This paper proposes an objective assessment method for perceptual image quality of tone mapped images. Tone mapping algorithms are used to display high dynamic range (HDR) images onto standard display devices that have low dynamic range (LDR). The proposed method implements visual attention to define perceived structural distortion regions in LDR images, so that a reasonable measurement of distortion between HDR and LDR images can be performed. Since the human visual system is sensitive to structural information, quality metrics that can measure structural similarity between HDR and LDR images are used. Experimental results with a number of HDR and tone mapped image pairs show the effectiveness of the proposed method.