Hu moment function

Hu矩函数是一种用于图像处理和模式识别的特征提取方法，它具有平移、旋转和尺度不变性。Hu矩由七个矩组成，分别为：m00、m01、m10、m11、m20、m02和m21。这些矩可以通过计算图像的几何矩得到。

以下是一个使用Hu矩函数计算图像特征的示例代码：

import cv2

# 读取图像
image = cv2.imread('lena.jpg', 0)

# 计算图像的Hu矩
moments = cv2.moments(image)
hu_moments = cv2.HuMoments(moments)

# 打印Hu矩
for i in range(7):
    print("Hu Moment", i+1, ":", hu_moments[i][0])

这段代码使用OpenCV库中的`cv2.moments()`函数计算图像的几何矩，然后使用`cv2.HuMoments()`函数计算Hu矩。最后，通过循环打印出计算得到的Hu矩。

相关问题

Hu矩提取matlab代码

Hu矩提取是一种基于轮廓分析的图像特征提取算法，其实现代码在Matlab中如下：

% 读取图像
I = imread('image.png');

% 将图像转化为二值图像
I_binary = imbinarize(I);

% 根据二值图像获取其轮廓
[B, L] = bwboundaries(I_binary, 'noholes');

% 计算轮廓的Hu矩
hu_moments = hu_moments(B{1});

% 输出Hu矩值
disp(hu_moments);

其中hu_moments是自定义的一个函数，实现如下：

function hu_moments = hu_moments(boundary)

% 计算轮廓的Hu矩
hu_moments = zeros(1, 7);
hu_moments(1) = inv_moment(boundary, 2, 0) + inv_moment(boundary, 0, 2);
hu_moments(2) = (inv_moment(boundary, 2, 0) - inv_moment(boundary, 0, 2))^2 + 4*inv_moment(boundary, 1, 1)^2;
hu_moments(3) = (inv_moment(boundary, 3, 0) - 3*inv_moment(boundary, 1, 2))^2 + (3*inv_moment(boundary, 2, 1) - inv_moment(boundary, 0, 3))^2;
hu_moments(4) = (inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 + (inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2;
hu_moments(5) = (inv_moment(boundary, 3, 0) - 3*inv_moment(boundary, 1, 2))*(inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))*((inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 - 3*((inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2)) + (3*inv_moment(boundary, 2, 1) - inv_moment(boundary, 0, 3))*(inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))*(3*(inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 - ((inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2));
hu_moments(6) = (inv_moment(boundary, 2, 0) - inv_moment(boundary, 0, 2))*((inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 - (inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2) + 4*inv_moment(boundary, 1, 1)*(inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))*(inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3));
hu_moments(7) = (3*inv_moment(boundary, 2, 1) - inv_moment(boundary, 0, 3))*(inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))*((inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 - 3*((inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2)) - (inv_moment(boundary, 3, 0) - 3*inv_moment(boundary, 1, 2))*(inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))*(3*(inv_moment(boundary, 3, 0) + inv_moment(boundary, 1, 2))^2 - ((inv_moment(boundary, 2, 1) + inv_moment(boundary, 0, 3))^2));

% 将Hu矩标准化
hu_moments = -sign(hu_moments).*log10(abs(hu_moments));

end

其中inv_moment也是自定义的一个函数，用来计算轮廓的非中心矩，实现如下：

function inv_m = inv_moment(boundary, p, q)

% 计算轮廓的非中心矩
inv_m = sum((boundary(:, 2).^p).*(boundary(:, 1).^q));

end

以上就是Hu矩提取的Matlab代码实现。

Hu不变矩，用matlab实现

实现Hu不变矩前需要先进行图像的预处理，包括灰度化、二值化和图片剪裁等。接下来是Hu不变矩的具体实现代码：

1. 首先导入图片，将其转换为灰度图像

I = imread('test.jpg'); % 导入图片
I = rgb2gray(I); % 转换为灰度图像

2. 对图像进行二值化处理

BW = imbinarize(I, graythresh(I)); % 对图像进行二值化
imshow(BW); % 显示二值化处理后的图像

3. 图片剪裁

x = 100; % 剪裁起点的x坐标
y = 100; % 剪裁起点的y坐标
w = 100; % 剪裁的宽度
h = 100; % 剪裁的高度
cropImage = imcrop(BW, [x y w h]); % 进行剪裁操作
imshow(cropImage); % 显示剪裁后的图像

4. 计算Hu不变矩

% 计算Hu不变矩
moment = hu_moments(cropImage); % hu_moments是自定义函数

5. 自定义函数hu_moments的实现

function [moment] = hu_moments(I)
    moment = zeros(1,7);

    % 计算几何中心
    [m, n] = size(I);
    x_sum = 0;
    y_sum = 0;
    for i = 1:m
        for j = 1:n
            x_sum = x_sum + i*I(i,j);
            y_sum = y_sum + j*I(i,j);
        end
    end
    x_center = x_sum/sum(I(:));
    y_center = y_sum/sum(I(:));
    
    % 矩阵归一化
    mu = zeros(3,3);
    for i = 0:2
        for j = 0:2
            mu(i+1,j+1) = moment_calc(I,i,j,x_center,y_center);
        end
    end
    
    % 计算二阶中心距
    m20 = mu(2,0) - mu(1,1)^2/mu(0,0);
    m02 = mu(0,2) - mu(1,1)^2/mu(0,0);
    m11 = (mu(1,1) - x_center*y_center)/mu(0,0);
    m30 = moment_calc(I,3,0,x_center,y_center) - 3*m11*m20 + 2*m11^3/mu(0,0);
    m03 = moment_calc(I,0,3,x_center,y_center) - 3*m11*m02 + 2*m11^3/mu(0,0);
    m21 = moment_calc(I,2,1,x_center,y_center) - 2*m11*m20 - m02*m11/mu(0,0) + 2*m11^3/mu(0,0)^2;
    m12 = moment_calc(I,1,2,x_center,y_center) - 2*m11*m02 - m20*m11/mu(0,0) + 2*m11^3/mu(0,0)^2;
    
    % 计算Hu不变矩
    moment(1) = m20 + m02;
    moment(2) = (m20 - m02)^2 + 4*m11^2;
    moment(3) = (m30 - 3*m12)^2 + (3*m21 - m03)^2;
    moment(4) = (m30 + m12)^2 + (m21 + m03)^2;
    moment(5) = (m30 - 3*m12)*(m30 + m12)*((m30 + m12)^2 - 3*(m21 + m03)^2)...
                + (3*m21 - m03)*(m21 + m03)*(3*(m30 + m12)^2 - (m21 + m03)^2);
    moment(6) = (m20 - m02)*((m30 + m12)^2 - (m21 + m03)^2) + 4*m11*(m30 + m12)*(m21 + m03);
    moment(7) = (3*m21 - m03)*(m30 + m12)*((m30 + m12)^2 - 3*(m21 + m03)^2)...
                - (m30 - 3*m12)*(m21 + m03)*(3*(m30 + m12)^2 - (m21 + m03)^2);
end

function [Iij] = moment_calc(I,i,j,x,y)
    [m, n] = size(I);
    Iij = 0;
    for p = 1:m
        for q = 1:n
            Iij = Iij + (p-x)^i*(q-y)^j*I(p,q);
        end
    end
end