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Hello every one, here is my function "optical_flow_using_schunck". on line "imshow("frame1", frame1)" it throws "Segmentation fault (Core dumped)" error.

Any idea?!

int optical_flow_using_schunck(char * video_url)
{
    int iteration_count = 20 ;
    double a = 0.001 ;

    namedWindow("frame1" , CV_WINDOW_AUTOSIZE) ;
    namedWindow("frame2" , CV_WINDOW_AUTOSIZE) ;

    cout << "Analyzing motion using Schunck approach for approximating optical flow..." << endl ;
    cout << "Reading video from " << video_url << endl ;
    VideoCapture vid (video_url);
    if(!vid.isOpened())
    {   
        cout << "An error has been occured. The video can not be opened!" << endl ;
        return -1 ;
    }

    Mat frame1, frame2 ;
    vid >> frame1 ;
    if(!frame1.empty())
        vid >> frame2 ;

    cvtColor(frame1 , frame1 , CV_BGR2GRAY) ;
    cvtColor(frame2 , frame2 , CV_BGR2GRAY) ;

    pyrDown(frame1, frame1, Size(frame1.cols/2, frame1.rows/2)) ;
    pyrDown(frame2, frame2, Size(frame2.cols/2, frame2.rows/2)) ;

    cout <<"initializing velocity to zero" << endl ;

    int sz[] = {frame1.rows, frame1.cols};
    Mat u(2, sz, CV_32FC1, Scalar::all(0));
    Mat v(2, sz, CV_32FC1, Scalar::all(0));
    Mat u_avg(2, sz, CV_32FC1, Scalar::all(0));
    Mat v_avg(2, sz, CV_32FC1, Scalar::all(0));
    Mat Ex(2, sz, CV_32FC1, Scalar::all(0));
    Mat Ey(2, sz, CV_32FC1, Scalar::all(0));
    Mat Et(2, sz, CV_32FC1, Scalar::all(0));

    while(!frame2.empty())
    {
        cout << "calculating Ex derivative..." << endl ;
        calculate_EX(frame1, frame2, &Ex) ;
        cout << "calculating Ey derivative..." << endl ;
        calculate_EY(frame1, frame2, &Ey) ;
        cout << "calculating Et derivative..." << endl ;
        calculate_ET(frame1, frame2, &Et) ;

        if(frame1.empty())
            cout << "WOW!" << endl ;
        imshow("frame1" , frame1) ;
        imshow("frame2" , frame2) ;

        for(int iter = 0 ; iter < iteration_count ; iter ++)
        {
            cout << "iteration: " << iter << endl ;

            for(int i = 0 ; i < u.rows ; i ++)
            {
                for(int j = 0 ; j < u.cols ; j++)
                {
//                  cout << "i: " << i << ", j:" << j << endl;  
                    double common_part = (Ex.at<double>(i,j)*u_avg.at<double>(i,j) + Ey.at<double>(i,j) * v_avg.at<double>(i,j) + Et.at<double>(i,j) ) / (pow(a,2) + pow(Ex.at<double>(i,j),2) + pow(Ey.at<double>(i,j),2) ) ;
                    double delta_u = ( Ex.at<double>(i,j) * common_part) ;
                    double delta_v = ( Ey.at<double>(i,j) * common_part) ;
                    u.at<double>(i,j) = u_avg.at<double>(i,j) - delta_u ; 
                    v.at<double>(i,j) = u_avg.at<double>(i,j) - delta_v ;
                }
            }

            // cout << "u_avg is being updated"<< endl ;
            update_veloc_avg(u, &u_avg) ;
            // cout << "u_avg has been updated"<< endl ;
            update_veloc_avg(v, &v_avg) ;
            // cout << "v_avg has been updated"<< endl ;

            // imshow("U_veloc" , u) ;
            // imshow("V_veloc" , v) ;
            // waitKey(0) ;
        }
                        cout << "6" << endl ;
        frame2.copyTo(frame1(Rect(0, 0, frame2.cols, frame2.rows)));
                        cout << "7" << endl ;
        vid >> frame2 ;
                        cout << "8" << endl ;
        cvtColor(frame2 , frame2 , CV_BGR2GRAY) ;
                        cout << "9" << endl ;
        pyrDown(frame2, frame2, Size(frame2.cols/2, frame2.rows/2)) ;
                        cout << "10" << endl ;
        waitKey(0) ;
    }
    cout << "**************************************************\nSchunk ego motion estimation.\n\n\tTHE VIDEO FINISHED\n**************************************************\n" << endl ;
}

here are my other functions "calculate_Ex", "calculate_Ey" , "calculate_Et" and "update_veloc_avg" .

