I want to track an object in a video. So i suppose that I could use "Gaussian Mixture Models" in Opencv and C++ . I want to know how to write Gaussian Mixture Models in C++ . Are there any better algorithms for this than GMM?
Sorry to not answer the question directly but:
Reading research papers is a great thing to do, but to be honest, you will get much more knowledge at this point by trying your own ideas on your specific data and getting a better understanding of the problem.
If you know the shapes, it's probably better to use a generalized Hough transform or matched filter for position estimates, combined with a Kalman filter for tracking. These will be relatively easy to implement. Or maybe you can find existing implementations.
Also, I'd prototype your idea in Matlab or Octave instead of C++ if you are not a very good C++ programmer as you'll wind up wasting most of your time with problems in C++ when the problem itself is what you really want to focus on.
As I said in the comment, I'd skip out on using GMM's for now until you get a better understanding of the problem and how you are going to use them. (Unless of course you already have a good idea of how you will use them.)