How do you know if an image is copyrighted? Always assume it is, in every case. The minute an artist creates an image, a writer creates a story, a musician develops a new song, then they own the copyright.
Registration may be required to enforce a copyright, but there’s nothing one must do to hold that right in place. Trademarks and patents are different and they require registration and a fee.
But you must also understand what “Fair Use” in regard to copyright law. The fair use section of the Copyright Act places limitations and exceptions on an owner’s copyright in the form of commentary, parody, news reporting, teaching, archiving, academic research, and search engines. If a professor is leading a discussion about DaVinci’s Mona Lisa, it’s not like they can really purchase the original painting or print, especially for every kind of painting they’d like to present and discuss. In this case, downloading and printing out the photo is likely covered under fair use, as the professor’s intention (an important aspect of the Copyright Act) is for nonprofit educational purposes.
Whether or not something falls under the category of fair use is mostly up to the court. Though we have an abundance of precedence for determining fair use in the offline world, laws are struggling to keep pace with rapidly developing digital technologies.
A recent ruling went against the digital reseller company, ReDigi, a company trying to create a second market for eBooks, unwanted MP3 files, and other digital files for which original owners no longer used. Lacking frameworks to process this modern issue, the judge turned to Star Trek and Willy Wonka to make a ruling. Fair use in the digital age is vastly open to interpretation.