Assign a picture URL to a page via PHP

You can use the add_post_meta function:

add_post_meta( get_the_ID(), 'my_custom_image_url', 'http://domain.com/image.jpg', true );

The code above assumes that a) you will have only one image per page; and b) you are in a loop so get_the_ID will return a valid ID of the page you want to attach the meta-data to. Documentation here.