Being able to automatically detect parking slots during navigation is an important part of an autonomous driving system. Most of the current parking slot detectors either work on images coming from static cameras or are based on hand-designed low-level visual features, limiting the domains of application of such systems considerably. Learning the most suitable features for the task directly from data would allow the system to function in a broader range of situations and be more robust to noise and different observation conditions. This paper presents an end-to-end deep neural network trained to perform automatic parking slot detection and classification on surround-view images, generated by fusing the views of four different cameras positioned on a vehicle. The network architecture is based on the Faster R-CNN baseline. To account for the fact that parking slots can be of different shapes and can be observed at different angles, the predicted bounding boxes are generic quadrilaterals rather than image-aligned rectangles. Moreover, instead of computing offsets wrt anchor boxes, the RPN regresses the region proposals directly. In order to train the network, a small training set comprised of a few hundred images has been manually annotated. The network shows good performance and generalization capability on new examples containing parking slots of the same kinds as those in the training set, suggesting that a wider array of parking slot types could easily be integrated into the system by expanding the dataset.