MATLAB – Image Edge Detection using Sobel Operator from Scratch

17 May, 2020
Sobel Operator: It is a discrete differentiation gradient-based operator. It computes the gradient approximation of image intensity function for image edge detection. At the pixels of an image, the Sobel operator produces either the normal to a vector or the corresponding gradient vector. It uses two 3 x 3 kernels or masks which are convolved with the input image to calculate the vertical and horizontal derivative approximations respectively –
    
Approach:
Step 1: Input – Read an imageStep 2: Convert the true-color RGB image to the grayscale imageStep 3: Convert the image to doubleStep 4: Pre-allocate the filtered_image matrix with zerosStep 5: Define Sobel Operator MaskStep 6: Edge Detection Process (Compute Gradient approximation and magnitude of vector)Step 7: Display the filtered imageStep 8: Thresholding on the filtered imageStep 9: Display the edge-detected image
Implementation in MATLAB:
% MATLAB Code | Sobel Operator from Scratch  % Read Input Imageinput_image = imread('[name of input image file].[file format]');  % Displaying Input Imageinput_image = uint8(input_image);figure, imshow(input_image); title('Input Image');  % Convert the truecolor RGB image to the grayscale imageinput_image = rgb2gray(input_image);  % Convert the image to doubleinput_image = double(input_image);  % Pre-allocate the filtered_image matrix with zerosfiltered_image = zeros(size(input_image));  % Sobel Operator MaskMx = [-1 0 1; -2 0 2; -1 0 1];My = [-1 -2 -1; 0 0 0; 1 2 1];  % Edge Detection Process% When i = 1 and j = 1, then filtered_image pixel  % position will be filtered_image(2, 2)% The mask is of 3x3, so we need to traverse % to filtered_image(size(input_image, 1) - 2%, size(input_image, 2) - 2)% Thus we are not considering the borders.for i = 1:size(input_image, 1) - 2    for j = 1:size(input_image, 2) - 2          % Gradient approximations        Gx = sum(sum(Mx.*input_image(i:i+2, j:j+2)));        Gy = sum(sum(My.*input_image(i:i+2, j:j+2)));                         % Calculate magnitude of vector        filtered_image(i+1, j+1) = sqrt(Gx.^2 + Gy.^2);             endend  % Displaying Filtered Imagefiltered_image = uint8(filtered_image);figure, imshow(filtered_image); title('Filtered Image');  % Define a threshold valuethresholdValue = 100; % varies between [0 255]output_image = max(filtered_image, thresholdValue);output_image(output_image == round(thresholdValue)) = 0;  % Displaying Output Imageoutput_image = im2bw(output_image);figure, imshow(output_image); title('Edge Detected Image');
Input Image –
Filtered Image:
Edge Detected Image:
Advantages:
Simple and time efficient computationVery easy at searching for smooth edges
Simple and time efficient computation
Very easy at searching for smooth edges
Limitations:
Diagonal direction points are not preserved alwaysSensitive to noiseNot very accurate in edge detectionDetect with thick and rough edges does not give appropriate results
Diagonal direction points are not preserved always
Sensitive to noise
Not very accurate in edge detection
Detect with thick and rough edges does not give appropriate results
Image-Processing
MATLAB
Advanced Computer Subject
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