MATLAB 亚像素边缘检测：基于Zernike矩的实现

以下是使用MATLAB编写的代码，用于计算Zernike矩和边缘检测：

% 图像读取
img = imread('image.jpg');
img = rgb2gray(img);

% Zernike矩阵模板
M = [1, 0, 2, 0, 3; 
     0, 1, 0, 1, 0; 
     1, 0, -2, 0, 3; 
     0, 3, 0, 3, 0; 
     6, 0, 0, 0, 0];

% 图像尺寸
[rows, cols] = size(img);

% 初始化边缘点坐标
edge_points = [];

% 遍历图像的每个像素点
for i = 2:rows-1
    for j = 2:cols-1
        % 计算Zernike矩
        Z = zeros(size(M));
        for m = 1:size(M, 1)
            for n = 1:size(M, 2)
                Z(m, n) = sum(sum(double(img(i-1:i+1, j-1:j+1)) .* M(m, n)));
            end
        end
        
        % 计算边缘角度
        phi = atan2(imag(Z(4, 1)), real(Z(4, 1)));
        
        % 计算边缘长度
        l1 = sqrt((5*real(Z(5, 1))+3*real(Z(3, 1)))/(8*real(Z(3, 1))));
        l2 = sqrt((5*real(Z(4, 2))+real(Z(2, 2)))/(6*real(Z(2, 2))));
        l = (l1 + l2) / 2;
        
        % 计算k和h
        k = 3*real(Z(2, 2))/(2*(1-l2^2)^(3/2));
        h = (real(Z(1, 1))-(k*pi)/2+k*asin(l2)+k*l2*sqrt(1-l2^2))/pi;
        
        % 判断是否为边缘点
        kt = 0.1;  % k的阈值
        lt = 0.1;  % |l2-l1|的阈值
        if k >= kt && abs(l2-l1) <= lt
            edge_points = [edge_points; j, i];
        end
    end
end

% 边缘检测
edge_img = zeros(size(img));
for i = 1:size(edge_points, 1)
    edge_img(edge_points(i, 2), edge_points(i, 1)) = 255;
end

% 显示结果
figure;
subplot(1, 2, 1);
imshow(img);
title('原始图像');
subplot(1, 2, 2);
imshow(edge_img);
title('边缘检测结果');

请注意，上述代码仅提供了一个基本的框架，需要根据具体的需求进行调整和完善。