Human-based segmentation of tomographic images can be a tedious time-consuming task. Deep learning algorithms and, particularly, convolutional neural networks have become state of the art techniques for pattern recognition in digital images that can replace human-based image segmentation. However, their use in materials science is beginning to be explored and their application needs to be adapted to the specific needs of this field. In the present work, a convolutional neural network is trained to segment the microstructural components of an Al-Si cast alloy imaged using synchrotron X-ray tomography. A pixel-wise weighted error function is implemented to account for microstructural features which are hard to identify in the tomographs and that play a relevant role for the correct description of the 3D architecture of the alloy investigated. The results show that the total operation time for the segmentation using the trained convolutional neural network was reduced to <1% of the time needed with human-based segmentation.