Crosstalk is one of the most severe factors affecting the perceived quality of stereoscopic 3D images. It arises from a leakage of light intensity between multiple views, as in auto-stereoscopic displays. Well-known determinants of crosstalk include the co-location contrast and disparity of the left and right images, which have been dealt with in prior studies. However, when a natural stereo image that contains complex naturalistic spatial characteristics is viewed on an auto-stereoscopic display, other factors may also play an important role in the perception of crosstalk. Here, we describe a new way of predicting the perceived severity of crosstalk, which we call the Binocular Perceptual Crosstalk Predictor (BPCP). BPCP uses measurements of three complementary 3D image properties (texture, structural duplication, and binocular summation) in combination with two well-known factors (co-location contrast and disparity) to make predictions of crosstalk on two-view auto-stereoscopic displays. The new BPCP model includes two masking algorithms and a binocular pooling method. We explore a new masking phenomenon that we call duplicated structure masking, which arises from structural correlations between the original and distorted objects. We also utilize an advanced binocular summation model to develop a binocular pooling algorithm. Our experimental results indicate that BPCP achieves high correlations against subjective test results, improving upon those delivered by previous crosstalk prediction models.