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Road network selection plays a key role in map generalization for creating multi-scale road network maps. Existing methods usually determine road importance based on road geometric and topological features, few evaluate road importance from the perspective of road utilization based on human travel data, ignoring the functional values of roads, which leads to a mismatch between the generated results and people's needs. This paper develops two functional semantic features (i.e. travel path selection probability and regional attractiveness) to measure the functional importance of roads and proposes an automatic road network selection method based on graph convolutional networks (GCN), which models road network selection as a binary classification. Firstly, we create a dual graph representing the source road network and extract road features including six graphical and two functional semantic features. Then, we develop an extended GCN model with connectivity loss for generating multi-scale road networks and propose a refinement strategy based on the road continuity principle to ensure road topology. Experiments demonstrate the proposed model with functional features improves the quality of selection results, particularly for large and medium scale maps. The proposed method outperforms state-of-the-art methods and provides a meaningful attempt for artificial intelligence models empowering cartography. [ABSTRACT FROM AUTHOR]

Cartographic map generalization involves complex rules, and a full automation has still not been achieved, despite many efforts over the past few decades. Pioneering studies show that some map generalization tasks can be partially automated by deep neural networks (DNNs). However, DNNs are still used as black-box models in previous studies. We argue that integrating explainable AI (XAI) into a DL-based map generalization process can give more insights to develop and refine the DNNs by understanding what cartographic knowledge exactly is learned. Following an XAI framework for an empirical case study, visual analytics and quantitative experiments were applied to explain the importance of input features regarding the prediction of a pre-trained ResU-Net model. This experimental case study finds that the XAI-based visualization results can easily be interpreted by human experts. With the proposed XAI workflow, we further find that the DNN pays more attention to the building boundaries than the interior parts of the buildings. We thus suggest that boundary intersection over union is a better evaluation metric than commonly used intersection over union in qualifying raster-based map generalization results. Overall, this study shows the necessity and feasibility of integrating XAI as part of future DL-based map generalization development frameworks. [ABSTRACT FROM AUTHOR]

The popularity of tag clouds has sparked significant interest in the geographic research community, leading to the development of map-based adaptations known as intrinsic tag maps. However, existing methodologies for tag maps primarily focus on tag layout at specific scales, which may result in large empty areas or close proximity between tags when navigating across multiple scales. This issue arises because initial tag layouts may not ensure an even distribution of tags with varying sizes across the region. To address this problem, we incorporate the negative spatial auto-correlation index into tag maps to assess the uniformity of tag size distribution. Subsequently, we integrate this index into a TIN-based intrinsic tag map layout approach to enhance its ability to support multi-scale visualization. This enhancement involves iteratively filtering out candidate tags and selecting optimal tags that meet the defined index criteria. Experimental findings from two representative areas (the USA and Italy) demonstrate the efficacy of our approach in enhancing multi-scale visualization capabilities, albeit with trade-offs in compactness and time efficiency. Specifically, when retaining the same number of tags in the layout, our approach achieves higher compactness but requires more time. Conversely, when reducing the number of tags in the layout, our approach exhibits reduced time requirements but lower compactness. Furthermore, we discuss the effectiveness of various applied strategies aligned with existing approaches to generate diverse intrinsic tag maps tailored to user preferences. Additional details and resources can be found on our project website: https://github.com/TrentonWei/Multi-scale-TagMap. [ABSTRACT FROM AUTHOR]

The partitioning of building groups is a prerequisite for map generalization. Existing methods center on the spatial relationships between individual buildings, neglecting the interrelations among building groups. As such, these methods prove suitable only for identifying building groups at a single scale. In this research, we introduce a novel methodology for partitioning building groups across multiple scales by employing image segmentation, thus enabling the simultaneous recognition of building groups of all scales within a recognition unit. First, image segmentation and merging approaches were employed to extract merged image regions, representing the spatial relationships of building groups. Then, the process commenced with the construction of a graphical representation encompassing buildings and merged regions, wherein the edges were assigned weights indicative of the closeness between groups of buildings. Finally, the graph underwent a progressive segmentation process, and a scale set of building groups was established. Based on the experimental findings, the proposed approach can proficiently partition building groups across various scales. This is demonstrated by the accuracy rate surpassing 90% in the complex experimental area. One can effortlessly derive building groups from the scale set by using a predetermined scale parameter. These findings may serve as a fundamental basis for the implementation of multiscale map generalization and the linkage updating of multiscale spatial data. [ABSTRACT FROM AUTHOR]

Continuous-scale representation of urban blocks is critical for enriching the web-based mapping experience in the modern era. Traditionally, continuous-scale merging methods for surface elements have been employed to deal with landscape features, such as patches and land-cover data. In comparison, the artificially constructed urban blocks offer complex semantics and unique shapes. Traditional methods face challenges in maintaining their fundamental characteristics, which can result in improper merging outcomes. Therefore, this paper proposes a progressive merging method that takes into account the functional semantics and grid features of blocks. Initially, the POI data is used to obtain the functional semantic vectors of the blocks for creating basic information about the starting map. The blocks are then abstracted into a graphical structure whereby a breadth-first algorithm is employed to generate their groups; thereby, forming the target map. The map-based geometric and semantic merging cost formula has been devised to calculate the optimal merging sequence by the A* algorithm. Experiments have been performed by defining the main urban area of Beijing city as the study area. The comparative analysis indicates that the proposed method can obtain more reasonable progressive merging results. [ABSTRACT FROM AUTHOR]

