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

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

Code:

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 (converted to .bmp)
This is the image and the marking at the contour are the detected points.
"m-004-1.pgm"-->attached (converted to .bmp)
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,
Tommy

Find the uppermost and lowermost points and get the average y-value of those points, this is the "most middle position" you are talking about. When looking through your 2 (or 3 or 4) leftmost/rightmost points, find the one with the y-value closest to this average y-value.