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Usually, lesions are not isolated but are associated with the surrounding tissues. For example, the growth of a tumour can depend on or infiltrate into the surrounding tissues. Due to the pathological nature of the lesions, it is challenging to distinguish their boundaries in medical imaging. However, these uncertain regions may contain diagnostic information. Therefore, the simple binarization of lesions by traditional binary segmentation can result in the loss of diagnostic information. In this work, we introduce the image matting into the 3D scenes and use the alpha matte, i.e., a soft mask, to describe lesions in a 3D medical image. The traditional soft mask acted as a training trick to compensate for the easily mislabelled or under-labelled ambiguous regions. In contrast, 3D matting uses soft segmentation to characterize the uncertain regions more finely, which means that it retains more structural information for subsequent diagnosis and treatment. The current study of image matting methods in 3D is limited. To address this issue, we conduct a comprehensive study of 3D matting, including both traditional and deep-learning-based methods. We adapt four state-of-the-art 2D image matting algorithms to 3D scenes and further customize the methods for CT images to calibrate the alpha matte with the radiodensity. Moreover, we propose the first end-to-end deep 3D matting network and implement a solid 3D medical image matting benchmark. Its efficient counterparts are also proposed to achieve a good performance-computation balance. Furthermore, there is no high-quality annotated dataset related to 3D matting, slowing down the development of data-driven deep-learning-based methods. To address this issue, we construct the first 3D medical matting dataset. The validity of the dataset was verified through clinicians' assessments and downstream experiments.