Extracting spatial network structure (SNS) from large-scale origin-destination flow data is an important approach for understanding interregional association patterns and interaction laws. Currently, the extraction of SNS primarily relies on complex network clustering or aggregated statistics with predefined regional constraints. However, these methods often overlook one or more fundamental principles essential for ensuring correctness and accuracy: 1) Aggregation of spatially proximate nodes is necessary when strong interactions exist, whereas separation is preferred in the absence of such interactions. 2) It is crucial to maintain strong interactions between non-spatially proximate nodes. 3) Ultimately, nodes within each group should exhibit spatial continuity. To address these challenges, a multi-hierarchical SNS extraction method is proposed, which focuses on raw node aggregating and generalization, measurement of interaction volume and strength between node groups and strategies for node/edge filtering. The effectiveness and value of the proposed method are demonstrated through a case study using city population migration data. Furthermore, the method provides a general approach for extracting SNSs from any origin-destination flow dataset that includes locations and weights, facilitating effective flow map generalization through aggregation of origin destination (OD) flow data. [ABSTRACT FROM AUTHOR]

Machine learning is increasingly used as a computing paradigm in cartographic research. In this extended editorial, we provide some background of the papers in the CaGIS special issue Machine Learning in Cartography with a special focus on pattern recognition in maps, cartographic generalization, style transfer, and map labeling. In addition, the paper includes a discussion about map encodings for machine learning applications and the possible need for explicit cartographic knowledge and procedural modeling in cartographic machine learning models. [ABSTRACT FROM AUTHOR]

Map generalization is a complex task that requires a high level of spatial cognition, and deep learning techniques have shown in numerous research fields that they could match or even outplay human cognition when knowledge is implicitly in the data. First experiments that apply deep learning techniques to map generalization tasks thereby adapt models from image processing, creating input data by rasterizing spatial vector data. Because image-based learning has major shortcomings for map generalization, this article investigates possibilities to learn directly from vector data, utilizing vector-based encoding schemes. First, we enhance preprocessing methods to match essential properties of deep learning models – namely regularity and feature description – and evaluate the performance of Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and Graph Convolutional Neural Networks (GCNN) in combination with a feature-based encoding scheme. The results show that feature descriptors improve the accuracy of all three neural networks, and that the overall performances of the models are quite similar for both polygon and polyline shape classification tasks. In a second step, we implement an exemplary building generalization workflow based on shape classification and template matching, and discuss the generalization results based on a case study. [ABSTRACT FROM AUTHOR]

The automation of map generalization has been an important research subject for decades but is not fully solved yet. Deep learning techniques are designed for various image generation tasks, so one may think that it would be possible to apply these techniques to cartography and train a holistic model for end-to-end map generalization. On the contrary, we assume that map generalization is a task too complex to be learnt with a unique model. Thus, in this article, we propose to resort to past research on map generalization and to separate map generalization into simpler sub-tasks, each of which can be more easily resolved by a deep neural network. Our main contribution is a workflow of deep models, called DeepMapScaler, which achieves a step-by-step topographic map generalization from detailed topographic data. First, we implement this workflow to generalize topographic maps containing roads, buildings, and rivers at a medium scale (1:50k) from a detailed dataset. The results of each step are quantitatively and visually evaluated. Then the generalized images are compared with the generalization performed using a holistic model for an end-to-end map generalization and a traditional semi-automatic map generalization process. The experiment shows that the workflow approach is more promising than the holistic model, as each sub-task is specialized and fine-tuned accordingly. However, the results still do not reach the quality level of the semi-automatic traditional map generalization process, as some sub-tasks are more complex to handle with neural networks. [ABSTRACT FROM AUTHOR]

Deep learning-backed models have shown their potential of conducting map generalization tasks. However, pioneering studies for raster-based building generalization encountered a common "wabbly-wall effect" that makes the predicted building shapes unrealistic. This effect was identified as a critical challenge in the existing studies. This work proposes a layered data representation model that separately stores a building for generalization and its context buildings in different channels. Incorporating adjustments to training sample generation and prediction tasks, we show how even without using more complex deep learning architectures, the widely used Residual U-Net can already produce straight walls for the generalized buildings and maintains rectangularity and parallelism of the buildings very well for building simplification and aggregation in the scale transition from 1:5,000 to 1:10,000 and 1:5,000 to 1:15,000, respectively. Experiments with visual evaluation and quantitative indicators such as Intersection over Union (IoU), fractality, and roughness index show that using a larger input tensor size is an easy but effective solution to improve prediction. Balancing samples with data augmentation and introducing an attention mechanism to increase network learning capacity can help in certain experiment settings but have obvious tradeoffs. In addition, we find that the defects observed in previous studies may be due to a lack of enough training samples. We thus conclude that the wabbly-wall challenge can be solved, paving the way for further studies of applying raster-based deep learning models on map generalization. Demonstrates the effectiveness of the proposed data structure with multiple evaluation indicators Identifies a "wabbly-wall effect" a challenge in deep-learning backed image based map generalization Proposes a layered data structure that separates a target building and its surrounding buildings to ease the learning task in training deep learning models for raster-based map generalization. [ABSTRACT FROM AUTHOR]

