How to get rid of the mirror feedbacks generated from a camera and a projector?

Dear List,

I'm using a webcam, a computer, a beamer and a screen to make a video
interactive installation. The installtion uses people's real shadow to
interactive with the virtual shadows. The setup is like this: There is a
screen with white cloth. A camera is behind and a beamer is opposite on the
screen. Both of the camera and projector are connected with a computer. The
player was supposed to cast their shadows on the screen and the camera will
catch the shadow image and send it to the computer and the beamer will
project it on the screen finally.

However, the feedback phenomena happend. For example, imagine you stand in
the front of the screen, when a real shadow is casting at the left side of
the screen, the camera behind will "see" the image on the right side. Then
the image will be projected by beamer on the right side of the screen. This
virtul shadow is the right image I want to show. But after that, the
feedbacks are comeing The camera catch the real shadow and the first
virtual shadow again and the beamer projects both of them again.So there
will be two extra virtual shadows which are faded and unclear, like a gray
fog. If the player moves, the phenomena will continue circularly even cover
the whole screen.

Now I am using jit.brcosa object to control by change the values of
brightness and contrast. However, I can't find the proper values at all.
Even the image is light gray with white at some part, the feedbacks are
still there. I try to contral the camera's exposure, brightness and
contrast, the problem is still there.

Does anybody has an idea to get rid of the feedbake? Any response would be
very appreciated!

Regards,

Xinmei