How to find the rotated angle of object

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I have changed your image to write my program because i don't need rectangle. only shape object is needed.

Image is

program is based on this paper (appendix)

#include <opencv2/opencv.hpp> 
#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <iostream>
#include <fstream>

using namespace cv;
using namespace std;
class MatchDescriptor {
public :
    vector<Point2d> sContour;
    vector<complex<float> > b;
    vector<complex<float> > a;
    vector<float> frequence;
    vector<float> rho,psi;
    double pi;
    int nbDesFit;

public :
    MatchDescriptor(){nbDesFit=7;pi=acos(-1.0);};;
    float AjustementRtSafe(vector<Point2d> &c,float &alphaMin,float &phiMin,float &sMin);
    float Ajustement(vector<Point2d> &c,float &alphaMin,float &phiMin,float &sMin);
    void falpha(float x,float *fn,float *df);
    void InitFrequence();
    float rtsafe(float x1,float x2,float xacc);
    float Distance(complex<float> r,float alpha)
    {
    long            i;
    complex<float>      j(0,1);
    float       d=0;

    for (i=1;i<=nbDesFit;i++)
    {
        d += abs(a[i]-b[i]*r*exp(j*float(alpha*frequence[i])))+ abs(a[a.size()-i]-b[a.size()-i]*r*exp(j*float(alpha*frequence[a.size()-i])));
    }
    return d;
    };

};

void MatchDescriptor::InitFrequence()
{
long i;
int nbElt=sContour.size();
frequence.resize(sContour.size());

for (i=0;i<=nbElt/2;i++)
    frequence[i] = 2*pi*(float)i/nbElt;
for (i=nbElt/2+1;i<nbElt;i++)
    frequence[i] = 2*pi*(float)(i-nbElt)/nbElt;
}


void MatchDescriptor::falpha(float x,float *fn,float *df)
{
long    n,nbElt = sContour.size();
float   s1=0,s2=0,s3=0,s4=0;
float   ds1=0,ds2=0,ds3=0,ds4=0;

for (n=1;n<=nbDesFit;n++)
    {
    s1 +=   rho[n] * sin(psi[n]+frequence[n]*x) + 
            rho[nbElt-n] * sin(psi[nbElt-n]+frequence[nbElt-n]*x);
    s2 +=   frequence[n] * rho[n] * cos(psi[n]+frequence[n]*x) +
            frequence[nbElt-n] * rho[nbElt-n] * cos(psi[nbElt-n]+frequence[nbElt-n]*x);
    s3 +=   rho[n] * cos(psi[n]+frequence[n]*x) +
            rho[nbElt-n] * cos(psi[nbElt-n]+frequence[nbElt-n]*x);
    s4 +=   frequence[n] * rho[n] * sin(psi[n]+frequence[n]*x) +
            frequence[nbElt-n] * rho[nbElt-n] * sin(psi[nbElt-n]+frequence[nbElt-n]*x);
    ds1 +=  frequence[n]*rho[n] * cos(psi[n]+frequence[n]*x) +
            frequence[nbElt-n]*rho[nbElt-n] * cos(psi[nbElt-n]+frequence[nbElt-n]*x);
    ds2 +=  -frequence[n]*frequence[n] * rho[n] * sin(psi[n]+frequence[n]*x) - 
            frequence[nbElt-n]*frequence[nbElt-n] * rho[nbElt-n] * sin(psi[nbElt-n]+frequence[nbElt-n]*x);
    ds3 +=  -frequence[n]*rho[n] * sin(psi[n]+frequence[n]*x) -
            frequence[nbElt-n]*rho[nbElt-n] * sin(psi[nbElt-n]+frequence[nbElt-n]*x);
    ds4 +=  frequence[n]*frequence[n] * rho[n] * cos(psi[n]+frequence[n]*x) +
            frequence[nbElt-n]*frequence[nbElt-n] * rho[nbElt-n] * cos(psi[nbElt-n]+frequence[nbElt-n]*x);
    }
*fn = s1 * s2 - s3 *s4;
*df = ds1 * s2 + s1 * ds2 - ds3 * s4 -  s3 * ds4;
}

float MatchDescriptor::AjustementRtSafe(vector<Point2d> &c,float &alphaMin,float &phiMin,float &sMin)
{
long            n,nbElt = sContour.size();
float           s1,s2,sign1,sign2,df,x1=nbElt,x2=nbElt,dx;
float           dist,distMin = 10000,alpha,s,phi;
complex<float>  j(0,1),zz;

InitFrequence();
rho.resize(nbElt);
psi.resize(nbElt);

b.resize(nbElt ...