## 1 Introduction  
In the field of medical imaging, segmentations are extremely useful for a plethora of tasks, including image-based diagnosis, lesion detection, image fusion, surgical planning or computer-aided surgery. For the prostate, in particular, fusion-guided biopsy and focal therapies are quickly gaining popularity due to the improved sensitivity and specificity for lesion detection [1], and the low complication profile [2], respectively, although they are still not fully accepted in clinical guidelines. Nevertheless, accurate prostate segmentations are still hard and laborious to obtain, since they have to be manually annotated by expert radiologists and, even then, the inter- and intra-observer variability may be significant due to factors such as the lack of clear boundaries between neighboring tissues or the huge size and texture variation of this gland among patients. In our experiments, 14 images were segmented by a second expert, and the inter-expert agreement was found to be of 0.8794 in terms of Sorensen-Dice Similarity Coefficient (_DSC_) and 1.5619 mm in terms of the Average Boundary Distance (ABD). Very similar results were obtained in [3], with experts achieving a _DSC_ and an ABD of 0.83 and 1.5 mm, respectively. Because of this, automatic segmentation algorithms for the prostate are increasingly sought-after. Before the rise of Deep Learning (DL) around 2012 [4], many different techniques for automatic prostate segmentation coexisted. For instance, in [5], MR images of the prostate were segmented by using voxel threshold-based classification followed by 3D statistical shape modeling. An alternative approach suggested by [6] attempted to match the probability distributions of the photometric variables inside the object of interest with an appearance model, and then evolved the shape of the object until both distributions matched best. Another technique that has been widely used in the literature for medical image segmentation is atlas matching, which consists in non-rigidly registering a set of labeled atlas images to the image of interest, and then somehow combining all resulting segmentations into a single one [7]. Despite the strengths of these methods, the true revolution in this field came with the advent of CNNs, which are a kind of DL algorithm formed by a stack of convolutional filters and non-linear activation functions, wherein the filter parameters are learned by stochastic gradient descent. New CNN architectures have been steadily raising state-of-the-art performance in computer vision tasks, such as image classification [8], image segmentation [9] or object detection [10]. Similarly, this trend has carried over to medical imaging, and prostate segmentation in particular. One of the first approaches to CNN-based segmentation consisted in sliding a classification CNN over a whole image to provide pixel-wise classifications, which then were combined into a single segmentation mask [11]. Shortly after, fully convolutional neural networks for semantic segmentation were proposed [12]; they allowed for much faster training and inference, as the whole image was processed at once, and also made a better use of spatial information by utilizing activation maps from different layers. Later, the U-net architecture [9] introduced the encoder-decoder design with skip connections that is still predominantly used. In a U-net, the image is first processed through an encoder CNN, which is similar to a classification CNN. The output of the encoder is then connected to the input of the decoder CNN, which is an inverted version of the encoder where the pooling operators have been exchanged by up-scaling convolutions. Additionally, skip connections transfer information from the encoder to the decoder at several stages other than the output. This idea, in combination with residual connections [13] and a cost function based on _DSC_, was quickly extended from two-dimensional (2D) convolutions to 3D convolutions by the V-net [14], in order to better deal with 3D medical images.