SSIM is the Structural SIMilarity index, a measure of similarity between two images originally invented by Zhou Wang, Alan C. Bovik, Hamid R. Sheikh and Eero P. Simoncelli (see "Links" below). In other words, SSIM is a replacement for RMSE, AAE and MAE. The main advantage of SSIM is that it more closely matches human perception.
The optiSSIM project aims at refactoring the computation of the SSIM index to make it more efficient, as well as reformulating it so that it varies more smoothly w.r.t. small changes in scale or minor cropping.