Feature extraction using a 2D laserscan

[Niurez]

Hi everyone,

As a school assignment I was given the task to detect chairs and tables using a 2D laser scan. It is allowed to just have set of polar coordinates and to perform the calculations afterwards, it doesn't need to be "online". Here are two scans of a room where a chair is put in the right below corner (I marked it with a red square).
http://img29.imageshack.us/img29/3932/scancs.jpg
http://img99.imageshack.us/img99/5599/scan2u.jpg
the chair is put in two different positions. I know these scans of the chair are pretty inaccurate. But I will solve this just by putting the chair closer and thus getting more "hits" on the legs of the chair.

My question towards to you guys is: after I put the chair closer I want to detect circles by just having three points on the legs of the chair. Afterwards I want to detect all circles and see if these are in a square form. But what algorithm is best suited for this? I stumbled upon the hough transform and this seemed nice but it its main use is with images after an edge detection has been performed, right?

I hope I made myself clear as english isn't my native language.
Thanks!

[Divinas]

Do you have a map of the room? If you do, it should be really easy to identify the parts that are part of the room, and the ones that aren't.
If not, some form of particle filters should be able to solve your problem, or some other supervised learning algorithm. By the way, that's a pretty ambitious school project