Multimodal medical volumetric data fusion using 3-D discrete shearlet transform and global-to-local rule

Traditional two-dimensional (2-D) fusion framework usually suffers from the loss of the between-slice information of the third dimension. For example, the fusion of three-dimensional (3-D) MRI slices must account for the information not only within the given slice but also the adjacent slices. In this paper, a fusion method is developed in 3-D shearlet space to overcome the drawback. On the other hand, the popularly used average-maximum fusion rule can capture only the local information but not any of the global information for it is implemented in a local window region. Thus, a global-to-local fusion rule is proposed. We firstly show the 3-D shearlet coefficients of the high-pass subbands are highly non-Gaussian. Then, we show this heavy-tailed phenomenon can be modeled by the generalized Gaussian density (GGD) and the global information between two subbands can be described by the Kullback-Leibler distance (KLD) of two GGDs. The finally fused global information can be selected according to the asymmetry of the KLD. Experiments on synthetic data and real data demonstrate that better fusion results can be obtained by the proposed method.