Question

I need help with the edge detection code.

Filter: Edge Detection Edge detection is a technique that creates an image that looks like a pencil sketch, by changing the pixels' colours to black or white. A simple algorithm for performing edge detection is: for every pixel that has a pixel below it, check the contrast between the two pixels. If the contrast is high, change the top pixel's colour to black, but if the contrast is low, change the top pixel's colour to white. For the bottom row (which has no pixels below it), simply set the pixel to white. One way to calculate the contrast between two colours is to calculate the brightness of the top pixel (the average of the red, green and blue components, with all three components weighted equally), and subtract the brightness of the pixel below it. We then calculate the absolute value of this difference. If this absolute value is greater than a threshold value, the contrast between the two pixels is high, so we change the top pixel's colour to black; otherwise, the contrast between the two pixels is low, so we change the top pixel's colour to white. Develop a filter named detect_edges that returns a copy of an image, in which the copy has been modified using the edge detection technique described in the preceding paragraphs. This filter has two parameters: an image and a threshold, which is a positive number. Before developing your filter, sketch some cases where the pixel will be changed to black or to white (e.g. sketch a few pairs of squares representing pairs of pixels, with the R/G/B values shown in each; show the pixel values before and after applying the filter logic).

Answer 1

About Edge Detection:

Edge detection is an image processing technique for finding the boundaries of objects within images. It works by detecting discontinuities in brightness. Edge detection is used for image segmentation and data extraction in areas such as image processing, computer vision, and machine vision.

Approach:
For edge detection, we take the help of convolution: Convolution = I * m where I is the image, m is the mask and * is convolutional operator. To perform convolution on an image following steps are required:

1. Flip the mask horizontally and then vertically. This will result in 180-degree rotation of an image.
2. Slide the mask onto the image such that every pixel in the image coincides with the center of the mask atleast once.
3. Multiply the corresponding elements with the pixel values below it and then add them.
4. Repeat this procedure until all pixel values of the image have been calculated for updation.

Now, we will take 3×3 mask for the same.

3×3 Mask for vertical edges : [1, 0, -1; 1, 0, -1; 1, 0, -1]
3×3 Mask for horizontal edges : [1, 0, -1; 1, 0, -1; 1, 0, -1]
3×3 Mask for principal diagonal edges : [1, 0, -1; 1, 0, -1; 1, 0, -1]
3×3 Mask for secondary diagonal edges : [1, 0, -1; 1, 0, -1; 1, 0, -1]

We’ll find these edges separately and finally combine them using max function or mean function, but max function is more accurate for this.

Matlab Code for vertical edges:filter_none

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I=double((imread('image1.jpg')); %read image In=I;      %copy image mask=[1, 0, -1;1, 0, -1;1, 0, -1]; %Rotate image by 180 degree first flip up to down then left to right mask=flipud(mask); mask=fliplr(mask); for i=2:size(I, 1)-1     for j=2:size(I, 2)-1         %multiplying mask value with the corresponding image pixel value         neighbour_matrix=mask.*In(i-1:i+1, j-1:j+1);         avg_value=sum(neighbour_matrix(:));         I(i, j)=avg_value;     end end figure, imshow(uint8(I));

Matlab code for horizontal edges:

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I=double((imread('image1.jpg')); In=I; mask=[1, 1, 1;0, 0, 0;-1, -1, -1]; mask=flipud(mask); mask=fliplr(mask); for i=2:size(I, 1)-1     for j=2:size(I, 2)-1         neighbour_matrix=mask.*In(i-1:i+1, j-1:j+1);         avg_value=sum(neighbour_matrix(:));         I(i, j)=avg_value;     end end figure, imshow(uint8(I));

Matlab code for principal diagonal edges:

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I=double((imread('image1.jpg')); In=I; mask=[0, -1, -1;1, 0, -1;1, 1, 0]; mask=flipud(mask); mask=fliplr(mask); for i=2:size(I, 1)-1     for j=2:size(I, 2)-1         neighbour_matrix=mask.*In(i-1:i+1, j-1:j+1);         avg_value=sum(neighbour_matrix(:));         I(i, j)=avg_value;     end end figure, imshow(uint8(I));

Matlab Code for secondary diagonal edges:

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brightness_4

I=double((imread('image1.jpg')); In=I; mask=[1, 1, 1;0, 0, 0;-1, -1, -1]; mask=flipud(mask); mask=fliplr(mask); for i=2:size(I, 1)-1     for j=2:size(I, 2)-1         neighbour_matrix=mask.*In(i-1:i+1, j-1:j+1);         avg_value=sum(neighbour_matrix(:));         I(i, j)=avg_value;     end end figure, imshow(uint8(I));

Final Matlab code for edge detection:

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brightness_4

I=double(imread('image1.jpg')); In=I; mask1=[1, 0, -1;1, 0, -1;1, 0, -1]; mask2=[1, 1, 1;0, 0, 0;-1, -1, -1]; mask3=[0, -1, -1;1, 0, -1;1, 1, 0]; mask4=[1, 1, 0;1, 0, -1;0, -1, -1]; mask1=flipud(mask1); mask1=fliplr(mask1); mask2=flipud(mask2); mask2=fliplr(mask2); mask3=flipud(mask3); mask3=fliplr(mask3); mask4=flipud(mask4); mask4=fliplr(mask4); for i=2:size(I, 1)-1     for j=2:size(I, 2)-1         neighbour_matrix1=mask1.*In(i-1:i+1, j-1:j+1);         avg_value1=sum(neighbour_matrix1(:));         neighbour_matrix2=mask2.*In(i-1:i+1, j-1:j+1);         avg_value2=sum(neighbour_matrix2(:));         neighbour_matrix3=mask3.*In(i-1:i+1, j-1:j+1);         avg_value3=sum(neighbour_matrix3(:));         neighbour_matrix4=mask4.*In(i-1:i+1, j-1:j+1);         avg_value4=sum(neighbour_matrix4(:));         %using max function for detection of final edges         I(i, j)=max([avg_value1, avg_value2, avg_value3, avg_value4]);     end end figure, imshow(uint8(I));