MATLAB – Image Edge Detection using Robert Operator from Scratch
Robert Operator: This gradient-based operator computes the sum of squares of the differences between diagonally adjacent pixels in an image through discrete differentiation. Then the gradient approximation is made. It uses the following 2 x 2 kernels or masks –
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 Robert 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 | Robert 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)); % Robert Operator Mask Mx = [1 0; 0 -1]; My = [0 1; -1 0]; % Edge Detection Process % When i = 1 and j = 1, then filtered_image pixel % position will be filtered_image(1, 1) % The mask is of 2x2, so we need to traverse % to filtered_image(size(input_image, 1) - 1 %, size(input_image, 2) - 1) for i = 1:size(input_image, 1) - 1 for j = 1:size(input_image, 2) - 1 % Gradient approximations Gx = sum(sum(Mx.*input_image(i:i+1, j:j+1))); Gy = sum(sum(My.*input_image(i:i+1, j:j+1))); % Calculate magnitude of vector filtered_image(i, j) = 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:
Advantages:
- Detection of edges and orientation are very easy
- Diagonal direction points are preserved
Limitations:
- Very sensitive to noise
- Not very accurate in edge detection