In this paper, we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform (2D-SMCWT). The fusion of the detail 2D-SMCWT coefficients is performed via a Bayesian Maximum a Posteriori (MAP) approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients. For the approximation coefficients, a new fusion rule based on the Principal Component Analysis (PCA) is applied. We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method. The obtained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics. Robustness of the proposed method is further tested against different types of noise. The plots of fusion metrics establish the accuracy of the proposed fusion method.