I managed to segment the two objects using the watershed transform. But will still need to measure that waist for further analysis.
My code is shown below the image. BW_erode is the BW image to the right in the picture above.
Distant_BW = -bwdist(~BW_erode,'chessboard');
mask = imextendedmin(Distant_BW,10);
Distant_BW = imimposemin(Distant_BW,mask);
Distant_BW(~BW_erode) = -Inf;
Watershed_BW = watershed(Distant_BW);
rgb = label2rgb(Watershed_BW,'jet',[.5 .5 .5]);
figure(2)
imshow(rgb)