The arduino is not fast enough to digitise a row of video but it is possible to digitise a column from a video signal. That is one sample per line. You can turn your camara through 90 degrees if you need to.
You need a sample and hold circuit and some way of triggering it like a digital time base.
This is the sort of thing radio hams did back in the 70s and 80s when they did slow scan TV.
Note you need a camera that gives you video out.