Prewitt运算符:这是一个基于梯度的运算符。这是检测图像方向和大小的最佳方法之一。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,Prewitt运算符生成矢量的法线或相应的梯度矢量。它使用两个与输入图像卷积的3 x 3内核或遮罩来计算导数的近似值-一个用于水平变化,一个用于垂直变化-
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
在MATLAB中的实现:
% 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');
输入图像–
过滤图像:
边缘检测图像:
好处:
- 在检测垂直和水平边缘方面表现出色
- 检测图像方向的最佳运算符
局限性:
- 系数的大小是固定的,无法更改
- 对角方向点不会始终保留