How to filter the points to get only the left most and right most?

[tommy_chai]

Hi all,
Kindly need your attention here.
Let say,

n = 0;  // number of corner points detected
if (......)
{
corner_list[n].x = j;  //x coordinate
corner_list[n].y = i;  //y coordinate
n++;
:
:
}

"m7.pgm"-->attached
This is the image and the marking at the contour are the detected points.
"m-004-1.pgm"-->attached
I want to get only the left most and right most points as corner. How can i write the codes to keep only these 2 corner points for every image?
From the left side, we can see there are two points with the same x-coordinate. From the right there are 3 or 4 points at the same x-coordinate.
How can we program to choose the most middle position for the left most and right most corner points?

Please help or give some ideas.
Thank you.

Best regards,