MATLAB –使用Scratch中的Sobel运算符进行图像边缘检测

Sobel算子：这是一个基于离散微分梯度的运算符。它计算图像强度函数的梯度近似值以进行图像边缘检测。在图像的像素处，Sobel运算符生成矢量的法线或相应的梯度矢量。它使用与输入图像卷积的两个3 x 3内核或蒙版分别计算垂直和水平导数近似值–

    $\[M_{x}=\left[\begin{array}{ccc}-1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1\end{array}\right] \quad M_{y}=\left[\begin{array}{ccc}-1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1\end{array}\right]\]$

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

在MATLAB中的实现：

% 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');

输入图像–

过滤图像：

边缘检测图像：

好处：

1. 简单且省时的计算
2. 很容易寻找光滑的边缘

局限性：

1. 对角方向点不会始终保留
2. 对噪音敏感
3. 边缘检测不是很准确
4. 检测到粗大和粗糙的边缘不会给出适当的结果