We present a framework for assessing the quality of, and determining the efficiency of foveated and compressed images and video streams. We develop unique algorithms for assessing the quality of foveated image/video data. By interpreting foveation as a coordinate transformation, we analyze the increase in compression efficiency that is afforded by our foveation approach.We demonstrate these concepts on foveated; compressed video streams using modified (foveated) versions of H.263 that are standard-compliant. In the simulations, quality vs. compression is enhanced considerably by the foveation approach. We obtain compression gains ranging from 8 % to 52 % for I pictures and from 7 % to 68 % for P pictures.