Minimum Binding Quadrilateral

In an image processing project (using opencv with python), I am trying to detect as precisely as possible the location of a rectangular object in a photograph. My final goal is to output the 4 corners of the object.

For example, an image could look like this: Original image

In the first stage I am able to detect an approximate boundary for the image, like so: Initial Detection

Now, I have the above red convex polygon.

Next, I would like to compute the Minimum Area Bounding Quadrilateral, and this is where I’m stuck.

My question is, given a convex polygon, what is an efficient algorithm to find a minimum area bounding quadrilateral?