Computer-implemented methods and systems of detecting and modeling curbs include receiving a cloud of three-dimensional (3D) data points acquired along street locations. A plurality of vertical scanlines (e.g., arrays of 3D data points obtained at given horizontal locations) are identified within the cloud of 3D data points. One or more curb points indicating the potential presence of a curb in the plurality of vertical scanlines are identified. A synthesized set of non-overlapping curb curves are generated in order to close gaps between certain curb points while removing certain other outlier curb points. Successive curb curves in the synthesized set of non-overlapping curb curves are then identified as belonging to one or more curb segments. A curb model that fits each of the one or more curb segments to one or more curb model shape representations can then be generated.