Most open source and free culture licenses (such as the GPL licenses or the Creative Commons licenses) are based in copyright law. They cannot prevent uses that do not violate the copyright of the original work. Copyright only protects a particular creative expression.
A work is a derivative work if it contains the creative expression of the original work in parts or in whole. E.g. your image that is a collage of multiple images is a derivative work of all source images. You cannot publish your image unless you have a suitable license for all source images, or are eligible for a copyright exemption under your local laws (e.g. fair use in the U.S.).
However, facts and ideas are not protected by copyright. They may be protected by other legal constructs (e.g. trade secrets, patents, database laws, sui generis rights, or private contracts), but open source/free culture license do not include such restrictions. Without such non-copyright restrictions, you are free to use any information from copyrighted works. So given an image, you are allowed to state facts about it (e.g. “white background”, “280px wide”, “depicts a donkey”) and are allowed to create your own work that references the image (e.g. publish a video inspired by the image, or write an in-depth analysis of the composition and artistic techniques used in the image).
So I'm pretty certain that publishing an analysis of the average brightness of an image violates neither the copyright of the original image, nor the copyright of the computer program used to perform the analysis.
