Get random item from huge array or random file from subfolders

I am trying to get a random file from all subfolders in a folder.

First I get an iterator of all files, using this code:

$path = "/path/to/folder";

$folder = new RecursiveDirectoryIterator($path);
$iterator = new RecursiveIteratorIterator($folder);

$files = new RegexIterator($iterator,
                           '/^.+\.(jpg|jpeg|png|gif)$/i',
                           RecursiveRegexIterator::GET_MATCH);

This appears to work (and finishes in a split second). Now I want to get a random item from the resulting iterator. I use this code (this is line 14):

$image = array_keys(iterator_to_array($files))[mt_rand(0,
                                           count(iterator_to_array($files)) - 1)];

The folder contains 334327 objects, and, after executing for a couple of seconds, iterator_to_array() dies with the following error:

Fatal error: Allowed memory size of 134217728 bytes exhausted
             (tried to allocate 1232 bytes) in /script.php on line 14

How do I need to change my code to avoid PHP running out of memory? Or is there a better way to grab a random item from such a huge array? (Or maybe it is even possible to grab a random file from all subfolders, directly?)

I do not want to override the memory limit!