Some of our users have been wondering where the data is processed and stored with Genius Scan. We know that people can keep important documents on their iPhone and this is a legitimate concern. As stated in the iTunes description:
Documents are processed on the phone, not sent to a third-party server
This means that the image processing - page detection, cropping, enhancement - happens on the phone. This also means that all the documents are stored on your iPhone. They will only leave your iPhone when you explicitly decide to send them by email, or export them using sharing features such as Wifi sharing, Dropbox, Evernote, Google Docs...