OCR PDF

After capturing/importing/attaching PDF, perform OCR on the content, making it possible to 1) make keywords part of general search 2) perform search within PDF.
Preferably there would be option to do this all the time / ask@ time of action / never.

In the context of multiple platform use (show me one that really does everything you need ...), it would be extremely useful , if the OCR results would be stored in the PDF (i.e. image + text).
In this way , platforms with less document focus could receive (automated) feeds from "the NoteApp".