Method to recognize abstract objects such as hand-drawn objects?
It sounds like you're looking for shape matching techniques.  Sven Loncaric's well-cited survey paper "A Survey of Shape Analysis Techniques" from 1998 can be found here.

In 2002, Belongie, Malik and Puzicha proposed a similarity measure between two shapes based on


  
  solving for correspondences between points on the two shapes, then
  using the correspondences to estimate an aligning transform.
  


David Marr's book 'Vision', particularly §3.6 and chapter 5, also provides some background about the correspondence between shape recognition in human visual systems and computers.