How to detect octogonal shapes using contours

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The following C++ code works OK. It finds all of the 8-gons, there's three of them. To differentiate between an octagon and some other shaped 8-gon, you would make sure that the 8-gon is convex, and that all 8 angles are roughly the same (2*pi / 8 radians).

#include <iostream>
using namespace std;

#include <opencv2/opencv.hpp>
using namespace cv;
#pragma comment(lib, "opencv_world340.lib")

int main(void)
{
    Mat stopsign_img = imread("stop.png", CV_LOAD_IMAGE_GRAYSCALE);

    threshold(stopsign_img, stopsign_img, 127, 255, THRESH_BINARY);

    vector<vector<Point> > contours;
    vector<Vec4i> hierarchy;

    findContours(stopsign_img, contours, hierarchy, RETR_TREE, CHAIN_APPROX_SIMPLE, Point(0, 0));

    vector<vector<Point> > contours_poly(contours.size());

    for (int i = 0; i < contours.size(); i++)
        approxPolyDP(Mat(contours[i]), contours_poly[i], 3, true);

    Mat stopsign_contours = Mat::zeros(stopsign_img.size(), CV_8UC3);

    for (int i = 0; i < contours_poly.size(); i++)
    {
        if(1 == contours_poly[i].size())
        {
            // a point
            line(stopsign_contours, contours_poly[i][0], contours_poly[i][0], Scalar(0, 255, 0), 1, 8, 0);
        }
        else if (2 == contours_poly[i].size())
        {
            // a line segment
            line(stopsign_contours, contours_poly[i][0], contours_poly[i][1], Scalar(0, 0, 255), 1, 8, 0);
        }
        else
        {
            if (8 == contours_poly[i].size())
                cout << "8-gon found" << endl;

            // an n-gon, where n = contours_poly[i].size()
            for (int j = 0; j < contours_poly[i].size() - 1; j++)
                line(stopsign_contours, contours_poly[i][j], contours_poly[i][j + 1], Scalar(255, 0, 0), 1, 8, 0);

            line(stopsign_contours, contours_poly[i][contours_poly[i].size() - 1], contours_poly[i][0], Scalar(255, 0, 0), 1, 8, 0);
        }
    }

    imshow("stopsign_contours", stopsign_contours);

    waitKey(0);

    destroyAllWindows();

    return 0;
}