I have a skeletonized image and I want to obtain a smoothened one from the image attached here below.
The main goal after smoothening is to locate any point nearby or exactly at the center of the horizontal plane, I just want to pick any point say (x, y) = (530, 355) and determine if it lies on the horizontal line whether exactly at the center or at any part of the skeleton. Any procedures to go through this?

My trial

I tried to find the contour and then determine the largest contour from the skeleton but I cannot determine any point that lies on the horizontal plane. Any idea to go through this