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When you zoom in or out of current multi-scale cartographic applications, it is common to feel lost and disoriented for a few seconds because dimensions and map symbols have changed. To make the exploration of these multi-scale maps more fluid, one option is to design maps where the transformations due to scale change are more progressive. This paper proposes to use cartographic generalization techniques to design these multi-scale maps with additional intermediate scales to improve progressiveness. These more progressive maps are tested in a user study with a task requiring multiple zooms in and out. The users perform better with the progressive maps, and in particular, the total quantity of required zooming is reduced compared to maps without additional intermediate scales. However, the survey is not fully conclusive on task performance due to the complexity of such a survey with real maps. This difficulty in assessing how well progressive map generalisation reduces disorientation is discussed and guidelines are proposed to design further studies.

The cluster patterns of features in map space represent a comprehensive reflection of individual feature geometric attributes and their spatial adjacency relationships. These patterns also embody spatial cognition results under the Gestalt principle. Describing non-linear spatial cluster patterns as effective regular structures is one of the fundamental tasks in deep learning for recognizing feature cluster patterns. In this study, based on the concept of texture co-occurrence matrices from regular gray-scale images, we utilized Voronoi diagrams to construct the tessellation structure of building polygons. Built upon the foundation of first-order texton co-occurrence matrices, we established three-dimensional texton co-occurrence matrices for building polygons, considered five attributes of building size, shape, orientation, and density, and encompassed 64 different combinations of second-order neighboring directions. This matrix concretizes the latent Gestalt spatial characteristics of building polygon clusters into a three-dimensional sparse matrix. It is then used as an input vector to construct a deep convolutional neural network for recognizing building polygon cluster patterns. Through adjustments and optimizations of neural network structure and strategies, along with validation through practical case studies and comparisons with other models, we have demonstrated the effectiveness of the second-order texton co-occurrence matrix in describing the characteristics of building polygon clusters.

Urban villages represent informal residential areas emerging since China’s rapid urbanization process. Scientific map generalization of urban villages with scientific maps aids readers in discerning their distribution and making informed decisions concerning them. However, there is still a scarcity of research on the automatic extraction and generalization of urban villages from vector data, which needs to be studied to further improve the expression of maps. To address this problem, this paper presents a methodology for the extraction and generalization of urban villages from Digital Line Graphics. Firstly, a heuristic approach is employed to analyze the atypical morphological characteristics of urban villages. Then, indices based on computational geometry and the modified Hausdorff distance are utilized to quantify these traits. Lastly, an automatic generalization principle for urban villages is offered. The approach was tested in experimental blocks and proved to be effective. It offers a novel method for the automatic extraction and cartography of urban villages.

Road network simplification is a complex decision-making process. Such a multi-factor decision and scaling operation traditionally applied rule-based methods. The establishment and adjustment of these rules involve many human-set parameters and conditions, which makes generalized results closely related to the cartographer’s experience and habits. On the other hand, existing methods tend to consider individual structures separately in different algorithms, such as strokes, meshes and graph networks, lacking a solution that brings the advantages of these methods together. Aiming at the above problems, this study designs a simplification method using the Mesh-Line Structure Unit (MLSU) to consider polyline and polygon characteristics simultaneously with the support of graph-based deep learning networks. In order to make generalization decisions, a model based on graph convolutional network (GCN) is constructed and trained using real data, thus realizing the road network selective omission. The experimental results indicate that the proposed method effectively achieves automatic road generalization.

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.

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.

ABSTRACTPolyline simplification is crucial for cartography and spatial database management. In recent decades, various rule-based algorithms for vector polyline simplification have been proposed. However, most existing algorithms lack parameter self-adaptive capabilities and require repeated manual parameter adjustments when applied to different polylines. While deep-learning-based methods have recently been introduced for raster polyline image simplification, they cannot achieve end-to-end simplification when the input data and output results are vector polylines. This paper proposes a new deep-learning-based method for vector polyline simplification by integrating both the vector and raster features of the polyline. Specifically, a deep separable convolutional residual neural network was first used to extract the convolutional features of each image. Then, the region proposal network was modified to generate proposal boxes using vector coordinates, and these proposal boxes were used to locate the convolutional feature maps of bends. Finally, convolutional feature maps were fed into a binary classification network to identify unimportant vertices that should be omitted for vector polyline simplification. The experimental results indicated that the proposed method can exploit raster and vector features to achieve automatic and effective polyline simplification without prior map generalization knowledge and manual settings of rules and parameters. The polyline simplification results of the proposed method have a higher compression ratio of coordinate points and lower shape deformation and deviation than the results generated by the classic Wang and Müller (WM) algorithm and Support Vector Machine (SVM) based algorithm, which shows the potential of the proposed method for future applications in map generalization.

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.

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.

