Arduino video communication devices over wifi

So my project idea is to have an arduino with a camera, screen and capability to connect to a wifi network. Then I want to be able to communicate over this network with a second exact same device. So basically a hand held video communicator over wifi. Where should I start? Is this even possible with an arduino? Should I look for something more powerful? What would be some major issue I would run into?

Edit: What about using something like this SimpleCortex, For When An Arduino Is Too Wimpy | Hackaday

What would be some major issue I would run into?

Probably about the same as turning an empty pizza box into a flat screen tv. Nobody has done what you discribe with an arduino yet.

theuglymonkey:
What would be some major issue I would run into?

That the Arduino is an absolutely lousy choice if it has to do anything with the actual video. The ATmega chips used in Arduino are microcontrollers, not microprocessors. Capturing, transmitting, decoding, and display video requires a relatively large amount of processing.

Probably about the same as turning an empty pizza box into a flat screen tv.

Nice analogy.