移动最小二乘法拟合三维曲面滤波matlab代码

以下是一个基于移动最小二乘法的三维曲面滤波的MATLAB代码示例：

function result = moving_least_squares_3d(data, window_size)
% 移动最小二乘法拟合三维曲面滤波
% data: 输入数据，形状为 (n, 4)，其中前三列是坐标，第四列是数值
% window_size: 窗口大小，必须为奇数
% result: 滤波后的数据，形状与输入数据相同

assert(mod(window_size, 2) == 1, '窗口大小必须为奇数');

n = size(data, 1);
result = zeros(size(data));

for i = 1:n
    % 计算当前窗口的索引
    indices = max(1, i - floor(window_size/2)):min(n, i + floor(window_size/2));

    % 构造矩阵 A 和向量 b
    m = length(indices);
    A = zeros(m, 10);
    b = zeros(m, 1);

    for j = 1:m
        x = data(indices(j), 1);
        y = data(indices(j), 2);
        z = data(indices(j), 3);
        v = data(indices(j), 4);
        A(j, 1) = x^2;
        A(j, 2) = y^2;
        A(j, 3) = z^2;
        A(j, 4) = x * y;
        A(j, 5) = x * z;
        A(j, 6) = y * z;
        A(j, 7) = x;
        A(j, 8) = y;
        A(j, 9) = z;
        A(j, 10) = 1;
        b(j, 1) = v;
    end

    % 计算最小二乘解
    x = (A' * A) \ A' * b;

    % 将拟合结果保存到结果数组中
    result(i, :) = data(i, :);
    result(i, 4) = A(floor(m/2)+1, 1) * x(1) + A(floor(m/2)+1, 2) * x(2) + A(floor(m/2)+1, 3) * x(3) + ...
        A(floor(m/2)+1, 4) * x(4) + A(floor(m/2)+1, 5) * x(5) + A(floor(m/2)+1, 6) * x(6) + ...
        A(floor(m/2)+1, 7) * x(7) + A(floor(m/2)+1, 8) * x(8) + A(floor(m/2)+1, 9) * x(9) + ...
        A(floor(m/2)+1, 10) * x(10);
end

end

使用方法与前面的例子类似。例如：

% 生成测试数据
[x, y, z] = meshgrid(linspace(-1, 1, 10));
v = sin(x) .* cos(y) .* z + 0.1 * randn(size(x));
data = [x(:), y(:), z(:), v(:)];

% 执行移动最小二乘法滤波
filtered_data = moving_least_squares_3d(data, 11);

% 绘制原始数据和滤波结果
scatter3(data(:, 1), data(:, 2), data(:, 3), 20, data(:, 4), 'filled');
hold on;
scatter3(filtered_data(:, 1), filtered_data(:, 2), filtered_data(:, 3), 20, filtered_data(:, 4), 'filled');
colorbar();

可以看到，使用移动最小二乘法可以有效地去除原始数据中的噪声，还原出数据的曲面趋势。