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Nowadays, it is evident that we must consider human perceptual properties to visualize information clearly and efficiently. We may utilize computational models of human visual systems to consider human perception well. Image quality assessment is a challenging task that is traditionally approached by such computational models. Recently, a new assessment methodology based on structural similarity has been proposed. We select two representative models of each group, the visible differences predictor and the structural similarity index, for evaluation. We begin with the description of these two approaches and models. We then depict the subjective tests that we have conducted to obtain mean opinion scores. Inputs to these tests included uniformly compressed images and images compressed non-uniformly with regions of interest. Then, we discuss the performance of the two models, and the similarities and differences between the two models. We end with a summary of the important advantages of each approach.