matlab读入ORL人脸数据集并利用kl变换实现人脸判断代码

以下是利用KL变换实现人脸判断的MATLAB代码，其中使用了ORL人脸数据集：

%% 读取ORL人脸数据集
clear all;
close all;
clc;

% 数据集路径
data_path = './orl_faces';

% 读取数据
for i=1:40
    for j=1:10
        file_name = strcat(data_path, '/', 's', num2str(i), '/', num2str(j), '.pgm');
        img = imread(file_name);
        img = double(img(:)');
        orl_data(i,j,:) = (img - mean(img))/std(img); % 标准化处理
    end
end

%% KL变换
% 计算平均脸
mean_face = mean(orl_data,2);
mean_face = reshape(mean_face, 40, []);

% 计算协方差矩阵
X = reshape(orl_data, [], 10);
X = X';
C = cov(X);

% 计算特征值和特征向量
[V,D] = eig(C);

% 特征向量按照特征值大小排序
[d,ind] = sort(diag(D),'descend');
Ds = D(ind,ind);
Vs = V(:,ind);

% 选择前k个主成分
k = 20;
Vs = Vs(:,1:k);
Ds = Ds(1:k,1:k);

% 计算投影矩阵
P = Vs';

% 计算投影系数
proj_coef = P*(orl_data - repmat(mean_face, [1, 10]));

%% 训练
% 每个人的前N张图像作为训练集，剩下的作为测试集
N = 8;
train_data = proj_coef(:,1:N:end);
test_data = proj_coef;
test_data(:,1:N:end) = [];

% 计算训练集中每个人的平均脸
train_mean_face = mean(train_data,2);

% 计算每个人的投影系数的均值向量
train_mean_proj = zeros(20,40);
for i=1:40
    train_mean_proj(:,i) = mean(train_data(:,i:N:i+N-1),2);
end

% 计算类内散度矩阵Sw和类间散度矩阵Sb
Sw = zeros(20,20);
Sb = zeros(20,20);
for i=1:40
    Sw = Sw + cov(train_data(:,i:N:i+N-1)');
    tmp = train_mean_proj(:,i) - train_mean_face;
    Sb = Sb + N*tmp*tmp';
end

% 计算广义特征值和广义特征向量
[Vg,Dg] = eig(Sb,Sw);
[d,ind] = sort(diag(Dg),'descend');
Vgs = Vg(:,ind);

% 选择前K个主成分
K = 19;
Vgs = Vgs(:,1:K);

% 计算投影矩阵
W = P*Vgs;

% 计算训练集和测试集的投影系数
train_proj = W'*train_data;
test_proj = W'*test_data;

% 判别阈值
threshold = 1.7;

%% 测试
correct = 0;
for i=1:size(test_proj,2)
    min_dist = Inf;
    for j=1:40
        dist = norm(train_proj(:,j) - test_proj(:,i));
        if dist < min_dist
            min_dist = dist;
            min_index = j;
        end
    end
    if min_dist < threshold
        fprintf('The %dth test image is recognized as the %dth person.\n', i, min_index);
        correct = correct + 1;
    else
        fprintf('The %dth test image is not recognized.\n', i);
    end
end

% 计算识别率
accuracy = correct / size(test_proj,2);
fprintf('The accuracy is %.2f%%.\n', accuracy*100);

注：代码中的KL变换指的是离散KL变换，也称为PCA。