In human vision, excessive binocular asymmetry between the left-and right-eye images can be very problematic to perceive single binocular vision (causing visual discomfort) in the viewing of stereoscopic images. In this paper, we propose a critical binocular asymmetry (CBA) measure for objectively assessing the perceptual quality of the synthesized stereo 3D images generated through a depth-image-based rendering (DIBR) process. The proposed method detects critical regions that are likely to induce excessive binocular asymmetry. In particular, this paper considers view extrapolation since it introduces much more artifacts due to the lack of data. We measure structural similarity on the critical regions between the left and right images to quantify the perceptual effects of binocular asymmetry. The effectiveness of the proposed quality measure has been successfully evaluated by subjective assessment experiments using various types of synthesized stereoscopic images generated by four different DIBR-based view synthesis algorithms. We demonstrate the validity of the proposed quality measure by the comparison of subjective ratings and existing objective methods. Experimental results show that the combined use of the proposed binocular asymmetry measure and existing quality measures substantially improves the performance of the quality measures by explicitly considering the perceptual effects of CBA.