how to find the REAL width and height of contours

edit

thanks for StevenPuttemans,I have get the final slove

#include "opencv2/imgcodecs.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#include "opencv2/photo.hpp"
using namespace std;
using namespace cv;
#define DEBUG FALSE

Point2f GetPointAfterRotate(Point2f inputpoint,Point2f center,double angle){
    Point2d preturn;
    preturn.x = (inputpoint.x - center.x)*cos(-angle) - (inputpoint.y - center.y)*sin(-angle)+center.x;
    preturn.y = (inputpoint.x - center.x)*sin(-angle) + (inputpoint.y - center.y)*cos(-angle)+center.y;
    return preturn;
}
Point GetPointAfterRotate(Point inputpoint,Point center,double angle){
    Point preturn;
    preturn.x = (inputpoint.x - center.x)*cos(-1*angle) - (inputpoint.y - center.y)*sin(-1*angle)+center.x;
    preturn.y = (inputpoint.x - center.x)*sin(-1*angle) + (inputpoint.y - center.y)*cos(-1*angle)+center.y;
    return preturn;
}

double getOrientation(vector<Point> &pts, Point2f& pos,Mat& img)
{
    //Construct a buffer used by the pca analysis
    Mat data_pts = Mat(pts.size(), 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 position of the object
    pos = Point2f(pca_analysis.mean.at<double>(0, 0),
        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,0);
    }


    return atan2(eigen_vecs[0].y, eigen_vecs[0].x);
}


int main( int argc, char** argv )
{

    Mat img = imread("e:/sandbox/leaf.jpg");
    pyrDown(img,img);
    pyrDown(img,img);

    Mat bw;
    bool dRet;
    cvtColor(img, bw, COLOR_BGR2GRAY);

    threshold(bw, bw, 150, 255, CV_THRESH_BINARY);

    vector<vector<Point> > contours;
    vector<Vec4i> hierarchy;
    findContours(bw, contours, hierarchy, CV_RETR_LIST, CV_CHAIN_APPROX_NONE);


    for (size_t i = 0; i < contours.size(); ++i)
    {

        double area = contourArea(contours[i]);

        if (area < 1e2 || 1e5 < area) continue;

        Point2f* pos = new Point2f();
        double dOrient =  getOrientation(contours[i], *pos,img);

        int xmin = 99999;
        int xmax = 0;
        int ymin = 99999;
        int ymax = 0;
        for (size_t j = 0;j<contours[i].size();j++)
        {
            contours[i][j] = GetPointAfterRotate(contours[i][j],(Point)*pos,dOrient);
            if (contours[i][j].x < xmin)
                xmin = contours[i][j].x;
            if (contours[i][j].x > xmax)
                xmax = contours[i][j].x;
            if (contours[i][j].y < ymin)
                ymin = contours[i][j].y;
            if (contours[i][j].y > ymax)
                ymax = contours[i][j].y;
        }
        Point lt = Point(xmin,ymin);
        Point ld = Point(xmin,ymax);
        Point rd = Point(xmax,ymax);
        Point rt = Point(xmax,ymin);    

        drawContours(img, contours, i, CV_RGB(255, 0, 0), 2, 8, hierarchy, 0);

        lt = GetPointAfterRotate((Point)lt,(Point)*pos,-dOrient);
        ld = GetPointAfterRotate((Point)ld,(Point)*pos,-dOrient);
        rd = GetPointAfterRotate((Point)rd,(Point)*pos,-dOrient);
        rt = GetPointAfterRotate((Point)rt,(Point)*pos,-dOrient);

        line( img, lt, ld,Scalar(0,255,255),2);
        line( img, lt, rt,Scalar(0,255,255),2);
        line( img, rd, ld,Scalar(0,255,255),2);
        line( img, rd, rt,Scalar(0,255,255),2);

    }
    return 0;
}