What segmentation methods can be used for simple images?
One of the simplest method you can use is 

"Region growing" scheme. Here the algorithm starts with a seed points, and keeps registering the pixel surrounded by it as long as the region as a whole has same property as before and after the inclusion of pixel. This is applied with reasonably good set of seed points recursively. 

This property can be color variations, statistical properties such as mean and variance of intensity of the regions, or it can be texture. And the criteria for segmentation is homogeneity of the region.

The same principle but alternative implementation is region split and merge approach. Here a image is first divided into fixed parts - say 4 parts and corresponding scores of above properties is computed. Now the each sub region is split further, and we can check if any region is significantly different from others or same. If homongenety of sub parts is same essentially it is merged back. But if the element is realized to have different properties it now fall in different regions. 

Read this for more details: http://vplab.iitm.ac.in/courses/CV_DIP/PDF/lect-Segmen.pdf