Region representation learning emerges as a new research paradigm to encode urban systems and facilitate geographic mapping. Recent studies have sought to reasonably introduce inductive biases, which refer to prior assumptions that guide model learning, from a geospatial perspective to improve the quality of region representations. However, there remain challenges in incorporating the spatial effects, e.g. spatial dependency and spatial heterogeneity, into inductive biases, as they are critical to the geographic awareness of region representations. In response, we developed a novel region representation learning framework, termed Region Graph Spatial Contrastive Learning (RGSCL), by leveraging building footprints and points of interest (POIs) along with prior spatial knowledge to derive region representations. Specifically, RGSCL first constructed multi-view region graphs with POIs, building footprints and their spatial proximity, to form a base representation space. Next, the algorithm adopted a contrastive learning mechanism with spatial effects to formulate a dual-spatial-contrast loss function to optimise the representation space. The dual-spatial-contrasts captured POI-building spatial dependency and the region’s spatial heterogeneity to compose semantics in region representations. Experimental results demonstrated that RGSCL improved performance in geographic mapping. This study offers new insights into GeoAI from the perspective of inductive biases with respect to spatial effects.

Understanding individual building functions is crucial for analyzing broader urban dynamics. Existing studies have incorporated multi-source data to predict building functions but often neglect the spatial and semantic relations between buildings and their surrounding geographic entities. This study proposes a knowledge graph-based approach for geographic context-aware building function prediction to address this gap. Based on multi-source data, we first constructed a building knowledge graph (BuildingKG), where nodes represent buildings and other related entities, and edges denote their spatial and semantic relations. Subsequently, we applied a knowledge graph embedding technique to the BuildingKG to capture the structural knowledge of entities, which encodes the interactions between them. The structural knowledge, combined with the attributes of individual entities, was concatenated to form the descriptive features of the entity nodes. Finally, we designed a meta-path-based graph transformer neural network model to process the graph, comprising nodes and edges from the BuildingKG, to classify building function types using a supervised learning method. Experiments demonstrated that our approach achieved an overall accuracy of 93.05%, outperforming baseline models with superior computational efficiency. Moreover, interpretability analysis revealed different entity features’ global and local contributions to the prediction results, underscoring the importance of considering geographic context.

Landform type recognition presents significant implications for understanding landform origins, evolutionary mechanisms, and morphological differences. Artificial intelligence (AI) techniques based on sample learning often lead to unsatisfactory outcomes due to the intricate genesis and regional heterogeneity of landforms. This study combines domain knowledge with a deep learning (DL) model to improve landform type recognition. Contour data serves as a valuable resource, offering rich morphological information across horizontal, vertical, local, and macro scales. Our approach incorporated morphological knowledge and proximity relationships derived from contours into a graph convolutional network using the DiffPool technique (GCN-DP). Guided by the First Law of Geography, contours within each landform unit were represented as graphs, incorporating morphological knowledge as node features. The GCN-DP model then employed convolution and pooling to extract hierarchical features from these graphs for landform type recognition. A performance evaluation demonstrated the effectiveness of our method with an F1-score of 87.40%, surpassing RF and GCN methods by 5.24–12.50%, respectively. Ablation experiments confirmed the usefulness of morphological knowledge. This study offers an efficient strategy for landform type recognition, improving the level of intelligent mining using contour data.

A hillshade is a visualization technique that represents three-dimensional terrain in a two-dimensional plane by illumination mapping. The digital relief shading promotes the visualization of the terrain efficiently using DEM data. However, compared with manual shading, the digital algorithm-based method still has a gap in the visual effect of illumination strategy and terrain generalization. The typical landform characteristics and micro-geomorphic properties usually are destroyed. The reason is that the complexity of illumination rules is hard to summarize for different terrain phenomena. In this study, namely the data-driven artificial intelligent method, an alternative strategy based on generative adversarial networks (GANs) is proposed rather than the rule-based method. The DEM and the terrain skeleton lines are input to the model and part of the manual relief shading of Swisstopo is used for the training samples. Through the GAN training and learning, the manual skill imbedded in the hillshade is discovered in the generation model. The results show that the proposed model performs better than the digital relief shading on various landforms in aesthetic visualization and geo-scientific representation. Compared to other models, including other convolution neural network (CNN) based methods, terrain structure is maintained more significantly through the proposed model.

