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Quantitative cancer image analysis relies on the accurate delineation of tumours, a very specialised and time-consuming task. For this reason, methods for automated segmentation of tumours in medical imaging have been extensively developed in recent years, being Computed Tomography one of the most popular imaging modalities explored. However, the large amount of 3D voxels in a typical scan is prohibitive for the entire volume to be analysed at once in conventional hardware. To overcome this issue, the processes of downsampling and/or resampling are generally implemented when using traditional convolutional neural networks in medical imaging. In this paper, we propose a new methodology that introduces a process of sparsification of the input images and submanifold sparse convolutional networks as an alternative to downsampling. As a proof of concept, we applied this new methodology to Computed Tomography images of renal cancer patients, obtaining performances of segmentations of kidneys and tumours competitive with previous methods (~84.6% Dice similarity coefficient), while achieving a significant improvement in computation time (2-3 min per training epoch).