To process an image (create thumbs) first you have to copy it to a local directory. You can't do any processing on an image which is on another server or url. So here is how i did it in one of my PS project.
1) First check if the image exists or not. You can do it by using fopen in read mode, if it returns true, then the file exists. It is a good practice to do it because it will avoid unnecessary calls to the remote server.
$imageUrl = "http://www.nordix.cz/img/p/824-2268.jpg";
@fopen($imageUrl, "r");
2) Now you have the image as the fopen returned true, you need to copy the image to the PS temp directory as below
$tmpName = tempnam(_PS_TMP_IMG_DIR_, 'PS');
copy($imageUrl , $tmpName);
after the copy function downloads the image to PS temp directory, then you can process that image as you want. Remember that you have to make all processing on $tempName, as it is the file now. $tempName is like $_FILES['imageFieldName']['tmp_name'].
Thank you