Point settlement selection is one of the critical tasks in map generalization, which should consider spatial distribution, spatial conflict, proximity to objects, and other factors. By analyzing the current research, spatial structure-preserving and conflict-avoiding methods are proposed in this article for point settlement selection. On the one hand, in view of the shortcomings of the Voronoi diagram in measuring settlement density and spatial distribution, a spatial conflict-avoiding strategy is proposed, which utilizes the minimum distance between adjacent settlements to weight the Voronoi diagram area to avoid local conflicts. On the other hand, in order to solve the problem of excessive temporary solidification of adjacent settlements, an adaptive temporary solidification strategy considering local spatial characteristics is proposed, with an improved novel distance-constrained Voronoi diagram model suggested and employed. Comparative experiments and related quantitative analysis on the National Land Survey of Finland Topographic Database confirm that the above methods have good effect. The conflict-avoiding strategy can effectively prioritize map readability and legibility, while the adaptive temporary solidification method can better deal with the boundary effect of settlement groups.

Building outlines are important for emergency response, urban planning, and change analysis and can be quickly extracted from remote sensing images and raster maps using deep learning technology. However, such building outlines often have irregular boundaries, redundant points, inaccurate positions, and unclear turns arising from variations in the image quality, the complexity of the surrounding environment, and the extraction methods used, impeding their direct utility. Therefore, this study proposes a simplification and regularization algorithm for right-angled polygon building outlines with jagged edges. First, the minimum bounding rectangle of the building outlines is established and populated with a square grid based on the smallest visible length principle. Overlay analysis is then applied to the grid and original buildings to extract the turning points of the outlines. Finally, the building orientation is used as a reference axis to sort the turning points and reconstruct the simplified building outlines. Experimentally, the proposed simplification method enhances the morphological characteristics of building outlines, such as parallelism and orthogonality, while considering simplification principles, such as the preservation of the direction, position, area, and shape of the building. The proposed algorithm provides a new simplification and regularization method for right-angled polygon building outlines with jagged edges.

Building displacement is a common operation to resolve the spatial conflicts between map features, and it has important theoretical value and practical application significance for multi-scale mapping. The prerequisite for a successful displacement operation is that there is extra space around the conflicting buildings into which they can be displaced. Otherwise, additional generalization operators need to be combined to resolve spatial conflicts. Based on this idea, this study proposes a new heuristic spatial conflict resolution framework that mainly resolves the spatial conflicts between buildings and other features in urban villages by combining three cartographic generalization operators: selection, displacement, and aggregation. This method first reduces the density of buildings in the block through selection operation, then resolves the spatial conflicts between buildings and other features through displacement operation, and finally, the aggregation operation is performed to eliminate any remaining conflicts and newly generated conflicts. Experiments were carried out using real urban village data, and visual inspection and quantitative analysis were used to evaluate the experimental results. The evaluation results show that the proposed framework can not only resolve spatial conflicts well, but also maintain the spatial distribution and area balance of the buildings in urban villages.

This paper aims to propose a new approach to calculate the quantitative relations between morphostructural similarity degree and map scale change in multi-scale contour clusters for automatic contour generalization. Terrain lines were extracted by pre-processing of unclosed contour lines, and an indirect quantitative expression method of morphostructural similarity relation was proposed based on terrain line hierarchical trees. Thirteen groups of multi-scale contour clusters with different drainage areas of loess geomorphy were employed to explore the changing regularity of morphostructural similarity indices with map scale. Finally, the quantitative relations between morphostructural similarity degree and map scale change were calculated using 52 groups of points. The results show that power function is the best fit among the candidate functions, and the quantitative relations between the morphostructural similarity degree and map scale change can be expressed using the same power function, which facilitates the automation of contour generalization.

The consistency of geospatial data is of great significance for the application and updating of geographic information in web maps. Due to the multiple data sources and different temporal versions, the tile web maps usually meet the inconsistency question across different layers. This study tries to develop a method to detect this kind of inconsistency utilizing a raster-based scaling approach. Compared with vector-based handling, this method can be directly available for multi-level tile images in a pixel representation form. The proposed cross-layer raster tile map rendering method (CRTMRM) consists of four primary aspects: geographic object separation, consistency rendering rules, data scaling and derivation with super-pixel segmentation, and inconsistency detection. The scale transformation strategy with the super-pixel attempts to obtain a simplified representation. Taking the scale lifespan variation and geometric consistency rules into account, the inconsistency detection of tile maps is conducted between temporal versions, multi-sources, and different scales through actual and derived data overlay analysis. The experiment focuses on features of cross-layer water or vegetation areas with Level 9 to Level 14 in Baidu Maps, Amap, and Google Maps. This method is able to serve as a basis for massive unstructured web map data inconsistency detection and support intelligent web map rendering.

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.

