Perivascular spaces (PVS) visible on MRI are currently emerging as an important potential neuroimaging marker for several pathologies in the brain like Alzheimer’s disease and cerebral small vessel disease. PVS are fluid-filled spaces surrounding vessels as they enter the brain. Although PVS are normally not noticeable on MRI scans acquired at clinical field strengths, when these spaces increase in size they become increasingly visible and quantifiable. To study these spaces it is important to have a robust method for quantifying PVS. Manual quantification of PVS is challenging, time-consuming and subject to observer bias due to the difficulty of distinguishing PVS from mimics and the large number of PVS that can occur in MRI scans. Many promising (semi-)automated methods have been proposed recently to decrease annotation time and intra- and inter-observer variability while providing more information about EPVS. However there are still various limitations in the current methods that need to be overcome. An important limitation is that most of the methods are based on elaborate preprocessing steps, feature extraction and heuristic fine-tuning of parameters, making the use of these methods on new datasets cumbersome. Furthermore the majority of the currently proposed methods have been evaluated on small sets of barely 30 images, as most of these methods aim to segment PVS and require voxel-wise annotations for evaluation. In this thesis we propose a method for automated detection of perivascular spaces that combines a convolutional neural network and geodesic distance transform (GDT). We propose to use dot annotations instead of voxel-wise segmentations as this is less time-consuming than fully segmenting PVS while still providing the location of PVS. This enables us to use a considerably larger dataset with ground truth locations than is used in all previously proposed (semi-)automatic methods that provide the location of PVS. We investigated two approaches of using geodesic distance transform to optimize the CNN to detect PVS. The first approach focuses on optimizing the CNN for voxel-wise regression of the geodesic distance map (GDM) computed from the dots and the intensity image. The second approach aims to predict segmentations of the PVS using a CNN that is trained on approximated segmentations obtained by thresholding GDMs. We use 1202 proton density-weighted (PDw) MRI scans to develop our methods and 1000 other scans are used to evaluate the performance of the methods. We show that our methods match human intra-rater performance on detecting PVS without the need for any user interaction. Additionally we show that GDMs are extremely useful for capturing complex morphologies when computed from dot annotations. Our experiments indicate that GDMs can be used to provide valuable additional information to CNNs during training.