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Much more optimization could be done, but at least this is working:

void add_piece_of_frame(const Mat &A, Mat &B, int r, int c)
{
     Rect Roi(r, c, 40, 40);
     A.copyTo(B(Roi));
}

void add_piece_of_frame_red(const Mat &A, Mat &B, int r, int c)
{
    Rect Roi(r, c, 40, 40);
    Scalar color = Scalar(0, 0, 255);
    Mat mask = Mat(40, 40, CV_8UC3, color);
    addWeighted(A, 0.5, mask, 0.5, 0, B(Roi), CV_8UC3);
}

void main()
{
    Mat bkg_read = imread("C:\\Users\\Fabrizio\\Desktop\\frame\\VIDEO_PER_TESI\\Scene1.jpg", CV_LOAD_IMAGE_COLOR);
    imshow("original", bkg_read);
    waitKey(1);     

    Mat ricostruzione[48];
    int aa[48];
    int bb[48];
    int m = 0;

    for (int a = 0; a<320; a += 40)
    {
        for (int b = 0; b<240; b += 40)
        {
            Mat SUPPORT(bkg_read, Rect(a, b, 40, 40));
            ricostruzione[m] = SUPPORT.clone();
            aa[m] = a;
            bb[m] = b;
            cout << "coordinate:  " << endl;
            cout << "a:  " << aa[m];
            cout << "\tb:  " << bb[m] << endl;
            m++;
        }
    }

   while (true) //what is this loop for???
   {
       Mat output = cv::Mat::zeros(240, 320, CV_8UC3);
       Mat output_red = cv::Mat::zeros(240, 320, CV_8UC3);

       for (int t = 0; t<48; t++)
       {
            add_piece_of_frame_red(ricostruzione[t], output_red, aa[t], bb[t]);
       }
       imshow("output_red", output_red);
       waitKey(0);

       for (int u = 0; u<48; u++)
       {
           add_piece_of_frame(ricostruzione[u], output, aa[u], bb[u]);
       }
       imshow("output", output);
       waitKey(0);
    }
}

Much more optimization could be done, but at least this is working:working, if that is all you want:

void add_piece_of_frame(const Mat &A, Mat &B, int r, int c)
{
     Rect Roi(r, c, 40, 40);
     A.copyTo(B(Roi));
}

void add_piece_of_frame_red(const Mat &A, Mat &B, int r, int c)
{
    Rect Roi(r, c, 40, 40);
    Scalar color = Scalar(0, 0, 255);
    Mat mask = Mat(40, 40, CV_8UC3, color);
    addWeighted(A, 0.5, mask, 0.5, 0, B(Roi), CV_8UC3);
}

void main()
{
    Mat bkg_read = imread("C:\\Users\\Fabrizio\\Desktop\\frame\\VIDEO_PER_TESI\\Scene1.jpg", CV_LOAD_IMAGE_COLOR);
    imshow("original", bkg_read);
    waitKey(1);     

    Mat ricostruzione[48];
    int aa[48];
    int bb[48];
    int m = 0;

    for (int a = 0; a<320; a += 40)
    {
        for (int b = 0; b<240; b += 40)
        {
            Mat SUPPORT(bkg_read, Rect(a, b, 40, 40));
            ricostruzione[m] = SUPPORT.clone();
            aa[m] = a;
            bb[m] = b;
            cout << "coordinate:  " << endl;
            cout << "a:  " << aa[m];
            cout << "\tb:  " << bb[m] << endl;
            m++;
        }
    }

   while (true) //what is this loop for???
   {
       Mat output = cv::Mat::zeros(240, 320, CV_8UC3);
       Mat output_red = cv::Mat::zeros(240, 320, CV_8UC3);

       for (int t = 0; t<48; t++)
       {
            add_piece_of_frame_red(ricostruzione[t], output_red, aa[t], bb[t]);
       }
       imshow("output_red", output_red);
       waitKey(0);

       for (int u = 0; u<48; u++)
       {
           add_piece_of_frame(ricostruzione[u], output, aa[u], bb[u]);
       }
       imshow("output", output);
       waitKey(0);
    }
}