Computer screens often constrain the level of detail and clarity of displays. High-density data require a predefined strategy to select significant features hierarchically to allow interactive data zooming. Although many methods are available for hierarchically selecting rivers from vector data, some approaches for raster data are better than others for maintaining accuracy when the original river data are in a raster format during generalization. In this study, a raster-based approach is proposed to allow hierarchical superpixel selection in river networks. Linear spectral clustering segmentation was applied to divide the original raster river networks into superpixels at multiple levels. A graph was constructed to organize the generated river network superpixels based on the distances between adjacent superpixels by considering the weights determined by the four types of rules. Finally, the total weight values were ranked, the river-network superpixels were selected according to their weights, and the redundant pixels at the river-network intersections were removed. Compared with the traditional vector selection method, the proposed superpixel river network selection method can effectively consider the characteristics of river width without artificial river grading and preserve the main structure and connectivity features during hierarchical mapping. Notably, the average geometry and density changes decreased by 15.8% and 5.1%, respectively.

Numerous methods based on square rasters have been proposed for polygon generalization. However, these methods ignore the inconsistent distance measurement among neighborhoods of squares, which may result in an imbalanced generalization in different directions. As an alternative raster, a hexagon has consistent connectivity and isotropic neighborhoods. This study proposed a hexagon-based method for polygon generalization using morphological operators. First, we defined three generalization operators: aggregation, elimination, and line simplification, based on hexagonal morphological operations. We then used corrective operations with selection, skeleton, and exaggeration to detect, classify, and correct the unreasonably reduced narrow parts of the polygons. To assess the effectiveness of the proposed method, we conducted experiments comparing the hexagonal raster to square raster and vector data. Unlike vector-based methods in which various algorithms simplified either areal objects or exterior boundaries, the hexagon-based method performed both simplifications simultaneously. Compared to the square-based method, the results of the hexagon-based method were more balanced in all neighborhood directions, matched better with the original polygons, and had smoother simplified boundaries. Moreover, it performed with shorter running time than the square-based method, where the minimal time difference was less than 1 min, and the maximal time difference reached more than 50 mins.

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.

Previous research has tended to use a global threshold of proximity to determine neighbors, neglecting spatial heterogeneity. Flexible thresholds implemented by adaptive search radii methods account for either the spatial structures or the non-spatial similarities of objects, but few consider both. By combining the spatial and non-spatial information of objects, we propose a novel approach that can automatically determine the neighbors that are strongly related to the object of interest. We introduce the sparse reconstruction technique from the signal processing domain, which aims to remove trivial relationships in a dataset. We extend the sparse reconstruction model by assuring three principles in spatial data, including retention of the correlation of data in the non-spatial attribute domain, preservation of local dependencies in the spatial domain, and removal of trivial relationships. Extensive experiments, based on road network missing value imputation and building clustering, show that our approach can make better use of both spatial and non-spatial information than a simple addition of them.

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 key focus of cartography and terrain analysis, the simplification of a digital elevation model (DEM) is used to preserve the pattern features of the terrain surface while suppressing its details over multiple scales. Statistical filtering and structural analysis methods are commonly used for this process. The structural analysis method performs well in identifying terrain structural edges, while it tends to discard the smooth morphology of a terrain surface. In addition, the filter that aims to reduce noise on a surface may over-smooth the terrain structural edges. Therefore, to preserve both the terrain structural edges and smooth morphology, we propose to combine the techniques of statistical filtering and structural analysis. Specifically, all the critical elevation points and structural edges are first detected from the DEM surface by using the structural analysis method. Then, the iterative guided normal filter is used to smooth the generalized DEM with the guidance of the structure of the original surface. After this process, the terrain structure is retained in the smooth surface of the DEM. The experimental results with a real-world dataset show that our method can inherit the merits of both structural analysis and statistical filter in preserving terrain features for multi-scale DEM representations.

This paper proposes a model to quantify the multiscale representation of a polyline based on iterative head/tail breaks. A polyline is first transformed into a corresponding Fourier descriptor consisting of normalized Fourier-series-expansion coefficients. Then, the most significant finite components of the Fourier descriptor are selected and ranked to constitute the polyline constrained Fourier descriptor. Using Shannon’s information theory, information content of the constrained Fourier-descriptor components is defined. Next, head/tail breaks are introduced to iteratively divide the constrained Fourier descriptor into head and tail components according to the heavy-tailed distribution of information contents. Thus, simplified polylines are reconstructed using ordered heads generated from head/tail breaks. Finally, the radical law is introduced and applied to model multiscale polyline representation by quantifying the scale of each simplified polyline. Three experiments are designed and conducted to evaluate the proposed model. The results demonstrate that the proposed model is valid and efficient for quantifying multiscale polyline representation.

