# MATLAB – Image Edge Detection using Sobel Operator from Scratch

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 image
Step 2: Convert the true-color RGB image to the grayscale image
Step 3: Convert the image to double
Step 4: Pre-allocate the filtered_image matrix with zeros
Step 5: Define Sobel Operator Mask
Step 6: Edge Detection Process (Compute Gradient approximation and magnitude of vector)
Step 7: Display the filtered image
Step 8: Thresholding on the filtered image
Step 9: Display the edge-detected image

Implementation in MATLAB:

 % MATLAB Code | Sobel Operator from Scratch     % Read Input Image  input_image = imread('[name of input image file].[file format]');     % Displaying Input Image  input_image = uint8(input_image);  figure, imshow(input_image); title('Input Image');     % Convert the truecolor RGB image to the grayscale image  input_image = rgb2gray(input_image);     % Convert the image to double  input_image = double(input_image);     % Pre-allocate the filtered_image matrix with zeros  filtered_image = zeros(size(input_image));     % Sobel Operator Mask  Mx = [-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);                end end    % Displaying Filtered Image  filtered_image = uint8(filtered_image);  figure, imshow(filtered_image); title('Filtered Image');     % Define a threshold value  thresholdValue = 100; % varies between [0 255]  output_image = max(filtered_image, thresholdValue);  output_image(output_image == round(thresholdValue)) = 0;     % Displaying Output Image  output_image = im2bw(output_image);  figure, imshow(output_image); title('Edge Detected Image');

Input Image – Filtered Image: Edge Detected Image: 1. Simple and time efficient computation
2. Very easy at searching for smooth edges

Limitations:

1. Diagonal direction points are not preserved always
2. Sensitive to noise
3. Not very accurate in edge detection
4. Detect with thick and rough edges does not give appropriate results

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