⑵利用矩不变量对字母A、B、C进行识别。利用matlab语言实现
时间: 2023-08-02 07:06:18 浏览: 62
矩不变量是一种用于图像识别的特征提取方法,可以将图片的形状特征转化为数值特征。在利用矩不变量对字母A、B、C进行识别时,我们可以先将字母转化为二值图像,然后计算其矩特征,最后利用机器学习算法对不同字母的矩特征进行分类。
下面是一个利用 MATLAB 实现矩不变量的示例代码:
```matlab
% 读取字母图像
A = imread('A.bmp');
B = imread('B.bmp');
C = imread('C.bmp');
% 将图像转化为二值图像
A = A < 128;
B = B < 128;
C = C < 128;
% 计算矩特征
m00_A = sum(sum(A));
m10_A = sum(sum(repmat((1:size(A,1))', 1, size(A,2)).*A));
m01_A = sum(sum(repmat(1:size(A,2), size(A,1), 1).*A));
m11_A = sum(sum(repmat((1:size(A,1))', 1, size(A,2)).*repmat(1:size(A,2), size(A,1), 1).*A));
m20_A = sum(sum(repmat((1:size(A,1))'.^2, 1, size(A,2)).*A));
m02_A = sum(sum(repmat((1:size(A,2)).^2, size(A,1), 1).*A));
m30_A = sum(sum(repmat((1:size(A,1))'.^3, 1, size(A,2)).*A));
m03_A = sum(sum(repmat((1:size(A,2)).^3, size(A,1), 1).*A));
mu20_A = m20_A - m10_A^2/m00_A;
mu02_A = m02_A - m01_A^2/m00_A;
mu11_A = m11_A - m10_A*m01_A/m00_A;
nu20_A = mu20_A/m00_A^2;
nu02_A = mu02_A/m00_A^2;
nu11_A = mu11_A/m00_A^(4/3);
m00_B = sum(sum(B));
m10_B = sum(sum(repmat((1:size(B,1))', 1, size(B,2)).*B));
m01_B = sum(sum(repmat(1:size(B,2), size(B,1), 1).*B));
m11_B = sum(sum(repmat((1:size(B,1))', 1, size(B,2)).*repmat(1:size(B,2), size(B,1), 1).*B));
m20_B = sum(sum(repmat((1:size(B,1))'.^2, 1, size(B,2)).*B));
m02_B = sum(sum(repmat((1:size(B,2)).^2, size(B,1), 1).*B));
m30_B = sum(sum(repmat((1:size(B,1))'.^3, 1, size(B,2)).*B));
m03_B = sum(sum(repmat((1:size(B,2)).^3, size(B,1), 1).*B));
mu20_B = m20_B - m10_B^2/m00_B;
mu02_B = m02_B - m01_B^2/m00_B;
mu11_B = m11_B - m10_B*m01_B/m00_B;
nu20_B = mu20_B/m00_B^2;
nu02_B = mu02_B/m00_B^2;
nu11_B = mu11_B/m00_B^(4/3);
m00_C = sum(sum(C));
m10_C = sum(sum(repmat((1:size(C,1))', 1, size(C,2)).*C));
m01_C = sum(sum(repmat(1:size(C,2), size(C,1), 1).*C));
m11_C = sum(sum(repmat((1:size(C,1))', 1, size(C,2)).*repmat(1:size(C,2), size(C,1), 1).*C));
m20_C = sum(sum(repmat((1:size(C,1))'.^2, 1, size(C,2)).*C));
m02_C = sum(sum(repmat((1:size(C,2)).^2, size(C,1), 1).*C));
m30_C = sum(sum(repmat((1:size(C,1))'.^3, 1, size(C,2)).*C));
m03_C = sum(sum(repmat((1:size(C,2)).^3, size(C,1), 1).*C));
mu20_C = m20_C - m10_C^2/m00_C;
mu02_C = m02_C - m01_C^2/m00_C;
mu11_C = m11_C - m10_C*m01_C/m00_C;
nu20_C = mu20_C/m00_C^2;
nu02_C = mu02_C/m00_C^2;
nu11_C = mu11_C/m00_C^(4/3);
% 构建特征矩阵
X = [nu20_A nu02_A nu11_A;
nu20_B nu02_B nu11_B;
nu20_C nu02_C nu11_C];
% 构建标签向量
Y = ['A', 'B', 'C'];
% 利用 k-近邻算法进行分类
k = 1;
mdl = fitcknn(X, Y, 'NumNeighbors', k);
```
在上面的代码中,我们首先读取了字母A、B、C的图像,并将它们转化为二值图像;然后分别计算了它们的矩特征,并利用矩特征构建了特征矩阵 X 和标签向量 Y。最后,我们使用 k-近邻算法进行分类,其中 k=1 表示只考虑最近的一个邻居。
如果要对一个新的字母进行识别,可以先计算它的矩特征,然后将矩特征作为输入传入分类模型,模型会输出字母的标签。下面是一个识别新字母的示例代码:
```matlab
% 读取新字母图像
D = imread('D.bmp');
% 将图像转化为二值图像
D = D < 128;
% 计算矩特征
m00_D = sum(sum(D));
m10_D = sum(sum(repmat((1:size(D,1))', 1, size(D,2)).*D));
m01_D = sum(sum(repmat(1:size(D,2), size(D,1), 1).*D));
m11_D = sum(sum(repmat((1:size(D,1))', 1, size(D,2)).*repmat(1:size(D,2), size(D,1), 1).*D));
m20_D = sum(sum(repmat((1:size(D,1))'.^2, 1, size(D,2)).*D));
m02_D = sum(sum(repmat((1:size(D,2)).^2, size(D,1), 1).*D));
m30_D = sum(sum(repmat((1:size(D,1))'.^3, 1, size(D,2)).*D));
m03_D = sum(sum(repmat((1:size(D,2)).^3, size(D,1), 1).*D));
mu20_D = m20_D - m10_D^2/m00_D;
mu02_D = m02_D - m01_D^2/m00_D;
mu11_D = m11_D - m10_D*m01_D/m00_D;
nu20_D = mu20_D/m00_D^2;
nu02_D = mu02_D/m00_D^2;
nu11_D = mu11_D/m00_D^(4/3);
% 将矩特征作为输入传入分类模型
X_test = [nu20_D nu02_D nu11_D];
Y_pred = predict(mdl, X_test);
disp(['预测的字母为:', Y_pred]);
```
在上面的代码中,我们读取了一个新的字母图像 D,并计算了它的矩特征。然后,我们将矩特征作为输入传入分类模型,模型会输出预测的字母标签。