Those serial cameras need far more processing power than a PICAXE can provide, so that idea is a non-starter.
However, somewhere on the net ( maybe even in this forum ) there is a camera which is ideal for robots, and easily interfaces to PICAXE.
The camera contains a processor running on-board image recognition, and the serial line just provides simple X,Y co-ordinates of the target objects it can currently see. It is pre-programmed to recognise a few colours and shapes, such as 'green ball', 'yellow square', etc.
A PICAXE controlled robot could easily process this co-ordinate based information, and perform logic like 'Turn Left until Green Ball in centre of view'.
This is a piece of kit I'd like to try, but I can't find the link !. ( Had major browser crash, and lost all bookmarks and history !. )
If anyone knows of this camera I'd be grateful for a link.
Cheers,
Buzby