Polyline and building simplification remain challenging in cartography. Most proposed algorithms are geometric-based and rely on specific rules. In this study, we propose a deep learning approach to simplify polylines and buildings based on a graph autoencoder (GAE). The model receives the coordinates of line vertices as inputs and obtains a simplified representation by reconstructing the original inputs with fewer vertices through pooling, in which the graph convolution based on graph Fourier transform is used for the layer-by-layer feature computation. By adjusting the loss functions, constraints such as area and shape preservation and angle-characteristic enhancement are flexibly configured under a unified learning framework. Our results confirmed the applicability of the GAE approach to the multi-scale simplification of land-cover boundaries and contours by adjusting the number of output nodes. Compared with existing Douglas‒Peukcer, Fourier transform, and Delaunay triangulation approaches, the GAE approach was superior in achieving morphological abstraction while producing reasonably low position, area, and shape changes. Furthermore, we applied it to simplify buildings and demonstrated the potential for preserving the diversified characteristics of different types of lines. [ABSTRACT FROM AUTHOR]

For point clusters, the conflict and crowding of map symbols is an inevitable problem during the transition from large to small scales. The cartographic generalization involved in this problem as a spatial decision-making process is usually related to the analysis of spatial context, the choice of abstraction operators, and the judgment of the resulting data quality. The rules summarized by traditional generalization methods usually require manual setting of conditions or thresholds and sometimes encounter special cases that make it difficult to directly match certain rules or integrate different rules together. An alternative method is using a data-driven strategy under AI technology background to simulate cartographer behaviors through typical sample training, such as deep learning. The integration of cartography domain knowledge and deep learning is a better choice to settle generalization decisions. This study uses a combination of domain knowledge and a data-driven approach to introduce graph neural networks into point cluster generalization. First, we construct a virtual graph structure of point clusters using Delaunay triangulation, secondly, we extract spatial features, contextual features, and attributes of each point separately, and then propose a generalization model based on the TAGCN network. Finally, this model is trained with the manually generalized sample to realize the automatic point cluster generalization. The results demonstrate that the proposed model is valid and efficient for point cluster generalization and that this algorithm can better maintain various characteristics of the point cluster in both the local area and the overall map compared to other methods. [ABSTRACT FROM AUTHOR]

Spatial similarity plays a critical role in the perception and cognition in capturing information from maps; it can be used as a constraint to automate map generalization. Although measuring similarities seems natural to humans, it can be challenging to quantify them. This is especially true when it comes to calculating spatial similarity degrees between groups of spatial objects at varying scales and quantitatively expressing the relations between spatial similarity and change of map scale in multiscale map spaces. Taking road networks as an example, this paper proposes an approach to measuring spatial similarity between a road network at a large scale and its generalized counterpart at a smaller scale. By fitting a power function to three typical types of road networks, this paper provides a formula for expressing the change in spatial similarity as the map scale changes. The proposed quantitative method lays a foundation for using spatial similarity as a constraint during road network generalization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper compiles guidelines for minimum dimensions of cartographic symbology from the literature on map design for printed and digital maps. Such minimum dimensions are relevant not only for the design of cartographic symbology, but also as fundamental parameters affecting the visual hierarchy of the overall map and the cartographic generalization of its elements. However, this review shows that only few studies have actually verified minimum dimensions in controlled empirical experiments, and most authors seem to have based their recommendations on anecdotal evidence or theoretical considerations only. Conclusions for a future research agenda in cartography, ranging from ethical questions to calls for empirical research on minimum dimensions, are drawn from the presented findings. [ABSTRACT FROM AUTHOR]

A polygonal building aggregation method is proposed in this study to address the shortcomings of existing aggregation methods that mostly focus on maintaining a few features, ignoring the requirement for a clear expression. First, visually conglutinated buildings were clustered considering obstacle elements. Unreasonable triangles, starting from the marginal triangles, were removed to extract the visual conglutinate areas. Bridging modes were designed and local shape features were considered to bridge the visual conglutinate areas. Then, the contours of the aggregated results were established through a minimum loop search on the path connection graph. An experiment was conducted using the data of OpenStreetMap from Nanjing, and the comparative experimental results showed that the proposed method preserved the aggregated results of right-angled and locally shaped features. The advantages of improving the visual clarity of the results were verified by introducing degrees of visual conglutination and complexity. [ABSTRACT FROM AUTHOR]

Shape morphing has been used to generate arbitrary scale maps in the field of continuous generalization in recent years. The morphing approach consists of two main steps: shape characteristic matching and trajectory interpolation. Most of the shape characteristic matching methods are difficult to consider the local and global characteristics of spatial data at the same time, which will result in distortion of interpolation results. This paper proposes a Dynamic Time Warping (DTW) distance-based morphing method for continuous generalization of linear features. In this method, the DTW distance is employed as shape similarity distance to find the optimal correspondence by minimizing the total cost between each pair of vertices, which considers both the local and global structure of two linear features. Firstly, we build a matrix to record the distance between vertices in two linear features at two different scales. Then we use the DTW algorithm to find the optimal warping path to establish the corresponding relationship between the vertices of two linear features. Finally, the linear interpolation method is used to dynamically generate the geometric shape at any intermediate scale. Experiment results demonstrate that the proposed method can generate continuous and smooth geometric shapes with a gradual transformation effect, and can be used for the continuous generalization of linear features. The generalization results are consistent with map representation rules and human cognition. [ABSTRACT FROM AUTHOR]

