Find minimal enclosing quadrilateral

Question

I have a polygon in the first picture below. This polygon was taken from yolov8-seg. I know that it should be rectangle. My task is to correct perspective of this mask. I can easily do this by finding four corners.

contours = cv2.findContours(mask, method=cv2.RETR_LIST, mode=cv2.CHAIN_APPROX_SIMPLE)[0]
epsilon = 0.1 * cv2.arcLength(contours[0], True)
approx = cv2.approxPolyDP(contours[0], epsilon, True)

So "approx" is my four corners of mask in the form of red dots in the first picture. But correction of perspective could be more precise if I could find green corners of enclosing quadrilateral which is shown in the second picture. How to find it? OpenCV has similar functions for finding the minimum triangle, rectangle and circle, but not quadrilateral.

points I have

points I want

How to find it? UPDATE: Source image

Answer 1

If you can use Imagemagick for the task. I have a bash unix shell script (at http://www.fmwconcepts.com/imagemagick/quadcorners1) for that task. It does not run on Windows (DOS), but could run on Windows Unix or Cygwin. Unfortunately, the script currently needs tuning for one argument in order to ensure you get 4 and only 4 lines in order to extract the intersections. The script requires Imagemagick 7 and will not run on Imagemagick 6. You can call Imagemagick and my script from Python using a subprocess call.

Input:

quadcorners1.sh -h 18% -i save -k final quad.png

1175.8,344.8 1042.5,842.2 166.5,719.1 166.5,93.1