High dynamic range (HDR) image and video technology has recently attracted a great deal of attention in the multimedia community, as a mean to produce truly realistic video and further improve the quality of experience (QoE) of emerging multimedia services. In this context, measuring the quality of compressed HDR content plays a fundamental role. However, full-reference (FR) HDR visual quality assessment poses new challenges with respect to the conventional low dynamic range case. Quality metrics have to be redesigned or adapted to HDR, and understanding their reliability to predict users’ judgments is even more critical due to the still limited availability of HDR displays to perform subjective evaluations. The goal of this paper is to provide a complete and thorough survey of the performance of the most popular HDR FR image quality metrics. To this end, we gather several existing HDR image databases with subjective quality annotations, in addition to a new one created by ourselves. After aligning the scores in these databases, we obtain an extensive set of 690 compressed HDR images, along with their subjective quality. Next, we analyze in depth many FR metrics, including those used in MPEG standardization, using both classical correlation analyses and classification accuracy. We believe that our results could serve as the most complete and comprehensive benchmark of image quality metrics in the field of HDR image compression.