In the multi-scale representation of maps, a selection operation is usually applied to reduce the number of map elements and improve legibility while maintaining the original distribution characteristics. During the past few decades, many methods for vector building selection have been developed; however, pixel-based methods are relatively lacking. In this paper, a multiple-strategy method for raster building selection is proposed. In this method, to preserve the distribution range, a new homogeneous linear spectral clustering (HLSC) superpixel segmentation method is developed for the relatively homogeneous spatial division of building groups. Then, to preserve the relative distribution density, multi-level spatial division is performed according to the local number of buildings. Finally, to preserve the local geometric, attributive and geographical characteristics, four selection strategies, namely, the minimum centroid distance, minimum boundary distance, maximum area and considering geographical element strategies, are designed to generate selection results. To evaluate the proposed method, dispersed buildings in a suburban area are utilized to perform selection tasks. The experimental results indicate that the proposed method can effectively select dispersed irregular buildings at different levels of detail while maintaining the original distribution range and relative distribution density. In addition, the use of multiple selection strategies considering various geometric, attributive and geographical characteristics provides multiple options for cartography. [ABSTRACT FROM AUTHOR]

Building pattern extraction is one of the crucial components in map generalization. Previous studies mainly focus on the homogeneity between individual buildings in the collinear patterns, while pay less attentions to the complex collinear patterns, in which buildings are locally heterogeneous. Therefore, we put forward a novel combined collinear pattern to extend the existing pattern typology. Then, we present an axis-matching pattern recognition approach which transforms pattern extraction into an axis-matching problem, taking the advantages of computational geometry and visual perception theories. First, we use the axes of the smallest bounding rectangle to represent buildings. Second, different candidate sets of matched axis pairs are built considering the project distance, length and orientation similarities. Third, the strategy for recognizing combined collinear patterns is designed according to similarity criteria. The proposed approach was tested using real topographic data. The experiment results show that the proposed approach is reasonable and efficient, and the correctness and completeness of extracted combined collinear patterns have been guaranteed. [ABSTRACT FROM AUTHOR]

This paper focuses on learning complex polyline generalization. First, the requirements for sampled images to ensure the effective learning of complex polyline generalization are analysed. To meet these requirements, new methods for segmenting complex polylines and sampling images are proposed. Second, using the proposed segmentation and sampling method, a use case for the learning of complex polyline generalization using the generative adversarial network model, Pix2Pix, is developed. Third, this use case is applied experimentally for the complex generalization of coastline data from a scale of 1:50,000 to 1:250,000. Additionally, contrast experiments are conducted to compare the proposed segmentation and sampling method with object-based and traditional fixed-size methods. Experimental results show that the images generated using the proposed method are superior to the other two methods in the learning and application of complex polyline generalization. The results generalized for the developed use case are globally reasonable and suitably accurate. [ABSTRACT FROM AUTHOR]

The recognition of structures is fundamental to map generalization, furnishing structural information that assists in choosing and parameterizing generalization operators. We specifically focus on the process of recognizing groups of small polygons in geological maps as a prerequisite to subsequent aggregation or typification operators. Proximity between polygons represents an essential criterion in identifying neighboring map objects. Here, network-based analysis is used for effective definition and refinement of candidate group members, applying criteria such as the distance between polygons, polygon size, shape, orientation, and feature attributes such as rock type. Starting off from the Delaunay triangulation of the polygon centroids, the global and local long edges, which initially define the network, are removed. The modified network is loaded with additional criteria, and edges are kept or removed based on the local similarities of the polygons they connect. This approach leads to more homogeneous, meaningful groups of polygon features in geological maps. [ABSTRACT FROM AUTHOR]

In map multiscale visualization, typification is the process of replacing original objects, such as buildings, using a smaller number of objects while maintaining initial geometrical and distribution characteristics. During the past few decades, many vector-based methods for building typification have been developed, whereas raster-based methods have received less attention. In this paper, a new method for the typification of buildings with different distribution patterns called superpixel building typification (SUBT) is developed based on raster data. Using this method, buildings with different distribution patterns, such as linear, grid and irregular patterns, are first grouped by image connected component detection and superpixel analysis. Then, the new positions for building typification are determined by superpixel resegmentation. Finally, a new representation of the buildings is determined through analysis of the orientation and shape of the buildings in each superpixel. To test the proposed SUBT method, buildings from both cities and countrysides in China are applied to perform typification. The experimental results show that the proposed SUBT method can realize typification for buildings with linear, grid and irregular distributions while effectively maintaining the original distribution characteristics of the buildings. [ABSTRACT FROM AUTHOR]

Maritime structures are significant man-made objects located along coastlines that have drawn considerable attention in maritime navigation, coastal engineering, and urban planning. During the process of map generalization, some maritime structures need to be collapsed. In our study, first, the representation characteristics of these maritime structures are analysed. Second, based on these characteristics, an automated approach of identifying these maritime structures that will potentially be collapsed while simultaneously extracting their partially proportional symbols is developed. Third, based on scale-driven thresholds, the collapse method is automated by selecting extracted partially proportional symbols and is collaborated with coastline simplification. Finally, the proposed approach is tested on various coastlines and maritime structures, and the experimental results demonstrate that our approach is effective for collapsing maritime structures and collaborating with the simplification operator for the automated generalization of coastlines. [ABSTRACT FROM AUTHOR]

