The shape of a geospatial object is an important characteristic and a significant factor in spatial cognition. Existing shape representation methods for vector-structured objects in the map space are mainly based on geometric and statistical measures. Considering that shape is complicated and cognitively related, this study develops a learning strategy to combine multiple features extracted from its boundary and obtain a reasonable shape representation. Taking building data as example, this study first models the shape of a building using a graph structure and extracts multiple features for each vertex based on the local and regional structures. A graph convolutional autoencoder (GCAE) model comprising graph convolution and autoencoder architecture is proposed to analyze the modeled graph and realize shape coding through unsupervised learning. Experiments show that the GCAE model can produce a cognitively compliant shape coding, with the ability to distinguish different shapes. It outperforms existing methods in terms of similarity measurements. Furthermore, the shape coding is experimentally proven to be effective in representing the local and global characteristics of building shape in application scenarios such as shape retrieval and matching.

As a basic and significant operator in map generalization, polyline simplification needs to work across scales. Perkal’s ε-circle rolling approach, in which a circle with diameter ε is rolled on both sides of the polyline so that the small bend features can be detected and removed, is considered as one of the few scale-driven solutions. However, the envelope computation, which is a key part of this method, has been difficult to implement. Here, we present a computational method that implements Perkal’s proposal. To simulate the effects of a rolling circle, Delaunay triangulation is used to detect bend features and further to construct the envelope structure around a polyline. Then, different connection methods within the enveloping area are provided to output the abstracted result, and a strategy to determine the best connection method is explored. Experiments with real land-use polygon data are implemented, and comparison with other algorithms is discussed. In addition to the scale-specificity inherited from Perkal’s proposal, the results show that the proposed algorithm can preserve the main shape of the polyline and meet the area-maintaining constraint during large-scale change. This algorithm is also free from self-intersection.

Identifying the spatial configurations of buildings and grouping them reasonably is an important task in cartography. This study developed a grouping approach using graph deep learning by integrating multiple cognitive features and manual cartographic experiences. Taking building center points as nodes, adjacent buildings were organized as a graph in which cognitive variables including size, orientation, and shape were defined for each node. Then, a learning model combining the graph convolution and neural network was designed to analyse the adjacent buildings modelled by the graph. The center points of groups were used as labels to train the positions of graph nodes and finally, a k-means algorithm was employed to obtain the grouping results based on the predicted node positions. Experiments confirmed that our approach can extract the inherent features describing the grouping relationship between buildings and performed better than two existing approaches referring to the ARI index (from 0.647 to 0.749).

Detecting interchanges in road networks benefit many applications, such as vehicle navigation and map generalization. Traditional approaches use manually defined rules based on geometric, topological, or both properties, and thus can present challenges for structurally complex interchange. To overcome this drawback, we propose a graph-based deep learning approach for interchange detection. First, we model the road network as a graph in which the nodes represent road segments, and the edges represent their connections. The proposed approach computes the shape measures and contextual properties of individual road segments for features characterizing the associated nodes in the graph. Next, a semi-supervised approach uses these features and limited labeled interchanges to train a graph convolutional network that classifies these road segments into an interchange and non-interchange segments. Finally, an adaptive clustering approach groups the detected interchange segments into interchanges. Our experiment with the road networks of Beijing and Wuhan achieved a classification accuracy >95% at a label rate of 10%. Moreover, the interchange detection precision and recall were 79.6 and 75.7% on the Beijing dataset and 80.6 and 74.8% on the Wuhan dataset, respectively, which were 18.3–36.1 and 17.4–19.4% higher than those of the existing approaches based on characteristic node clustering.

Research has developed numerous algorithms to simplify building data. Each algorithm has strengths and weaknesses in addressing shape characteristics, but no single algorithm can appropriately simplify all buildings. This study proposes a hybrid approach that identifies the best simplified representation of a building among four existing algorithms. The proposed approach applies the four algorithms to generate simplification candidates. With a backpropagation neural network, an evaluator is built through supervised learning based on measurements describing the changes in position, size, orientation, and shape between the original building and the candidates of its simplified representations. The evaluator determines the most appropriate candidate. Experiments on buildings from residential and commercial areas in Shenzhen city show that the hybrid approach can combine the advantages of different algorithms. The percentages of unreasonable simplified buildings in the results obtained using the hybrid algorithm are 3.8% in the residential area and 0 in the commercial area, respectively, which are significantly lower than those in the results of standalone applications of the four algorithms. Furthermore, comparison with the simplification algorithm in the popular software, ArcGIS, confirms that our approach shows better results in terms of corner squaring and maintaining the regional characteristics of buildings.