# MATLAB – Image Edge Detection using Prewitt Operator from Scratch

Prewitt Operator: It is a gradient-based operator. It is one of the best ways to detect the orientation and magnitude of an image. It computes the gradient approximation of image intensity function for image edge detection. At the pixels of an image, the Prewitt 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 approximations of the derivatives – one for horizontal changes, and one for vertical – 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 Prewitt 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 | Prewitt 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));     % Prewitt Operator Mask  Mx = [-1 0 1; -1 0 1; -1 0 1];  My = [-1 -1 -1; 0 0 0; 1 1 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. Good performance on detecting vertical and horizontal edges
2. Best operator to detect the orientation of an image

Limitations:

1. The magnitude of coefficient is fixed and cannot be changed
2. Diagonal direction points are not preserved always

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