OpenCV3.3中主成分分析(Principal Components Analysis, PCA)接口简介及使用

OpenCV3.3中给出了主成分分析(Principal Components Analysis, PCA)的实现，即cv::PCA类，类的声明在include/opencv2/core.hpp文件中，实现在modules/core/src/pca.cpp文件中,其中：

(1)、cv::PCA::PCA：构造函数；

(2)、cv::PCA::operator()：函数调用运算符；

(3)、cv::PCA::project：将输入数据投影到PCA主成分空间；

(4)、cv::PCA::backProject：重建原始数据；

(5)、cv::PCA::write：将特征值、特征向量、均值写入指定的文件；

(6)、cv::PCA::read：从指定文件读入特征值、特征向量、均值；

(7)、cv::PCA::eigenvectors：协方差矩阵的特征向量；

(8)、cv::PCA::eigenvalues：协方差矩阵的特征值；

(9)、cv::PCA::mean：均值。

关于PCA的介绍可以参考： http://blog.csdn.net/fengbingchun/article/details/78977202 

以下是使用ORL Faces Database作为测试图像。关于ORL Faces Database的介绍可以参考： http://blog.csdn.net/fengbingchun/article/details/79008891 

测试代码如下：

#include "opencv.hpp"
#include <string>
#include <vector>
#include <memory>
#include <algorithm>
#include <opencv2/opencv.hpp>
#include <opencv2/ml.hpp>
#include "common.hpp"

// PCA(Principal Component Analysis) ///
int test_opencv_pca()
{
	// reference: opencv-3.3.0/samples/cpp/pca.cpp
	const std::string image_path{ "E:/GitCode/NN_Test/data/database/ORL_Faces/" };
	const std::string image_name{ "1.pgm" };

	std::vector<cv::Mat> images;
	for (int i = 1; i <= 15; ++i) {
		std::string name = image_path + "s" + std::to_string(i) + "/" + image_name;
		cv::Mat mat = cv::imread(name, 0);
		if (!mat.data) {
			fprintf(stderr, "read image fail: %s\n", name.c_str());
			return -1;
		}

		images.emplace_back(mat);
	}

	cv::Mat data(images.size(), images[0].rows * images[0].cols, CV_32FC1);
	for (int i = 0; i < images.size(); ++i) {
		cv::Mat image_row = images[i].clone().reshape(1, 1);
		cv::Mat row_i = data.row(i);
		image_row.convertTo(row_i, CV_32F);
	}

	cv::PCA pca(data, cv::Mat(), cv::PCA::DATA_AS_ROW, 0.95f);

	std::vector<cv::Mat> result(images.size());
	for (int i = 0; i < images.size(); ++i) {
		// Demonstration of the effect of retainedVariance on the first image
		cv::Mat point = pca.project(data.row(i)); // project into the eigenspace, thus the image becomes a "point"
		cv::Mat reconstruction = pca.backProject(point); // re-create the image from the "point"
		reconstruction = reconstruction.reshape(images[i].channels(), images[i].rows); // reshape from a row vector into image shape
		cv::normalize(reconstruction, reconstruction, 0, 255, cv::NORM_MINMAX, CV_8UC1);
		reconstruction.copyTo(result[i]);
	}
	save_images(result, "E:/GitCode/NN_Test/data/pca_result_.jpg", 5);

	// save file
	const std::string save_file{ "E:/GitCode/NN_Test/data/pca.xml" }; // .xml, .yaml, .jsons
	cv::FileStorage fs(save_file, cv::FileStorage::WRITE);
	pca.write(fs);
	fs.release();

	// read file
	const std::string& read_file = save_file;
	cv::FileStorage fs2(read_file, cv::FileStorage::READ);
	cv::PCA pca2;
	pca2.read(fs2.root());
	fs2.release();

	return 0;
}

        结果图像如下：