// ok you have this filename, you generate a tag
$filename = '...with/some/folders/file.ext';
$tag = 'resized-by-'.$width.'x'.$height; // not sure if spaces are accepted

$thumbCache = sfImageCache::getInstance('thumbnails'); // thumbnails is like a namespace to manage many caches

$thumbnail = $thumbCache->get($filename, $tag);

if (!$thumbnail) { ... do your resize here ... }

return $thumbnail;