用matlab写一段Zernik矩亚像素边缘检测的代码

以下是一个基于Zernike矩的亚像素边缘检测的MATLAB代码：

% 读取图像并转换为灰度图像
img = imread('example.jpg');
gray = rgb2gray(img);

% 对图像进行高斯滤波
sigma = 1;
hsize = 2*ceil(3*sigma)+1;
h = fspecial('gaussian', hsize, sigma);
gray_filtered = imfilter(gray, h, 'replicate');

% 计算图像的Zernike矩
n = 7; % 设置Zernike矩的阶数
m = 0; % 设置Zernike矩的次数
zernike = zeros(n+1, n+1); % 初始化Zernike矩矩阵
for i = 0:n
    for j = 0:n
        if (i-j) >= 0 && mod(i-j,2) == 0
            zernike(i+1,j+1) = sum(sum(gray_filtered.*zernike_poly(j,i,gray_filtered)));
        end
    end
end

% 计算图像的亚像素边缘位置
edge_pos = zeros(size(gray_filtered));
for i = 1:size(gray_filtered,1)
    for j = 1:size(gray_filtered,2)
        if gray_filtered(i,j) > 50 % 阈值设为50
            % 计算当前像素的Zernike矩
            zernike_i = zeros(n+1, n+1);
            for ii = 0:n
                for jj = 0:n
                    if (ii-jj) >= 0 && mod(ii-jj,2) == 0
                        zernike_i(ii+1,jj+1) = sum(sum(gray_filtered.*zernike_poly(jj,ii,gray_filtered).*...
                            (i.^(jj+1)).*((1:size(gray_filtered,2)).^(ii+1))));
                    end
                end
            end
            % 计算当前像素的亚像素边缘位置
            edge_pos(i,j) = (zernike_i(n+1,m+1)*zernike(1,1)-zernike_i(1,1)*zernike(n+1,m+1))/...
                (zernike(1,1)*zernike(n+1,n+1)-zernike(1,n+1)*zernike(n+1,1));
        end
    end
end

% 显示亚像素边缘检测结果
figure;
imshow(img);
hold on;
contour(edge_pos, [0,0], 'r', 'LineWidth', 2);

需要注意的是，该代码中使用了一个名为`zernike_poly`的辅助函数，用于计算Zernike多项式。该函数的代码如下：

function poly = zernike_poly(j, i, img)
    [x, y] = meshgrid(1:size(img,2), 1:size(img,1));
    rho = sqrt((2*x-size(img,2)-1).^2 + (2*y-size(img,1)-1).^2)/(size(img,1)-1);
    theta = atan2((size(img,1)-1-2*y+1), (2*x-1-size(img,2)));
    poly = sqrt((2*(i+1))./(1+delta(j,0))).*zernike_r(j,i,rho).*zernike_t(j,theta);
end

function delta_val = delta(a,b)
    if a == b
        delta_val = 1;
    else
        delta_val = 0;
    end
end

function r = zernike_r(j, i, rho)
    r = zeros(size(rho));
    for s = 0:(i-j)/2
        r = r + (-1)^s*factorial(i-s)/(factorial(s)*factorial((i+j)/2-s)*factorial((i-j)/2-s)).*...
            rho.^(i-2*s);
    end
end

function t = zernike_t(j, theta)
    t = zeros(size(theta));
    if j == 0
        t = ones(size(theta));
    elseif mod(j,2) == 0
        t = cos(j*theta);
    else
        t = sin(j*theta);
    end
end