Road centerline extraction is the foundation for integrating the segmented road map from a remote sensing image into a geographic information system (GIS) database. Considering that existing approaches tend to have a decline in performance for centerline and junction extraction when segmented road structures are irregular, this paper proposes a novel method which models the road network as a sequence of connected spline curves. Based on this motivation, the ratio of cross operators is firstly proposed to detect direction and width features of roads. Then, road pixels are divided into different clusters by local features using three perceptual grouping principles (i.e., direction grouping, proximity grouping, and continuity grouping). After applying a polynomial curve fitting on each cluster using pixel coordinates as observation data, the internal control points are determined according to the adjacency relation between clusters. Finally, road centerlines are generated based on spline fitting with constraints. We test our approach on segmented road maps which were obtained previously by machine recognition, or manual extraction from real optical (WorldView-2) and synthetic aperture radar (TerraSAR-X, Radarsat-2) images. Depending on the accuracy of the input segmented road maps, experimental results from our test data show that both the completeness and correctness of extracted centerlines are over 84% and 68% for optical and radar images, respectively. Furthermore, experiments also demonstrate the advantages of our proposed method, in contrast to existing methods for gaining smooth centerlines and precise junctions.