sigmoid函数拟合边缘灰度梯度变化，并确定亚像素级边缘点，如何用MATLAB编写

以下是一种可能的 MATLAB 代码实现：

% 读取图像并转为灰度图像
img = imread('image.jpg');
gray_img = rgb2gray(img);

% 计算边缘灰度梯度
gx = imfilter(double(gray_img), [-1 0 1], 'replicate');
gy = imfilter(double(gray_img), [-1; 0; 1], 'replicate');
grad_mag = sqrt(gx.^2 + gy.^2);

% 对梯度幅值进行归一化到[0,1]范围
grad_mag = grad_mag / max(grad_mag(:));

% 对梯度幅值进行sigmoid函数拟合
sigmoid = @(x) 1 ./ (1 + exp(-x));
sigmoid_grad_mag = sigmoid(10 * (grad_mag - 0.5));

% 寻找亚像素级边缘点
[rows, cols] = size(gray_img);
subpixel_pts = zeros(rows, cols);
for r = 2:(rows-1)
    for c = 2:(cols-1)
        % 如果当前像素点是边缘点，则进行亚像素级插值
        if sigmoid_grad_mag(r, c) > 0.5 && ...
           sigmoid_grad_mag(r, c-1) < 0.5 && sigmoid_grad_mag(r, c+1) < 0.5 && ...
           sigmoid_grad_mag(r-1, c) < 0.5 && sigmoid_grad_mag(r+1, c) < 0.5
            % 利用二次拟合求解亚像素级边缘点位置
            dx = (sigmoid_grad_mag(r, c+1) - sigmoid_grad_mag(r, c-1)) / 2;
            dy = (sigmoid_grad_mag(r+1, c) - sigmoid_grad_mag(r-1, c)) / 2;
            dxx = sigmoid_grad_mag(r, c-1) - 2 * sigmoid_grad_mag(r, c) + sigmoid_grad_mag(r, c+1);
            dyy = sigmoid_grad_mag(r-1, c) - 2 * sigmoid_grad_mag(r, c) + sigmoid_grad_mag(r+1, c);
            dxy = (sigmoid_grad_mag(r+1, c+1) - sigmoid_grad_mag(r+1, c-1) - ...
                   sigmoid_grad_mag(r-1, c+1) + sigmoid_grad_mag(r-1, c-1)) / 4;
            A = [dxx, dxy; dxy, dyy];
            b = [-dx; -dy];
            p = A \ b;
            subpixel_pts(r, c) = c + p(1);
            subpixel_pts(r, c) = r + p(2);
        end
    end
end

% 可视化结果
imshow(gray_img);
hold on;
[y, x] = find(subpixel_pts);
plot(x, y, 'r.');