Recent advances in 3-D graphics technologies have led to an increasing use of processing techniques on 3-D meshes, such as filtering, compression, watermarking, simplification, deformation, and so forth. Since these processes may modify the visual appearance of the 3-D objects, several metrics have been introduced to properly drive or evaluate them, from classic geometric ones such as Hausdorff distance, to more complex perceptually-based measures. This paper presents a survey on existing perceptually-based metrics for visual impairment of 3-D objects and provides an extensive comparison between them. In particular, different scenarios which correspond to different perceptual and cognitive mechanisms are analyzed. The objective is twofold: 1) catching the behavior of existing measures to help Perception researchers for designing new 3-D metrics and 2) providing a comparison between them to inform and help computer graphics researchers for choosing the most accurate tool for the design and the evaluation of their mesh processing algorithms.