Objective Building contours play an important role in urban planning, urban change analysis and three- dimensional city modeling. Extracting accurate building information from multi-source data is a necessary guarantee for building model reconstruction. The building contours extracted from historical raster maps, remote sensing images and LiDAR point cloud data have errors in position, direction, size and shape due to the influence of original data quality and algorithm performance. However, most of the traditional contour optimization methods are aimed at a class of data, which have the problems of low universality and accuracy. In this study, a new building contour optimization method which is applicable to multi-source data is proposed, which can effectively improve the regularity and accuracy of the initial building contours. We hope that the proposed method can enrich the existing contour optimization methods and contribute to further automatic regularization of building contours. Methods The method proposed in this paper mainly consists of five steps. Firstly, the modified Douglas-Peucker ( D- P) algorithm is used to simplify the contour. The convex hull method is used to obtain the starting and ending points of the contour, and the vertical distance method is used to obtain the distance threshold of simplifying the contour. Secondly, the least square method is used for line fitting, and then to find the intersection points of lines to further optimize the contour. Subsequently, the defined feature edges and feature angles are regularized. Then, rectangular processing is carried out according to the angle relationship between the main direction of the building and each contour edge. Finally, a method based on the maximum area overlap degree is designed to improve the precision of contour position. Furthermore, the accuracies of experimental results are evaluated with four indexes including position similarity, direction similarity, size similarity and shape similarity. Results and Discussions In this paper, we carry out experiments by using multi- source vector data of building contours. The results show that the proposed method is effective, and has high building contour accuracy and strong universality. For the initial building contour extracted from the historical raster map, the proposed method has high accuracy for both complex building contours and simple building contours (Fig. 10). The accuracies of the experimental results are above 0. 95 (Table 2). For the initial contours of buildings extracted from remote sensing images, compared with method A, the contour optimization results of the proposed method are more accurate (Fig. 11), especially for the results of nonrectangular buildings, the accuracy is improved significantly (Table 3). For the initial building contours extracted from LiDAR point cloud data, the results of the proposed method are basically consistent with those of Method B (Fig. 12), which have high accuracy ( Table 4). The optimized contours are close to the real building contours (Fig. 13). In addition, the time complexity of each stage is analyzed ( Table 5), and experiments and discussions on special buildings are conducted with circular arc structures ( Fig. 14). Conclusions To improve the accuracy and universality of building contour optimization method, a new multi- source data oriented building contour optimization method is proposed in this paper. The main innovations and contributions of this paper include: the improved D-P algorithm is designed to simplify the building contour, in which the convex hull method and vertical distance method are used to effectively overcome the difficult problems of the selection of starting and ending points and the selection of the simplified distance threshold, which enhances the adaptability of the threshold value and improves the accuracy of the simplified results; the location precision method based on the maximum area overlap degree is designed, which improves the accuracy of the building contour to a certain extent; different from the existing literatures which only focus on the contour optimization for a class of data, the method proposed in this paper carries out optimization experiments on building contours extracted from common three types of data, which verifies the effectiveness and universality of the proposed method. Compared with some existing literatures, the method designed in this paper has the advantages of high precision and strong universality. However, the proposed method also has some limitations. For example, this method is not suitable for the optimization of the contours of buildings with curved structure and topologically adjacent buildings, and manual thresholds (such as angle thresholds during right-angle) are also needed in some links of the contour optimization process. In addition, the optimization results of building contours largely depend on the quality of initially extracted contours. In order to further improve the accuracy and universality of the contour optimization method, the deep learning-based building contour prediction method should be explored in the next step.
