OpenCV convexhull doesn't give correct output - c++

Question

This is my input binary image:
Now I want to get its convex hull using OpenCV. For that, I wrote the following code:
cv::Mat input = cv::imread("input.jpg", CV_LOAD_IMAGE_GRAYSCALE);
cv::vector<cv::vector<cv::Point>> contours;
cv::vector<cv::Vec4i> hierarchy;
// Find contours
cv::findContours(input, contours, hierarchy, CV_RETR_EXTERNAL, CV_CHAIN_APPROX_NONE);
// Find the convex hull
cv::vector<cv::vector<cv::Point>> hull(contours.size());
for(int i = 0; i < contours.size(); i++)
{
cv::convexHull(cv::Mat(contours[i]), hull[i], false);
}
cv::Mat drawing = cv::Mat::zeros(input.size(), CV_8UC3);
cv::Scalar color = cv::Scalar(0, 0, 255);
for (int j = 0; j < hull.size(); j++)
{
cv::drawContours(drawing, hull, j, color, 1, 8, cv::vector<cv::Vec4i>(), 0, cv::Point());
}
cv::imshow("Convex hull", drawing);
cv::waitKey();
And this is the output:
In Matlab however, when I write the following code:
input = imread('input.jpg');
[x, y] = find(input);
k = convhull(x, y);
plot(y(k), x(k), 'r-', y, x, 'b.');
This gives me exactly what I want (the red line represents the convex hull that I want):
So, how can I obtain the same result in OpenCV? What should I've done incorrectly here? Thank you.

Answer 1

May be this answer is late, but for those who is still in search here it is.
You don't need to take contours. Just take all non-zero point from binary image using findNonZero() method and then apply convexHull to that set of points. It will work perfectly.