Merging is an important operation in the map generalization of land-cover and other coverages. We define structured geographic objects as collections of adjacent areas with homogeneous semantics that are regularly arranged as spatial structures. Existing studies have concentrated on unstructured objects, which will lead to the structured ones losing part or even most of the typical characteristics during merging. Therefore, as a supplement to the existing mature merging method, a targeted method was proposed in this paper to address the merging problem of structured geographic objects. First, structured geographic objects were classified into four typical patterns, and they were identified automatically according to seven spatial structure parameters. Second, a Miter-type buffer transformation was introduced to extract the overall boundary of structured geographic objects, and areas inside the overall boundary were processed with the most appropriate merging operations for their pattern. Finally, the corresponding merged results of structured geographic objects were inserted back into the merged result of the original land-cover data by using the NOT operation, and the spatial conflicts near the boundary were adjusted. We test our method for a dataset of geographical census data for a city in China. The experimental results revealed that compared with state-of-the-art method, the proposed method produces more reasonable generalization result by effectively identifying and maintaining the typical spatial structures; moreover, the proposed method also preserves the planar tessellation characteristic of land-cover data and the balance of area variation in each land-cover class. [ABSTRACT FROM AUTHOR]

Map generalization is the process of deriving small-scale target maps from a large-scale source map or database while preserving valuable information. In this paper we focus on topographic data, in particular areas of different land-use classes and line features representing the road network. When reducing the map scale, some areas need to be merged to larger composite regions. This process is known as area aggregation. Given a planar partition of areas, one usually aims to build geometrically compact regions of sufficient size while keeping class changes small. Since line features (e.g. roads) are perceived as separating elements in a map, we suggest integrating them into the process of area aggregation. Our aim is that boundaries of regions coincide with line features in such a way that strokes (i.e. chains of line features with small angles of deflection) are not broken into short sections. Complementing the criteria of compact regions and preserving land-use information, we consider this aim as a third criterion. Regarding all three criteria, we formalize an optimization problem and solve it with a heuristic approach using simulated annealing. Our evaluation is based on experiments with different parameter settings. In particular, we compare results of a baseline method that considers two criteria, namely compactness and class changes, with results of our new method that additionally considers our stroke-based criterion. Our results show that this third criterion can be substantially improved while keeping the quality with respect to the original two criteria on a similar level. [ABSTRACT FROM AUTHOR]

Modern technology has given thousands of amateur cartographers not only the opportunity but also the means to make a valuable contribution to mapping at all scales. However, web maps made by amateurs are prone to legibility shortcomings, such as coalescence, complexity, and congestion. These problems can be solved by map generalization; however, for amateurs participating in web mapping, the crucial decision is when to activate generalization. Such a decision is difficult, as the original and target map scales are sometimes uncertain owing to heterogeneous data quality and different output devices. In this study, starting from the identification of different pixels in a rasterized line, we developed a new scale-specific measure to evaluate the degree of legibility (DoL) of individual lines. Our experimental results showed that this measure could reflect the legibility of a line at a given map scale effectively, and could facilitate accurate decisions on whether generalization is necessary. In addition, we fitted a multi-scale legibility function (MSLF) for each line based on DoLs at multiple scales. This function can be used to estimate the legible scale for each line accurately. Our measures are easy to understand, tolerant of data quality, and have great potential for multi-scale spatial data processing. [ABSTRACT FROM AUTHOR]

The generalization of building footprints acts as the basis of multi-scale mapping. Most of the previous studies focus on the generalization of regular building clusters within a wide neighbourhood, but only few has concerned about the generalization of cluttered building clusters within the narrow space such as urban village. The buildings in urban villages show special characteristics in terms of individual properties and group properties, and thus their map generalization processes are often limited. This study proposes a framework to generalize the cluttered building clusters that allows for multi-scale mapping. It first adopts a heuristic method to group adjacent buildings based on the Delaunay triangulation model and then aggregates and simplifies each building group separately. Given that the aggregated buildings in urban villages often show cluttered alignments, our method further trims the jagged boundaries of building footprints by extracting the gap space between neighbouring buildings from the Delaunay triangulation model. [ABSTRACT FROM AUTHOR]

During map generalization, the collapse of geometry, which is also called geometric dimension reduction, is a basic generalization operation. When the map scale decreases, rivers with long, shallow polygonal shapes, usually require their dual-line representation to be collapsed to a single line. This study presents a new algorithm called superpixel river collapse (SURC) to convert dual-line rivers to single-line rivers based on raster data. In this method, dual-line rivers are first segmented at different levels of detail using a superpixel method called simple linear iterative clustering. Then, by connecting the edge midpoints and centre of mass of each superpixel, single-line rivers are preliminarily generated from dual-line rivers. Finally, an interpolation algorithm called polynomial approximation with an exponential kernel is applied to maintain the uniform distribution of the feature points of single-line rivers at different levels of detail (LOD). The presented method can progressively collapse the river during scale transformation to support the LOD representation in a highly sensitive way. The results show that compared with three typical thinning algorithms, the SURC method can generate smooth single-line rivers from dual-line rivers considering different river widths while effectively avoiding burrs and fractured intersections. [ABSTRACT FROM AUTHOR]

Mapping applications display multi-scale maps where zooming in and out triggers the display of different maps at different scales. Multi-scale maps strongly augmented the potential uses of maps, compared to the traditional single-scaled paper maps. But the exploration of the multi-scale maps can be cognitively difficult for users because the content of the maps can be very different at different scales. This paper seeks to identify the factors in the design of map content and style that increase or decrease the exploration cognitive load, in order to improve multi-scales map design. We studied sixteen existing examples of multi-scale maps to identify these factors that influence a fluid zooming interaction. Several different analyses were conducted on these sixteen multi-scale maps. We first conducted a guided visual exploration of the maps, and a detailed study of the scales of the maps, to identify general trends of good practices (e.g. the WMTS standard that defines zoom levels is widely used) and potential ways of improvement (e.g. a same map is often used at multiple successive zoom levels). Then, we focused on the visual complexity of the multi-scale maps by analyzing how it varies, continuously or not, across scales, using clutter measures, which showed a peak of complexity at zoom level 12 of the WMTS standard. Finally, we studied how buildings and roads are subject to abstraction changes across scales (e.g. at what zoom level individual buildings turn into built-up areas), which can be one of the causes of exploration difficulties. We identified some good practices to reduce the impact of abstraction changes, for instance by mixing different levels of abstraction in the same map. [ABSTRACT FROM AUTHOR]

