Matlab | Erosion of an Image

Morphology is known as the broad set of image processing operations that process images based on shapes. It is also known as a tool used for extracting image components that are useful in the representation and description of region shape. 

The basic morphological operations are: 

• Erosion 
• Dilation

In this article, we will be discussing Erosion.

Erosion:

• Erosion shrink-ens the image pixels i.e. it is used for shrinking of element A by using element B.
• Erosion removes pixels on object boundaries.:
• The value of the output pixel is the minimum value of all the pixels in the neighborhood. A pixel is set to 0 if any of the neighboring pixels have the value 0.

Approach: 

• Read the RGB image.
• Using function im2bw(), convert the RGB image to a binary image.
• Create a structuring element or you can use any predefined mask eg. special(‘sobel’).
• Store the number of rows and columns in an array and loop through it.
• Create a zero matrix of the size same as the size of our image.
• Leaving the boundary pixels start moving the structuring element on the image and start comparing the pixel with the pixels present in the neighborhood.
• If the value of the neighborhood pixel is 0, then change the value of that pixel to 0.

Example: 

MATLAB

% Matlab code for Erosion
% read image
I=imread('lenna.png');

% convert to binary
I=im2bw(I);

% create structuring element
se=ones(5, 5);

% store number of rows
% in P and number of columns in Q.
[P, Q]=size(se);

% create a zero matrix of size I.
In=zeros(size(I, 1), size(I, 2));

for i=ceil(P/2):size(I, 1)-floor(P/2)
    for j=ceil(Q/2):size(I, 2)-floor(Q/2)

        % take all the neighbourhoods.
        on=I(i-floor(P/2):i+floor(P/2), j-floor(Q/2):j+floor(Q/2));

        % take logical se
        nh=on(logical(se));

        % compare and take minimum value of the neighbor
        % and set the pixel value to that minimum value.
        In(i, j)=min(nh(:));
    end
end

imshow(In);

Output:

figure: Input image

figure: Output Image

Let’s take another image to perform Erosion and here we use different MATLAB functions.

Syntax:

• imread() function is used to read the image.
• strel() function is used to define the structuring element. We have chosen disk-shaped SE, of radius 5.
• imerode() function is used to perform the erosion operation.
• imtool() function is used to display the image.

Example:

Matlab

% MATLAB code for Erison
% read the image.
k=imread("erosion.png");

%define the structuring element.
SE=strel('disk',5);

%apply the erosion operation.
e=imerode(k,SE);

%display all the images.
imtool(k,[]);
imtool(e,[]);

%see the effective reduction in org,image
imtool(k-e,[]);

Output:

Figure: Left: Original image, Right: Eroded image

Figure: Output image

Code explanation:

• k=imread(“erosion_exmp.png”); this line reads the image.
• SE=strel(‘disk’,5); this line defines the structuring element.
• e=imerode(k,SE); this line applies the erosion operation.
• imtool(k,[]); this line displays the original image.
• imtool(e,[]); this line displays the eroded image.
• imtool(k-e,[]); this line shows the effective reduction in original image.

The last image shows the extent to which the original image got eroded. We have used the Structuring element of disk-shaped and the image we used is also circular in shape. This gives us the very desired output to understand erosion.