I've been using Sibelius on Windows, along with PhotoScore Lite to scan and transcribe sheet music to date. Recently I set out to find a Linux alternative.
Audiveris is a Java-based open source (therefore free) sheet music notation scanner. It will import a PDF or image file (single page as far as I can see) and automatically transcribe the notes into an on-screen digital version. You can then export to MIDI or MusicXML files, which can be edited in another program such as Rosegarden or MuseScore.
While this program is cross-platform and runs on Windows, Linux and Mac OS, it's advanced OCR features are limited to the Windows platform due to a dependency on Microsoft's C++ libraries. This may change in the future if more developers commit time to the project, but for now I have found it to be a very capable Linux alternative to some of the commercial Optical Music Recognition software. I particularly like the fine-grained reports and control you have over the entire process. In fact, you can examine any stage of the transcription in detail thanks to the multi-step procedure. Not the prettiest display, but then who wants pretty - so long as it gets the job done?