# 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

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:

• 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:

• 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:

• 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.

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