Whenever you take an existing image and modify it to create a different image, you are making a "derivative work." For example, you might composite several images in the darkroom, or you might use Photoshop’s tools to distort a digital photo. Another kind of derivative is the compilation, such as a coffee-table book. In law, it does not matter whether the change is great or small, or whether the result is recognizably like the original; what matters is whether your creative process began with an existing image.
There are three copyright issues that may affect a derivative: original rights, new copyright and disclosure.
Original rights. One of the many rights that a copyright owner enjoys is control over the preparation of derivatives. Thus, if you are building on the work of others, you must obtain permission (unless the original is in the public domain) and you must respect any limitations that the respective owners of the originals may impose. Obviously, if you own the original copyrights, this is not a problem — unless you have sold an exclusive license to someone else.
There are some circumstances where you don’t need the blessing of the original copyright holder, such as for a parody or other fair use. However, you can expect some hostility if you take this route, and you should probably consult a lawyer early on. We also recommend reading the relevant discussion on the Chilling Effects website, including its FAQ about derivative works.
New copyright. The law holds that there can be original authorship if the derivative contains a significant amount of new material or is sufficiently different that it can be regarded as a new work. For instance, in a coffee-table book, the selection and arrangement of the photos is considered “new material” that is worthy of copyright. If there is a new copyright, it covers only the aspects that are original. Thus, the book’s copyright doesn’t affect the copyrights of the photos.
Disclosure. Even though your derivative work is entitled to its own copyright, you must reveal the work’s ancestry when you register. There is a screen for this purpose in the eCO online registration form. (On the old paper Form VA, see section 6a.) Detailed instructions are in the Copyright Office’s Circular 14.