First, the left and right views of stereo images are decomposed by quaternion wavelet transform to obtain the amplitude and phase information of different scales and directions, and then cyclopean images are generated by combining human visual characteristics. The left views, right views, and cyclopean images are processed via mean subtracted contrast normalization (MSCN). The MSCN coefficient map is then obtained. The MSCN coefficient and the product of MSCN four-direction neighborhood coefficients are fitted via a generalized Gauss distribution model to extract statistical parameter features. The feature vectors are formed by combining the kurtosis, skewness, standard deviation, and energy. The image quality perception score is then predicted using the XGBoost model. Experimental results show that the proposed stereo image quality assessment algorithm is superior to other reported methods in the LIVE 3D image database and it greatly improves the running speed.