preprocessing - What segmentation methods can be used for simple images?

As related to the project I am currently involved in, I have come to realize that one thing that might help is for me to 'segment' my image. To that end, I have shown a very simple example below.

How do segmentation methods work in general, and what class of them would help getting me from the first image:

...to the second:

Please ignore the scaling that might seem to have occured here, but you get the general idea.