Using javascript you'll need to build an array of ids in each container like this:
var selected = [],
unselected = [];
$('#gallery img').each(function(){
selected.push($(this.attr('id'));
});
$('#trash img').each(function(){
unselected.push($(this.attr('id'));
});
You may trigger this action using an event such as after each drop or when a user clicks a done button, whatever. Now pass those arrays to the server however you like(refresh the page or ajax call).