Replacing connected regions by their skeleton

Here I show a binary Image having many connected regions(white). I want to replace these regions by single pixel edges. how can I do it?

please help someone

I want this type of result

BWMORPH with the skel option finds the skeleton of the image. Note that I needed to clean up the image a little bit to get a decent result

img = imread('https://i.sstatic.net/0Paok.jpg');
img = imopen(img,strel('disk',3)); %# you may want to play with the radius here
border = bwmorph(img,'skel',inf);