MATLAB 亚像素边缘提取：基于 Zernike 矩的边缘检测代码

以下是一个使用 MATLAB 计算 Zernike 矩和进行边缘检测的示例代码：

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

% 定义Zernike矩模板
M = [1 0 2 0 6];

% 计算Zernike矩
Z = zeros(size(img, 1), size(img, 2), numel(M));
for i = 1:numel(M)
    Z(:,:,i) = conv2(double(img), double(flipud(fliplr(zernike(M(i))))), 'same');
end

% 取一像素点
x = 100;
y = 100;

% 计算边缘角度
phi = atan2d(imag(Z(y,x,4)), real(Z(y,x,4)));

% 计算边缘长度
l1 = sqrt((5*real(Z(y,x,5))+3*real(Z(y,x,3)))/(8*real(Z(y,x,3))));
l2 = sqrt((5*real(Z(y,x,4))+real(Z(y,x,2)))/(6*real(Z(y,x,2))));
l = (l1 + l2) / 2;

% 计算k和h
k = 3 * real(Z(y,x,2)) / (2 * (1 - l2^2)^(3/2));
h = (real(Z(y,x,1)) - (k*pi)/2 + k*asin(l2) + k*l2*sqrt(1-l2^2)) / pi;

% 设置判断阈值
kt = 0.5;
lt = 0.1;

% 判断是否为边缘点
if k >= kt && abs(l2 - l1) <= lt
    disp('该像素点为边缘点');
    % 计算亚像素边缘点坐标
    x_subpixel = x + h * cosd(phi);
    y_subpixel = y + h * sind(phi);
else
    disp('该像素点不是边缘点');
end

% 边缘检测
edge_img = zeros(size(img));
for i = 1:size(img, 1)
    for j = 1:size(img, 2)
        if k >= kt && abs(l2 - l1) <= lt
            edge_img(i,j) = 255;
        end
    end
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');

% Zernike矩函数
function Z = zernike(m)
    [x, y] = meshgrid(-1:0.01:1);
    r = sqrt(x.^2 + y.^2);
    theta = atan2(y, x);
    Z = zeros(size(r));
    Z(r <= 1) = zernike_rad(m, 0, r(r <= 1)) .* zernike_ang(m, 0, theta(r <= 1));
end

% Zernike径向多项式函数
function R = zernike_rad(m, n, r)
    R = zeros(size(r));
    for s = 0:((n - abs(m)) / 2)
        c = (-1)^s * factorial(n - s) / (factorial(s) * factorial((n + abs(m)) / 2 - s) * factorial((n - abs(m)) / 2 - s));
        R = R + c * r.^(n - 2*s);
    end
end

% Zernike角向多项式函数
function T = zernike_ang(m, n, theta)
    T = zeros(size(theta));
    if m > 0
        T = sqrt(2) * cos(m * theta);
    elseif m < 0
        T = sqrt(2) * sin(-m * theta);
    else
        T = ones(size(theta));
    end
end

请注意，此代码仅提供了一个示例，具体实现可能需要根据您的具体需求进行调整。