The accurate prediction of quality from an end-user perspective has received increased attention with the growing demand for compression and communication of digital image and video services over wired and wireless networks. The existing quality assessment methods and metrics have a vast reach from computational and memory efficient numerical methods to highly complex models incorporating aspects of the human visual system. It is hence crucial to classify these methods in order to find the favorable approach for an intended application. In this paper a survey and classification of contemporary image and video quality metrics is therefore presented along with the favorable quality assessment methodologies. Emphasis is given to those metrics that can be related to the quality as perceived by the end-user. As such, these perceptual-based image and video quality metrics may build a bridge between the assessment of quality as experienced by the end-user and the quality of service parameters that are usually deployed to quantify service integrity.