We present an algebraic structure, known as the AFATL (Air Force Armament Technical Laboratory) Image Algebra, that is capable of expressing all image-to-image transformations. After presenting a brief overview of the operands and operations of the algebra, we show how a subalgebra of the full Image Algebra generalizes the theory of mathematical morphology. We provide examples which include 1) morphological operations expressed in the algebra, 2) Image Algebra algorithms not expressible in terms of morphological operations, and 3) a fractal target detection algorithm expressed in terms of the Image Algebra.