Building clustering is an important task that should be performed prior to building generalization operations. One of the most common approaches for building clustering is the use of density-based algorithms. Current density-based algorithms encounter problems in detecting accurate clusters in a region with varying density. To overcome this problem, a new density-based spatial clustering algorithm, local-adaptive DBSCAN (LA-DBSCAN), which can cluster polygonal buildings in urban blocks with noise and non-uniform density, is developed. The advantage of LA-DBSCAN is that it can select parameters that are adaptive to different local situations. To evaluate the performance of the proposed model, the complete building generalization process is implemented using four datasets at 1:25k scale. An evaluation of the results allowed us to conclude that the LA-DBSCAN algorithm yields more homogeneous and accurate results than the DBSCAN algorithm. Thus, the presented approach is beneficial for the detection of building patterns and the generalization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Building pattern extraction is an essential step in building generalization. Although many studies have already been conducted, there is a lack of a framework for extracting building patterns. To overcome this problem, an integrated framework for extracting building linear patterns is presented. First, an aggregation function is presented based on the TOPSIS method, which determines the similarity index in terms of area, shape, rectangularity and distance similarities. This results in the extraction of straight and perpendicular patterns using the similarity index and orientation difference criteria. Second, a refinement strategy is proposed, which refines the extracted patterns using a novel definition of the pattern interaction index. To evaluate the proposed model, the complete building group generalization process is implemented using a data-set at 1:25 k scale. The evaluation results allowed us to conclude that the proposed model produces meaningful results, and therefore it would be beneficial in the generalization process. [ABSTRACT FROM AUTHOR]

The automation of map generalization has been keeping researchers in cartography busy for years. Particularly great progress was made in the late 90s with the use of the multi-agent paradigm. Although the current use of automatic processes in some national mapping agencies is a great achievement, there are still many unsolved issues and research seems to stagnate in the recent years. With the success of deep learning in many fields of science, including geographic information science, this paper poses the controversial question of the title: is deep learning the new agent, i.e. the technique that will make generalization research bridge the gap to fully automated generalization processes? The paper neither responds a clear yes nor a clear no but discusses what issues could be tackled with deep learning and what the promising perspectives. Some preliminary experiments with building generalization or data enrichments are presented to support the discussion. [ABSTRACT FROM AUTHOR]

Tactile maps are essential tools for visually impaired people to comprehend space and to support the simple pedestrian trips made difficult by their disability. Tactile maps are created manually and printed by specialists, and it takes a large amount of time to create a new one, which prevents using them on demand for everyday use. As a consequence, researchers and cartographers try to automate this creation process, but the existing automated derivation processes do not include generalization or advanced stylization steps, which limits their effectiveness. This paper reports first experiments to include such complex automated cartography processes to provide on-demand tactile maps for visually impaired people. These first experiments were more intended to raise real research issues than solve them, and the paper discusses these issues in a research agenda to achieve automatically derived tactile maps. [ABSTRACT FROM AUTHOR]

Information on spatial distribution of buildings must be explored as part of the process of map generalization. A new approach is proposed in this article, which combines building classification and clustering to enable the detection of class differences within a pattern, as well as patterns within a class. To do this, an analysis of existing parameters describing building characteristics is performed via principal component analysis (PCA), and four major parameters (i.e. convex hull area, IPQ compactness, number of edges, and smallest minimum bounding rectangle orientation) are selected for further classification based on similarities between building characteristics. A building clustering method based on minimum spanning tree (MST) considering rivers and roads is then applied. Theory and experiments show that use of a relative neighbor graph (RNG) is more effective in detecting linear building patterns than either a nearest neighbor graph (NNG), an MST, or a Gabriel graph (GssG). Building classification and clustering are therefore conducted separately using experimental data extracted from OpenStreetMap (OSM), and linear patterns are then recognized within resultant clusters. Experimental results show that the approach proposed in this article is both reasonable and efficient for mining information on the spatial distribution of buildings for map generalization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recognition of building groups is a critical step in building generalization. To find building groups, various approaches have been developed based on the principles of grouping (or the Gestalt laws of grouping), and the effectiveness of these approaches needs to be evaluated. This study presents a comparative analysis of nine typical such approaches, including three approaches that only consider proximity principle and six approaches that consider multiple grouping principles. Real-life dataset at 1:5000, 1:10,000, and 1:50,000 scales provided by National Geomatics Center of China is used to evaluate the performance of these approaches. Buildings at smaller scales are used to construct the benchmarks to test the grouping results at larger scales, and the adjusted Rand index is adopted to indicate the accuracy of the detected groups. Significant tests (Friedman test and Wilcoxon signed-rank test) are also performed to provide both the overall and pairwise comparisons of these approaches. The results show that (1) the average accuracy of most existing approaches is between 0.3 and 0.5, and the performances of these approaches are significantly different; (2) when only proximity is considered, thebuffer analysis approachperforms significantly better than other approaches; (3) when multiple grouping principles are considered, thelocal constraint-based approachusually performs better than other approaches; (4) existing approaches that consider similarity and/or continuity seldom improve the performance of building grouping. [ABSTRACT FROM AUTHOR]