void calculate_EX(Mat frame1, Mat frame2, Mat *E) 
{
    for(int i = 0 ; i < E->rows ; i++)
    {
        for(int j = 0 ; j < E->cols ; j++)
        {
            double res = 0 - (frame1.at<double>(i,j) + frame2.at<double>(i,j)) ;

            if(j < frame1.cols - 1)
                res += frame1.at<double>(i,j+1) ;
            if(j < frame1.cols - 1 && i < frame1.rows - 1)
                res += frame1.at<double>(i+1,j+1) ;
            if(i < frame1.rows - 1)
                res -= frame1.at<double>(i+1,j) ;

            if(j < frame2.cols - 1)
                res += frame2.at<double>(i,j+1) ;
            if(j < frame2.cols - 1 && i < frame2.rows - 1)
                res += frame2.at<double>(i+1,j+1) ;
            if(i < frame2.rows - 1)
                res -= frame2.at<double>(i+1,j) ;

            res *= 0.25 ;
            E->at<double>(i,j) = res ;
        }
    }
}

void calculate_EY(Mat frame1, Mat frame2, Mat* E) 
{
    // int sz[] = {frame1.rows, frame1.cols};
    // Mat E(2, sz, CV_32FC1, Scalar::all(0));
    // Mat E = Mat::zeros(frame1.rows , frame1.cols , CV_32FC1) ;
    for(int i = 0 ; i < E->rows ; i++)
    {
        for(int j = 0 ; j < E->cols ; j++)
        {
            // cout << "EY: " << i << ", " << j << " in " << frame1.rows << ", " << frame1.cols << endl ; 
            double res = 0 - (frame1.at<double>(i,j) + frame2.at<double>(i,j)) ;

            if(i < frame1.rows - 1)
                res += frame1.at<double>(i+1,j) ;
            if(j < frame1.cols - 1 && i < frame1.rows - 1)
                res += frame1.at<double>(i+1,j+1) ;
            if(j < frame1.cols - 1)
                res -= frame1.at<double>(i,j+1) ;

            if(i < frame2.rows - 1)
                res += frame2.at<double>(i+1,j) ;
            if(j < frame2.cols - 1 && i < frame2.rows - 1)
                res += frame2.at<double>(i+1,j+1) ;
            if(j < frame2.cols - 1)
                res -= frame2.at<double>(i,j+1) ;

            res *= 0.25 ;
            E->at<double>(i,j) = res ;
        }
    }

}

void calculate_ET(Mat frame1, Mat frame2, Mat* E) 
{
    // int sz[] = {frame1.rows, frame1.cols};
    // Mat E(2, sz, CV_32FC1, Scalar::all(0));
    // Mat E = Mat::zeros(frame1.rows , frame1.cols , CV_32FC1) ;
    for(int i = 0 ; i < E->rows ; i++)
    {
        for(int j = 0 ; j < E->cols ; j++)
        {
            double res = frame2.at<double>(i,j) - frame1.at<double>(i,j) ;

            if(i < frame2.rows - 1)
                res += frame2.at<double>(i+1,j) - frame1.at<double>(i+1,j) ;
            if(j < frame2.cols - 1)
                res += frame2.at<double>(i,j+1) - frame1.at<double>(i,j+1) ;
            if(j < frame2.cols - 1 && i < frame2.rows - 1)
                res += frame2.at<double>(i+1,j+1) - frame1.at<double>(i+1,j+1) ;

            res *= 0.25 ;
            E->at<double>(i,j) = res ;
        }
    }

}

void update_veloc_avg(Mat v, Mat* v_avg)
{
    // int sz[] = {v.rows, v.cols};
    // Mat v_avg(2, sz, CV_32FC1, Scalar::all(0));
    // Mat v_avg = Mat::zeros(v.rows, v.cols, CV_32FC1) ;
    for(int i = 0 ; i < v_avg->rows ; i++)
    {
        for(int j = 0 ; j < v_avg->cols ; j++)
        {
            // cout << i << ", " << j << " in " << v.rows << ", " << v.cols << endl ; 
            double res = 0 - v.at<double>(i,j) ;
            double res1 = 0 , res2 = 0 ;
            if(i > 0)
                res1 += v.at<double>(i-1,j) ;
            if(j < v.cols - 1)
                res1 += v.at<double>(i,j+1) ;
            if(i < v.rows - 1)
                res1 += v.at<double>(i+1,j) ;
            if(j > 0)
                res1 += v.at<double>(i,j-1) ;

            if(i > 0 && j > 0)
                res2 += v.at<double>(i-1,j-1) ;
            if(i > 0 && j < v.cols - 1)
                res2 += v.at<double>(i-1,j+1) ;
            if((i < (v.rows -1)) && (j < (v.cols -1)))
                res2 += v.at<double>(i+1,j+1) ;
            if(i < v.rows -1 && j > 0)
                res2 += v.at<double>(i+1,j-1) ;

            res = res + ((double)1/6) * res1 + ((double)1/12) * res2 ;

            v_avg->at<double>(i,j) = res ;
        }
    }