As one of the major concerns in cartographic generalization, road network generalization aims at maintaining the patterns of road networks across map scales. Previous methods define the pattern of road networks mainly from the perspectives of geometry and topology. However, for navigation purposes, traffic flow information is also important to generalize road networks. More specifically, road segments that have a proximity relationship in the traffic flow system should be retained together on small-scale maps to preserve the completeness of the driving route. In this regard, this study proposes an improved method for road network generalization that considers network geometry, topology, and traffic flow patterns. First, strokes are constructed from the road network data based on the ‘every best fit’ geometric principle. Then, the relationships among strokes are developed on the basis of traffic flow patterns, which are extracted from taxi trajectory data. The strokes are then selected in sequence based on the indicators of geometry, topology, and traffic flow. Our experimental results demonstrate that the proposed method can preserve both the ‘Good Continuity’ principle and the transport function relationship of roads after generalization.

Colocation mining is one of the major spatial data mining tasks. When discovering colocation patterns, spatial statistics or data mining approaches are commonly used. Colocation mining results are typically presented in a textual form and do not provide any spatial information; thus, the results lack an intuitive approach to obtain cognition of colocation rules. Here, we propose a visualization approach to discover colocation patterns for two independent point distributions and generate visual results. This approach makes use of the ability of human color perception. For two geographic features, our approach first generates density surfaces of the input features and then visualizes the density surfaces using a red or green light with different intensities. Then, based on the law of additive color mixing, our approach mixes the colors of the two density surfaces to generate a colocation rule map. The visualization approach can also provide local details of colocation and be used for local colocation analysis. Users can detect colocation patterns and their distribution from the colocation rule maps. We use both synthetic data and real data to test the performance of our approach.

One important classical research area in automated cartographic generalization is simplification. Over the past few decades, numerous scholars have proposed various methods for polygon and line simplification, most of which have focused on vector data. However, with the rapid development of computer vision technology, unstructured image analysis and processing has provided a plethora of information, as well as new challenges. Therefore, in this article, we propose a new method for simplifying polygonal and linear features: a superpixel segmentation (SUSS) method specially designed for image data. In this method, polygonal boundaries are first divided by a superpixel algorithm called simple linear iterative clustering. Then, three types of curves – convex, concave, and flat – are globally simplified by comparing and selecting superpixels. Finally, uneven local features are removed by Fourier descriptors. In addition, the proposed SUSS method is extended for linear features, and it maintains topological relationships. To demonstrate the effectiveness of this approach, we use contours and water area data to perform experiments. Compared with the classic Douglas–Peucker and Wang and Muller algorithms, the proposed method is able to properly simplify the curves of polygonal and linear features while maintaining their essential shapes, and it maintains a steady change in area for large-scale applications while effectively avoiding self-intersection issues. Compared with the typical smoothing and Raposo algorithms, the proposed SUSS method can simplify lines at different scales and guarantee effective smoothing while maintaining displacement.

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.

Street patterns reflect the distribution characteristics of a street network and affect the urban structure and human behavior. The recognition of street patterns has been a topic of interest for decades. In this study, a linear tessellation model is proposed to identify the spatial patterns in street networks. The street segments are broken into consecutive linear units with equal length. We define five focal operations using neighborhood analysis to extract the geometric and topological characteristics of each linear unit for the purpose of grid-pattern recognition. These are then classified by Support Vector Machine, and the result is optimized based on Gestalt principles. The experimental results demonstrate that our method is effective for mining grid patterns in a street network.

The aim of mining spatial co-location patterns is to find the corresponding subsets of spatial features that have strong spatial correlation in the real world. This is an important technology for the extraction and comprehension of implicit knowledge in large spatial databases. However, existing methods of co-location mining consider events as taking place in a homogeneous and isotropic context in Euclidean space, whereas the physical movement in an urban space is usually constrained by a road network. Furthermore, previous works do not take the ‘distance decay effect’ of spatial interactions into account, which may reduce the effectiveness of the result. Here we propose an improved spatial co-location pattern mining method, including the network-constrained neighborhood and addition of a distance-decay function, to find the spatial dependence between network phenomena (e.g. urban facilities). The underlying idea is to utilize a model function in the interest measure calculation to weight the contribution of a co-location to the overall interest measure instance inversely proportional to the separation distance. Our approach was evaluated through extensive experiments using facility points-of-interest data sets. The results show that the network-constrained approach is a more effective method than the traditional one in network-structured space. The proposed approach can also be applied to other human activities (e.g. traffic accidents) constrained by a street network.