We present a study on human perception of map complexity, with the objective of better understanding design decisions that may lead to undesirable levels of complexity in web maps. We compare three complexity metrics to human ratings of complexity obtained through a user survey. Specifically, we use two algorithmic approaches published by others, which measure feature congestion (FC) and subband entropy (SE), as well as our own approach of counting object types rather than individual objects. We compare these metrics with each other as well as with human complexity ratings for three maps of the same area from map providers Google Maps, Bing Maps, and OpenStreetMap. Each map design is assessed at three different scales (levels of detail). We find that (1) the FC and SE metrics appear to be adequate predictors of what humans consider complex; (2) object-type counts are slightly less successful at predicting human-rated complexity, implying that clutter is more important in perceived complexity than diversity of symbology; and (3) generalization choices do impact human complexity ratings. These findings contribute to our understanding of what makes a map complex, with implications for designing maps that are easy to use. [ABSTRACT FROM AUTHOR]

Sounding acts as the main feature in a digital nautical chart as it describes the concerned marine topography for the safety of navigation. Unlike the geometry-oriented selection of point feature, the generalization of soundings for chart compiling is expected to be context-oriented, which means bathymetry complexity variations across the study region should be preserved in the sounding selection process. However, such variations are not explicitly accessible to automated systems. This paper proposes an approach that effectively analyzes and measures bathymetry complexity from sounding data, with a focus on topography variations among different regions. The presented approach first divides the exploring region into several subregions, by adopting techniques of computational geometry and graph theory. Then, the approach quantitatively measures the bathymetry complexity of the subregions from grid-based digital terrain model. Finally, a composite bathymetry complexity index integrating aspects of steepness and depth variation is developed to guide the operation of sounding selection in different subregions. Generally, when seafloor is rugged with steep slopes, the number of soundings is high. While in flatter areas, a smaller amount of soundings is retained. The potential of our approach is demonstrated by an application to a real data set. [ABSTRACT FROM PUBLISHER]

Dot maps have become a popular way to visualize discrete geographic data. Yet, beyond showing how the data are spatially distributed, dot maps are often visually cluttered in terms of consistency, overlap, and representativeness. Existing clutter reduction techniques like jittering, refinement, distortion, and aggregation also address this issue, but do so by arbitrarily displacing dots from their exact location, removing dots from the map, changing the spatial reference of the map, or reducing its level of detail, respectively. We present BinSq, a novel visualization technique to compare variations in dot density patterns without visual clutter. Based on a careful synthesis of existing clutter reduction techniques, BinSq reduces the wide variety of dot density variations on the map to a representative subset of density intervals that are more distinguishable. The subset is derived from a nested binning operation that introduces order and regularity to the map. Thereafter, a dot prioritization operation improves the representativeness of the map by equalizing visible data values to correspond with the actual data. In this paper, we describe the algorithmic implementation of BinSq, explore its parametric design space, and discuss its capabilities in comparison to six existing clutter reduction techniques for dot maps. [ABSTRACT FROM PUBLISHER]

As a basic and significant operator in map generalization, polyline simplification needs to work across scales. Perkal’sε-circle rolling approach, in which a circle with diameterεis 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. [ABSTRACT FROM AUTHOR]

Selective omission in a road network (or road selection) means to retain more important roads, and it is a necessary operator to transform a road network at a large scale to that at a smaller scale. This study discusses the use of the supervised learning approach to road selection, and investigates how many samples are needed for a good performance of road selection. More precisely, the binary logistic regression is employed and three road network data with different sizes and different target scales are involved for testing. The different percentages and numbers of strokes are randomly chosen for training a logistic regression model, which is further applied into the untrained strokes for validation. The performances of using the different sample sizes are mainly evaluated by an error rate estimate. Significance tests are also employed to investigate whether the use of different sample sizes shows statistically significant differences. The experimental results show that in most cases, the error rate estimate is around 0.1–0.2; more importantly, only a small number (e.g., 50–100) of training samples is needed, which indicates the usability of binary logistic regression for road selection. [ABSTRACT FROM AUTHOR]

Automatic generation of multi-scale representations from the same spatial data source has been the research focus in map generalization for a long time. Based on the Fourier technique, this paper proposes a continuous, multi-scale representation model for progressive transformation of cartographic curves on the Internet. In our method, all the curves, whether closed or open, are depicted as periodical functions which are further expressed as Fourier series. The convergence degrees of the Fourier series are explored for different kinds of curves, and truncating frequencies are derived based on the similarity between the original and reconstructed curves. Using information theory and the Radical Law in cartography, the relationship between map scales and Fourier frequencies is established. Based on the proposed multi-scale model, we also introduce the principles and implementation of a progressive transmission method. Our method is evaluated using the contours from a topographic map. The results show that our model is a valid approach to multi-scale representation of cartographic curves. [ABSTRACT FROM AUTHOR]

