MATLAB 亚像素边缘提取：基于 Zernike 矩的边缘检测代码

以下是 MATLAB 代码示例，用于计算 Zernike 矩和边缘检测：

% 计算 Zernike 矩
function [Z00, Z11, Z20, Z31, Z40] = calculateZernikeMoments(image)
    % 定义 Zernike 矩的模板
    M = [1, 0, 2, 0, 3, 0, 4;
         0, 1, 0, 3, 0, 5, 0;
         0, 0, 1, 0, 3, 0, 4;
         0, 0, 0, 1, 0, 3, 0;
         0, 0, 0, 0, 1, 0, 2];
    
    % 初始化 Zernike 矩
    Z00 = 0;
    Z11 = 0;
    Z20 = 0;
    Z31 = 0;
    Z40 = 0;
    
    % 获取图像尺寸
    [height, width] = size(image);
    
    % 遍历图像的每个像素点
    for i = 1:height
        for j = 1:width
            % 获取像素值
            pixel = image(i, j);
            
            % 计算 Zernike 矩
            Z00 = Z00 + M(1, 1) * pixel;
            Z11 = Z11 + M(2, 2) * pixel;
            Z20 = Z20 + M(3, 3) * pixel;
            Z31 = Z31 + M(4, 4) * pixel;
            Z40 = Z40 + M(5, 7) * pixel;
        end
    end
end

% 计算边缘角度和边缘长度
function [angle, length] = calculateEdge(image, Z31, Z40, Z20, Z11)
    % 获取图像尺寸
    [height, width] = size(image);
    
    % 初始化边缘角度和边缘长度
    angle = zeros(height, width);
    length = zeros(height, width);
    
    % 遍历图像的每个像素点
    for i = 1:height
        for j = 1:width
            % 获取 Zernike 矩的实部和虚部
            ReZ31 = real(Z31(i, j));
            ImZ31 = imag(Z31(i, j));
            ReZ40 = real(Z40(i, j));
            ReZ20 = real(Z20(i, j));
            ReZ11 = real(Z11(i, j));
            
            % 计算边缘角度
            angle(i, j) = atan2(ImZ31, ReZ31);
            
            % 计算边缘长度
            l1 = sqrt((5 * ReZ40 + 3 * ReZ20) / (8 * ReZ20));
            l2 = sqrt((5 * ReZ31 + ReZ11) / (6 * ReZ11));
            l = (l1 + l2) / 2;
            length(i, j) = l;
        end
    end
end

% 边缘检测
function [edgeImage] = detectEdge(image, kt, lt)
    % 获取图像尺寸
    [height, width] = size(image);
    
    % 初始化边缘图像
    edgeImage = zeros(height, width);
    
    % 计算 Zernike 矩
    [Z00, Z11, Z20, Z31, Z40] = calculateZernikeMoments(image);
    
    % 计算边缘角度和边缘长度
    [angle, length] = calculateEdge(image, Z31, Z40, Z20, Z11);
    
    % 遍历图像的每个像素点
    for i = 1:height
        for j = 1:width
            % 获取边缘参数
            k = 3 * real(Z11(i, j)) / (2 * (1 - real(Z11(i, j))^2)^(3/2));
            h = (Z00 - (k * pi) / 2 + k * asin(real(length(i, j))) + k * real(length(i, j)) * sqrt(1 - real(length(i, j))^2)) / pi;
            
            % 判断边缘点条件
            if k >= kt && abs(real(length(i, j)) - imag(length(i, j))) <= lt
                % 设置边缘点
                edgeImage(i, j) = 1;
            end
        end
    end
end

% 示例用法
image = imread('example.jpg'); % 读取图像
grayImage = rgb2gray(image); % 转为灰度图像
edgeImage = detectEdge(grayImage, 0.5, 0.1); % 边缘检测
imshow(edgeImage); % 显示边缘图像

请注意，上述代码仅提供了一种实现方法，具体实现可能因应用场景和需求而有所不同。您可以根据自己的需求进行适当的修改和调整。