The representation and analysis of building patterns are critical for characterizing urban scenes and making decisions in urban planning. The evaluation of building patterns is a difficult spatial analysis problem that exhibits properties of symbolization, homogeneity and regularity. Open issues in this field include the development of approaches for representing building patterns and vector-based methods for computing various pattern metrics. In the image analysis domain, there are many methods for pattern recognition (e.g., texture analysis), but there are few corresponding solutions for vector data. The aim of this research is to develop several building pattern metrics and offer a texton co-occurrence matrix (TCM)-based method to quantitatively evaluate the features of building patterns. The procedure first constructs a spatial field based on a Delaunay triangulation skeleton to partition a set of buildings into a set of tessellation cells. The tessellations of building clusters have a similar structure as image representations, in that each cell corresponds to an image pixel. We then use the texton analysis to establish a matrix to describe the tessellation structure, including the neighboring relationships and individual attribute information. Finally, a set of feature descriptors is obtained from the TCM to capture the texture-related information of building groups. Through experiments on building pattern analysis and spatial queries, we show that the results of TCM-based evaluation of building patterns are consistent with those of human cognition.

In map generalization, the displacement operation attempts to resolve proximity conflicts to guarantee map legibility. Owing to the limited representation space, conflicts may occur between both the same and different features under different contexts. A successful displacement should settle multiple conflicts, suppress the generation of secondary conflicts after moving some objects, and preserve the distribution patterns. The effect of displacement can be understood as a force that pushes related objects away with properties of propagation and distance decay. This study borrows the idea of vector fields from physics discipline and establishes a vector field model to handle the displacement of multiple conflicts in building generalization. A scalar field is first constructed based on a Delaunay triangulation skeleton to partition the buildings being examined (e.g., a street block). Then, we build a vector field to conduct displacement measurements through the detection of conflicts from multiple sources. The direction and magnitude of the displacement force are computed based on an iso-line model of vector field. The experiment shows that this global method can settle multiple conflicts and preserve the spatial relations and important building patterns.

Building patterns are important features that should be preserved in the map generalization process. However, the patterns are not explicitly accessible to automated systems. This paper proposes a framework and several algorithms that automatically recognize building patterns from topographic data, with a focus on collinear and curvilinear alignments. For both patterns two algorithms are developed, which are able to recognize alignment-of-center and alignment-of-side patterns. The presented approach integrates aspects of computational geometry, graph-theoretic concepts and theories of visual perception. Although the individual algorithms for collinear and curvilinear patterns show great potential for each type of the patterns, the recognized patterns are neither complete nor of enough good quality. We therefore advocate the use of a multi-algorithm paradigm, where a mechanism is proposed to combine results from different algorithms to improve the recognition quality. The potential of our method is demonstrated by an application of the framework to several real topographic datasets. The quality of the recognition results are validated in an expert survey.

Evaluation is a key step to examine the quality of generalized maps with respect to map requirements. Map generalization facilitates the recognition of pattern generating processes by preserving and highlighting the patterns at smaller scales. This article focuses specifically on the evaluation of building patterns in topographic maps that are generalized from large to mid scales. Currently, there is a lack of knowledge and functionality on automatically evaluating how these patterns are generalized. The issues of the evaluation range from missing formal map requirements on building alignments to missing automated evaluation techniques. This article firstly analyses the requirements (constraints) related to the generalization of building alignments. Then, it focuses on three more specific constraints, i.e. on existence, orientation of alignments and spatial distribution of composing buildings. Later, a three-step approach is proposed to (1) recognize and (2) match alignments from source and generalized datasets and (3) evaluate building alignments in generalized datasets. Besides, many-to-many and partial matching between initial and target alignments is a side effect of generalization, which reduces the reliability of the evaluation results. This article introduces a confidence indicator to document the reliability and to inform intended users (e.g. cartographers) and/or systems about the reliability of evaluation decisions. The effectiveness of our approach is demonstrated by evaluating the alignments in both interactively (manually) generalized maps and automated generalized maps. Finally, we discuss how our approach can be used to control automated generalization and identify further improvements.

Building generalization is a difficult operation due to the complexity of the spatial distribution of buildings and for reasons of spatial recognition. In this study, building generalization is decomposed into two steps, i.e. building grouping and generalization execution. The neighbourhood model in urban morphology provides global constraints for guiding the global partitioning of building sets on the whole map by means of roads and rivers, by which enclaves, blocks, superblocks or neighbourhoods are formed; whereas the local constraints from Gestalt principles provide criteria for the further grouping of enclaves, blocks, superblocks and/or neighbourhoods. In the grouping process, graph theory, Delaunay triangulation and the Voronoi diagram are employed as supporting techniques. After grouping, some useful information, such as the sum of the building's area, the mean separation and the standard deviation of the separation of buildings, is attached to each group. By means of the attached information, an appropriate operation is selected to generalize the corresponding groups. Indeed, the methodology described brings together a number of well-developed theories/techniques, including graph theory, Delaunay triangulation, the Voronoi diagram, urban morphology and Gestalt theory, in such a way that multiscale products can be derived.