Selective omission in a road network is a necessary operation for road network generalization. Most existing selective omission approaches involve one or two geometric parameters at a specific scale to determine which roads should be retained or eliminated. This study proposes an approach for determining the empirical threshold for such a parameter. The idea of the proposed approach is to first subdivide a large road network, and then to use appropriate threshold(s) obtained from one or several subdivisions to infer an appropriate threshold for the large one. A series of experiments was carried out to validate the proposed approach. Specifically, the road network data for New Zealand and Hong Kong at different scales (ranging from 1:50,000 to 1:250,000) were used as the experimental data, and subdivided according to different modes (i.e. administrative boundary data, a regular grid of different sizes, different update years, and different road network patterns). Not only geometric parameters, but also structural and hybrid parameters of existing selective omission approaches were involved in the testing. The experimental results show that although the most appropriate thresholds obtained from different subdivisions are not always the same, in most cases, the appropriate threshold ranges often overlap, especially for geometric parameters, and they also overlap with those obtained from the large road network data. This finding is consistent with the use of different subdivision modes, which verifies the effectiveness of the proposed approach. Several issues involving the use of the proposed approach are also addressed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Quantitative relations between spatial similarity degree and map scale change in multi-scale map spaces play important roles in map generalization and construction of spatial data infrastructure. Nevertheless, no achievements have been made regarding this issue. To fill the gap, this paper firstly proposes a model for calculating spatial similarity degrees between an individual linear object at one scale and its generalized counterpart at the other scale. Then psychological experiments are designed to validate the new model, taking four different individual linear objects at five different scales as test samples. The experiments have shown that spatial similarity degrees calculated by the new model can be accepted by a majority of the subjects. After this, it constructs a formula that can calculate spatial similarity degree using map scale change (and vice versa) for individual linear objects in multi-scale map spaces by the curve fitting method using the point data from the psychological experiments. Both the formula and the model can calculate quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces, which facilitates automation of map generalization algorithms for linear features. [ABSTRACT FROM AUTHOR]

A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, for example, far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale maps for a geographic region. This article attempts to argue and provide evidence for the fractal nature of maps and mapping. It is the underlying fractal structure of geographic features, either natural or man-made, that make reality mappable, large-scale maps generalizable, and cities imageable. The fractal nature is also what underlies the beauty of maps. After introducing some key fractal concepts such as recursion, self-similarity, scaling ratio, and scaling exponent, this article demonstrates that fractal thought is rooted in long-standing map-making practices such as series maps subdivision, visual hierarchy, and Töpfer’s radical law. Drawing on previous studies on head/tail breaks, mapping can be considered a head/tail breaks process; that is to divide things around an average, according to their geometric, topological and/or semantic properties, into the head (for those above the average) and the tail (for those below the average), and recursively continue the dividing process for the head for map generalization, statistical mapping, and cognitive mapping. Given the fractal nature of maps and mapping, cartography should be considered a perfect combination of science and art, and scaling must be formulated as a law of cartography or that of geography in general. [ABSTRACT FROM PUBLISHER]

To meet the requirements of multi-scale mapping in maritime applications, marine charts need to be produced at various levels of detail (LOD) using map generalization. As a prominent geographic feature, the coastline has to be generalized considering the geomorphologic characteristics rather than from a pure geometric perspective. Morphologic and domain-specific constraints (e.g., safety) should be incorporated in designing a coastline generalization algorithm. Motivated by the generalization of ria coastlines, this article proposes a simplification algorithm that is specific to coastlines. An analysis of ria coasts results in several morphologic constraints that have to be satisfied in coastline generalization, such as the dendritic pattern of estuaries. To satisfy these constraints, a hierarchical estuary tree model is first established by Delaunay triangulation, which helps to represent the dendritic pattern of ria coastlines. Minor estuaries are then deleted to achieve a reasonable coastline simplification. To imitate manual generalization, an indicator is designed to calculate the importance of estuaries in a context dependent manner. By comparing with a well-known bend simply algorithm, we show that the presented method can maintain dendritic pattern of coastline and is free from self-intersection and also granted for navigation safety. This article also demonstrates that the proposed approach is applicable to coastlines in general. [ABSTRACT FROM AUTHOR]

The scale dependences of topological relations are caused by the changes of spatial objects at different scales, which are induced by the reduction of attributes. Generally, the detailed partitions and multi-scale attributes are stored in spatial databases, while the coarse partitions are not. Consequently, the detailed topological relations can be computed and regarded as known information, while the coarse relations stay unknown. However, many applications (e.g., multi-scale spatial data query) need to deal with the topological relations at multiple scales. In this study new methods are proposed to model and derive the scale dependences of topological relations between lines and multi-scale region partitions. The scale dependences of topological relations are modeled and used to derive the relations between lines and coarse partitions from the relations about the detailed partitions. The derivation can be performed in two steps. At the first step, the topological dependences between a line and two meeting, covered and contained regions are computed and stored into composition tables, respectively. At the second step, a graph is used to represent the neighboring relations among the regions in a detailed partition. The scale dependences and detailed relations are then used to derive topological relations at the coarse level. Our methods can also be extended to handle the scale dependences of relations about disconnected regions, or the combinations of connected and disconnected regions. Because our methods use the scale dependences to derive relations at the coarse level, rather than generating coarse partition and computing the relations with geometric information, they are more efficient to support scale-dependent applications. [ABSTRACT FROM AUTHOR]

This paper presents a method for automated detection of changes between updated larger-scale (1:10,000) maps and to-be-updated smaller-scale (1:50,000) maps, with settlements as an example. In the method, (i) discrepancies between two maps are detected and recognized through an exhaustive comparison of map features; (ii) these discrepancies are then quantified and represented in a formalized way; (iii) with a combination of cause analysis and quantification of discrepancies, a series of rules are formulated to distinguish updates from discrepancies. Real-life data are used to verify the effectiveness of this method and the results suggest that the new method works well. [ABSTRACT FROM AUTHOR]