[Solved] Simple algorithm for approximation image contour for line segment

A possible approach.

Find the convex hull of these points.

Then find the two vertices which are the furthest apart. This gives a first diagonal.

Then find the two other vertices that are the farthest from the first diagonal. This gives a second diagonal.

Now you can just use the quadrilateral formed by these four vertices.

If you want a tighter fit, you can consider the subsets of points in the four quadrants defined by the diagonals, and compute best fit lines, for example by least squares.