opencv PCA主成分分析的使用

简介

主成分分析(PCA)是提取数据集最重要特征的统计程序。
PCA(Principal Components Analysis,中文名叫主成分分析,是数据降维很常用的算法。按照书上的说法是:寻找最小均方意义下,最能代表原始数据的投影方法。PCA的一个经典应用就是人脸识别,感兴趣的可以在网上搜eigenface。
PCA的主要思想是寻找到数据的主轴方向,由主轴构成一个新的坐标系,这里的维数可以比原维数低,然后数据由原坐标系向新的坐标系投影,这个投影的过程就可以是降维的过程。

使用
//绘制向量轴
void drawAxis(Mat& img, Point p, Point q, Scalar colour, const float scale = 0.2)
{
    double angle;
    double hypotenuse;
    angle = atan2( (double) p.y - q.y, (double) p.x - q.x ); // angle in radians
    hypotenuse = sqrt( (double) (p.y - q.y) * (p.y - q.y) + (p.x - q.x) * (p.x - q.x));
//    double degrees = angle * 180 / CV_PI; // convert radians to degrees (0-180 range)
//    cout << "Degrees: " << abs(degrees - 180) << endl; // angle in 0-360 degrees range
    // Here we lengthen the arrow by a factor of scale
    q.x = (int) (p.x - scale * hypotenuse * cos(angle));
    q.y = (int) (p.y - scale * hypotenuse * sin(angle));
    line(img, p, q, colour, 1, LINE_AA);
    // create the arrow hooks
    p.x = (int) (q.x + 9 * cos(angle + CV_PI / 4));
    p.y = (int) (q.y + 9 * sin(angle + CV_PI / 4));
    line(img, p, q, colour, 1, LINE_AA);
    p.x = (int) (q.x + 9 * cos(angle - CV_PI / 4));
    p.y = (int) (q.y + 9 * sin(angle - CV_PI / 4));
    line(img, p, q, colour, 1, LINE_AA);
}

//pca 使用过程
double getOrientation(const vector<Point> &pts, Mat &img)
{
    //Construct a buffer used by the pca analysis
    int sz = static_cast<int>(pts.size());
    Mat data_pts = Mat(sz, 2, CV_64FC1);
    for (int i = 0; i < data_pts.rows; ++i)
    {
        data_pts.at<double>(i, 0) = pts[i].x;
        data_pts.at<double>(i, 1) = pts[i].y;
    }
    //Perform PCA analysis
    PCA pca_analysis(data_pts, Mat(), CV_PCA_DATA_AS_ROW);
    //Store the center of the object
    Point cntr = Point(static_cast<int>(pca_analysis.mean.at<double>(0, 0)),
                       static_cast<int>(pca_analysis.mean.at<double>(0, 1)));
    //Store the eigenvalues and eigenvectors
    vector<Point2d> eigen_vecs(2);
    vector<double> eigen_val(2);
    for (int i = 0; i < 2; ++i)
    {
        eigen_vecs[i] = Point2d(pca_analysis.eigenvectors.at<double>(i, 0),
                                pca_analysis.eigenvectors.at<double>(i, 1));
        eigen_val[i] = pca_analysis.eigenvalues.at<double>(i);
    }
    // Draw the principal components
    circle(img, cntr, 3, Scalar(255, 0, 255), 2);
    Point p1 = cntr + 0.02 * Point(static_cast<int>(eigen_vecs[0].x * eigen_val[0]), static_cast<int>(eigen_vecs[0].y * eigen_val[0]));
    Point p2 = cntr - 0.02 * Point(static_cast<int>(eigen_vecs[1].x * eigen_val[1]), static_cast<int>(eigen_vecs[1].y * eigen_val[1]));
    drawAxis(img, cntr, p1, Scalar(0, 255, 0), 1);
    drawAxis(img, cntr, p2, Scalar(255, 255, 0), 5);
    double angle = atan2(eigen_vecs[0].y, eigen_vecs[0].x); // orientation in radians
    return angle;
}

void main(){
        // Load image
        Mat src = mRgb.clone();
        // Convert image to grayscale
        Mat gray;
        cvtColor(src, gray, COLOR_BGR2GRAY);
        // Convert image to binary
        Mat bw;
        threshold(gray, bw, 50, 255, CV_THRESH_BINARY | CV_THRESH_OTSU);
        // Find all the contours in the thresholded image
        vector<Vec4i> hierarchy;
        vector<vector<Point> > contours;
        findContours(bw, contours, hierarchy, CV_RETR_LIST, CV_CHAIN_APPROX_NONE);
        for (size_t i = 0; i < contours.size(); ++i) {
            // Calculate the area of each contour
            double area = contourArea(contours[i]);
            // Ignore contours that are too small or too large
            if (area < 1e2 || 1e5 < area) continue;
            // Draw each contour only for visualisation purposes
            drawContours(src, contours, static_cast<int>(i), Scalar(0, 0, 255), 2, 8, hierarchy, 0);
            // Find the orientation of each shape
            getOrientation(contours[i], src);
        }
}

效果

opencv PCA主成分分析的使用_第1张图片

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