB programming language is used.
At first the original
image (linkon.tif) is represented to the Binary image by using the matlab
built-in function of imread(). And then I select structuring element of size 3 x 3 long diagonal line for dilation and structuring element of size 3 x 3 long vertical line.
The
matrix is generated by using the Matlab image processing toolbox functions. The matrix has a
1-valued center pixel and R is the radius of the disc which is 3 here. For the dilation process, I need two images
where A is the original image and B is the structuring element considering as a
subimage. Then applying the dilation process by using equation (1) which grows
or thickens objects of the binary image Fig 2(a) with matlab function of imdilate() and Fig
2(B)
has got after dilation. Next, the
boundary extraction algorithm for dilation is applied and extracts the boundary
from the original image and finally got the Fig 2(C).
In similar way, to
extract the boundary of original image by using erosion process need to
represent the image as binary then create an structuring element of size 3x3 Then
applying the erosion process by using equation (2) which Shrinks or thins objects
of the binary image Fig 3(a) with matlab function of
imerode() and Fig 3(B) has got after erosion. After
completing the erosion process then apply the boundary extraction algorithm to
extract the boundary from the original image and got the Fig 3(C).
So, the objective in this project is to extract the boundary of an image performing two binary dilation and
erosion operation with an arbitrary structuring element of size 3 x 3. Now the
project is successfully completed and extracted the boundary from any types of
binary image.
Appendix:
¨ Boundary
Extraction with the help of Dilation:
A=imread('linkon.tif');
s=strel('disk',3);
%Structuring element
F=imdilate(A,s);
%Dialte the image by structuring
element
figure,imshow(A);title('Original Image');
figure,imshow(F);title('Imdilate
Image');
figure,imshow(F-A);title('Boundary
extracted Image with using imdilate');
¨ Boundary
Extraction with the help of Erosion:
A=imread('linkon.tif');
s=strel('disk',3) %Structuring element
F=imerode(A,s); %Erode the image by structuring
element
figure,imshow(A);title('Original
Image');
figure,imshow(A-F);title('Boundary
extracted Image with using imerode');
References
1. "Fundamentals
of Digital Image Processing", Chris Solomon and Toby Breckon, Wiley
Publications. 1st edition.
2. “Digital Image
Processing Using Matlab”, Rafael C. Gonzalez, Richard E. Woods and Steven L.
Eddins, 2nd edition.
3. “Discrete
Mathematics”, Seymour Lipschutz and Marc Lars Lipson, 2nd edition,
Mcgraw-hill publication.
4. Images can be downloaded
from: http://www.imageprocessingplace.com/DIP-3E/dip2e_book_images_downloads.htm
