As already documented in the literature, fractal image encoding is a family of techniques that achieves a good compromise between compression and perceived quality by exploiting the self-similarities present in an image. Furthermore, because of its compactness and stability, the fractal approach can be used to produce a unique signature, thus obtaining a practical image indexing system. Since fractal-based indexing systems are able to deal with the images in compressed form, they are suitable for use with large databases. We propose a system called FIRE, which is then proven to be invariant under three classes of pixel intensity transformations and under geometrical isometries such as rotations by multiples of π/2 and reflections. This property makes the system robust with respect to a large class of image transformations that can happen in practical applications: the images can be retrieved even in the presence of illumination and/or color alterations. Additionally, the experimental results show the effectiveness of FIRE in terms of both compression and retrieval accuracy.