To preserve the spatial consistency of low-level features, generalized Riesz-wavelet transform (GRWT) is adopted for fusing multi-modality images. The proposed method can capture the directional image structure arbitrarily by exploiting a suitable parameterization fusion model and additional structural information. Its fusion patterns are controlled by a heuristic fusion model based on image phase and coherence features. It can explore and keep the structural information efficiently and consistently. A performance analysis of the proposed method applied to real-world images demonstrates that it is competitive with the state-of-art fusion methods, especially in combining structural information.