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This paper presents a novel 3D multimodality medical image fusion algorithm based on wavelet multiresolution analysis, a powerful tool able to decompose an image into multiple frequency bands that can be independently analyzed and merged. The focus of this work is to merge 3D medical images coming from several modalities (CT, PET, MRI, etc.), organized as series of 2D image slices, while preserving the salient information. The algorithm aims also at enhancing the visualization of fused images by applying a color to source images. A pre-processing stage using rescaling and resampling filters makes the spatial resolution and the image slice number of the input series equal. Images are i) decomposed by 3D RDWT, ii) combined through appropriate fusion rules based on average, variance and energy, and iii) reconstructed by 3D IRDWT. Experimental results validate the superiority of the proposed 3D technique over other existing algorithms on the basis of subjective and objective criteria.