Curtis Rueden & the ImageJ development team at LOCI, U. Wisconsin-Madison
Fiji is an image processing package—a "batteries-included" distribution of ImageJ, bundling a lot of plugins which facilitate scientific image analysis.
Fiji is easy to install and has an automatic update function, bundles a lot of plugins and offers comprehensive documentation.
Like ImageJ itself, Fiji is an open source project hosted in Git version control repositories, with access to the source code of all internals, libraries and plugins, easing the development and scripting of plugins.
Fiji is licensed under the GNU General Public License. It builds on top of the ImageJ2 core, which is licensed under the permissive BSD 2-clause license. Plugins and other components have their own licenses.
(And P.S., FIJI is Just Image J)