Your definition of 'less connected' is not clear to me. However, if you want just the big round component, you can use regionprops to find the largest component and remove the smaller components using bwareaopen.
Here's an example:
% read image and convert to binary.
im = imread('http://www.mathworks.com/matlabcentral/answers/uploaded_files/7873/fake.png');
bw = logical(rgb2gray(im));
% use regionprops to find area of all components.
cc = regionprops(bw,'Area');
% find area of largest component.
maxarea = max([cc.Area]);
% use bwareaopen to remove smaller components.
out = bwareaopen(bw,maxarea);
Hope this helps!
