Maps have been a unique source of knowledge for centuries. Such historical documents provide invaluable information for analyzing complex spatial transformations over important time frames. This is particularly true for urban areas that encompass multiple interleaved research domains: humanities, social sciences, etc. The large amount and significant diversity of map sources call for automatic image processing techniques in order to extract the relevant objects as vector features. The complexity of maps (text, noise, digitization artifacts, etc.) has hindered the capacity of proposing a versatile and efficient raster-to-vector approaches for decades. In this thesis, we propose a learnable, reproducible, and reusable solution for the automatic transformation of raster maps into vector objects (building blocks, streets, rivers), focusing on the extraction of closed shapes. Our approach is built upon the complementary strengths of convolutional neural networks which excel at filtering edges while presenting poor topological properties for their outputs, and mathematical morphology, which offers solid guarantees regarding closed shape extraction while being very sensitive to noise. In order to improve the robustness of deep edge filters to noise, we review several, and propose new topology-preserving loss functions which enable to improve the topological properties of the results. We also introduce a new contrast convolution (CConv) layer to investigate how architectural changes can impact such properties. Finally, we investigate the different approaches which can be used to implement each stage, and how to combine them in the most efficient way. Thanks to a shape extraction pipeline, we propose a new alignment procedure for historical map images, and start to leverage the redundancies contained in map sheets with similar contents to propagate annotations, improve vectorization quality, and eventually detect evolution patterns for later analysis or to automatically assess vectorization quality. To evaluate the performance of all methods mentioned above, we released a new dataset of annotated historical map images. It is the first public and open dataset targeting the task of historical map vectorization. We hope that thanks to our publications, public and open releases of datasets, codes and results, our work will benefit a wide range of historical map-related applications.