Traditionally, U.S. copyright law has looked askance at protecting what in Europe are known as moral rights. These moral rights include the right of attribution, and the preservation of the integrity of the work from any distortion. In other words, moral rights hold up as sacred the creative bond between the author and her work. Some legal scholars contend U.S. law has been reluctant to embrace moral rights because of the primary of property rights: that copyright shouldn't infringe in the rights of the owner of the physical work itself. But in 1990, this all changed. The U.S. adopted the Visual Artists Rights Act (VARA) that protected certain types of visual art works from mutilation or distortion. VARA provides its protection only to paintings, drawings, prints, sculptures and still photographic images produced for exhibition only, and existing in single copies or in limited editions of 200 or fewer copies, signed and numbered by the artist.
One of the most famous cases reliant on this law occurred in 2018, when a judge awarded $6.7 million to several graffiti artists whose graphic art in New York City at 5 Pointz was destroyed by a developer of the property.
VARA has been an issue particularly for commissioned public sculptures. Without a waiver, sculptures cannot easily be removed from a property owner's land once they have been commissioned and placed there.
If a work is in the public domain (published/publicly displayed over 95 years ago), like the Mona Lisa, then you can take pictures of the original if the museum permits (many museums forbid photography). However, if you make a reproduction/copy of another person's photograph of the painting, that photograph may not be in the public domain, and so permission may need to be obtained from the photographer.
For a work art still under copyright, like Grant Wood's American Gothic, permission may need to be granted from the copyright owner to make any reproductions of the original painting other than for personal use. For reproductions of existing photographs of American Gothic, permission would need to sought from the photographer.
For photographs of public art, such as sculpture or graffiti that are still protected by copyright, permission is still needed for any use that would result in any commercial benefit to the photographer. This is because the art work, though public, still attaches to all the protection afforded by copyright, including the making of derivative works such as photographs, and benefitting financially therefrom. Photographs made for personal use do not necessitate permission.
How about photographs of architecture? Architectural works have been protected by copyright since 1990. Fortunately, according to U.S. copyright law, photographs can be taken of any building that can be viewed from a public space without the need to request permission, even if these photographs result in commercial benefit to the photographer.
How about the making of collages or other art work that borrow from existing copyrighted art work or otherwise makes modifications to copyrighted painting or photographs or other art work? Well, this circles back to fair use. If the new work makes sufficient changes to the existing work(s), then the courts may consider the new work to be transformative, and thus a fair use. For example, if the work parodies the original, this may be considered transformative of the original work and thus a fair use. But if the use is not sufficiently different in character or purpose or content from the original, then the new work may be considered merely derivative and thus not a fair use, but liable as an infringement.