matlab实现基于PCA算法的人脸识别
时间: 2023-08-02 16:09:39 浏览: 59
在Matlab中,可以使用以下步骤实现基于PCA算法的人脸识别:
1. 首先,需要准备一个人脸图像数据集。将每张人脸图像转换为灰度图像,并将其保存为矩阵形式。
2. 对数据矩阵进行中心化处理,即将每个像素点的灰度值减去该列像素点灰度值的均值。
3. 计算数据矩阵的协方差矩阵,并对其进行特征值分解。
4. 根据特征值的大小,选择前k个特征向量,构成投影矩阵。这里的k可以根据实际情况进行设定,通常取前80%~90%的特征值。
5. 将每张人脸图像乘以投影矩阵,得到降维后的数据矩阵。
6. 对降维后的数据矩阵进行分类和识别。可以使用KNN(K-Nearest Neighbor)算法或SVM(Support Vector Machine)算法进行分类和识别。
以下是一个简单的Matlab代码示例,演示如何实现基于PCA算法的人脸识别:
```matlab
%% Step 1: prepare face image dataset
face_data = []; % a matrix to store all face images
for i = 1:40 % assume there are 40 people in the dataset, and each person has 10 face images
for j = 1:10
% read image and convert to grayscale
img = imread(sprintf('person%d_%d.jpg', i, j));
img_gray = rgb2gray(img);
% convert to column vector and add to face_data matrix
img_col = img_gray(:);
face_data = [face_data img_col];
end
end
%% Step 2: center data matrix
mean_face = mean(face_data, 2); % calculate mean face
centered_face_data = face_data - mean_face; % center data matrix
%% Step 3: calculate covariance matrix and perform eigenvalue decomposition
covariance_matrix = centered_face_data' * centered_face_data; % calculate covariance matrix
[eig_vectors, eig_values] = eig(covariance_matrix); % perform eigenvalue decomposition
%% Step 4: choose top k eigenvectors and form projection matrix
eig_values_vec = diag(eig_values); % extract eigenvalues
[eig_values_sorted, eig_values_idx] = sort(eig_values_vec, 'descend'); % sort eigenvalues in descending order
total_eig_value = sum(eig_values_sorted); % calculate total sum of eigenvalues
ratio = 0; k = 0; % initialize ratio and k
while ratio < 0.9 % choose top k eigenvectors that capture 90% of variance
k = k + 1;
ratio = sum(eig_values_sorted(1:k)) / total_eig_value;
end
proj_matrix = eig_vectors(:, eig_values_idx(1:k)); % form projection matrix
%% Step 5: project each face image onto projection matrix
proj_face_data = proj_matrix' * centered_face_data; % project face data onto projection matrix
%% Step 6: perform classification and recognition (using KNN as an example)
labels = repmat([1:40], 10, 1); % create labels for each face image
labels = labels(:); % convert to column vector
accuracy = 0; % initialize classification accuracy
for i = 1:size(face_data, 2) % for each face image
test_face = proj_face_data(:, i); % use current face image as test data
train_data = proj_face_data(:, [1:i-1 i+1:end]); % use all other face images as training data
train_labels = labels([1:i-1 i+1:end]); % corresponding labels
predicted_label = knn(train_data', train_labels, test_face', 1); % use KNN algorithm to predict label
if predicted_label == labels(i) % if predicted label matches true label
accuracy = accuracy + 1; % increment accuracy count
end
end
accuracy = accuracy / size(face_data, 2); % calculate classification accuracy
disp(['Classification accuracy: ' num2str(accuracy)]);
```
上述代码中,假设每个人有10张人脸图像,文件名格式为"personX_Y.jpg",其中X表示人的编号,Y表示第几张人脸图像。代码中使用KNN算法进行分类和识别,使用投影后的数据矩阵作为输入数据。最后输出分类的准确率。