Road networks are the skeletal elements of topographic maps at different scales, and road selection is a prerequisite for implementing continuous multiscale spatial representations of road networks. The mesh-based approach is a common, advanced and powerful method for road selection in dense road areas in which small meshes are removed and road segments with the least importance in each mesh are eliminated. However, small meshes in a map can be classified into two types: aggregated small meshes and isolated small meshes. The number of the former is small, and that of the latter is large. Existing methods are generally applicable for the latter, and some or even most spatial characteristics will be lost when they are applied to the former; as a result, the road selection quality will be affected. Therefore, as a supplement to the mesh-based selection method, this paper proposed an automatic generalization method of dense road network areas (areas formed by aggregated small meshes) considering spatial structural features as constraints. First, the aggregated areas of small meshes were identified based on the number of adjoining small meshes, and the boundaries of aggregated areas are extracted and used as hard constraints during mesh elimination. Second, the starting meshes were redefined by simultaneously considering the edge features and mesh density of small meshes, and an ordinal elimination algorithm was proposed to eliminate the meshes in the stroke connection direction. Third, road selection was implemented by identifying the starting meshes and sequentially processing the related mesh pairs. This iterative process continued until all mesh densities of the newly formed meshes are beyond the threshold or the problem becomes a simple elimination problem involving two adjoining small meshes or one isolated small mesh. Finally, a 1:10,000 standard topographic road map for Jiangsu Province, China, was used for validation. The experimental results showed that in the aggregated areas with two small meshes, 31% of the areas obtained the same selection results by using the mesh-based method and the proposed method, and the remaining 69% obtained a more compact result with the proposed method. Moreover, for all aggregated areas with more than two small meshes, the spatial distribution structure of small meshes was preserved better by the proposed method.

Point cluster generalization is a major concern in cartography. This problem is complicated by how to preserve the distribution patterns (e.g., density) of points during the process of deriving small-scale maps from a large-scale map. To address this problem, existing methods adopt geometric models such as planar Voronoi diagram, which considers the geographic space as an ideal Euclidean one. The associated operations determine the relationships of points based on the Euclidean straight-line distance. However, many map features are in different geographic environments. For example, as one of the most significant features on a map, urban facilities rely on the transport function of street networks to compete for service areas, and thus their distributions, in reality, are constrained to the spatial layout of street networks. To preserve such characteristic after generalization, this paper establishes a network-constrained Voronoi model for delimitating service areas of facility points-of-interest (POIs). With the help of Voronoi model, the proposed method further treats the generalization process of facility POIs as a compete and merge iterative process of service areas: a facility that has a relatively small service area faces more intense competition from its neighbors and by deleting it from the resulting small-scale map in the first priority its service area will be partitioned and merged to the neighbors. The experimental results demonstrate that our method considers the service patterns of facility POIs is particularly useful in applications related to navigation.

The network Voronoi diagram has been extensively applied in many fields, such as influence area construction, location selection and urban planning, owing to its high accuracy and validity in space division. Taking advantage of parallel processing and auto-wave division of the pulse coupled neural network (PCNN), an algorithm for generating a weighted network Voronoi diagram is proposed in this paper. First, in order to better accommodate the scenes of urban facility points and road networks, the PCNN is improved. Second, the speed of the auto-wave in the improved PCNN is calculated by the weights of the facility points and the attributes of the related road network. Third, the nodes in the road network are considered as neurons, the facility points are projected onto the nearest road segments and the projected points are treated as initial neurons. The initial neurons generate auto-waves simultaneously, and the auto-waves transmit along the shortest path from neurons to other neurons with the calculated speed until all the neurons are fired. During this procedure, the road network and the corresponding space are assigned to the initial neurons and the weighted network Voronoi diagram is constructed. The experiments on the specific region with the real POIs present the feasibility, applicability and efficiency of the algorithm.

Recognizing building group patterns is fundamental to numerous fields, such as urban landscape evaluation, social analysis, and map generalization. Despite the increasing number of algorithms available for building group pattern recognition, there is still a lack of satisfactory grouping results due to insufficient information and only geometric features being provided to recognition methods. This study aims to provide a novel building grouping method that combines building function and geometric information. We specifically focus on the process of recognizing building groups in topographic maps as a prerequisite to subsequent map generalization. First, the building functions are inferred using the dynamic time warping (DTW) algorithm based on Tencent user density data and POIs (points of interest). Then, two types of constrained Delaunay triangulations (CDTs) are created for each building block, from which several spatial indices, such as the continuity index (SCI), direction, and distance of every two adjacent buildings, are derived. Finally, each building block is modeled as a graph on the grounds of derived matrices and building function information, and a graph segmentation approach is proposed to extract building groups. A case study is conducted to test the proposed approach. The experimental results indicate that the proposed approach can produce satisfactory results, given that the correctness value is above 81.63% for our study area. Comparative studies reveal that the method without building function information is an ineffective grouping method when buildings with different functions are close to each other. In addition, generalization results derived from the proposed method are more in line with those of maps for daily use, as they provide users with more accurate spatial divisions of urban buildings.

Quantitative relations between topological similarity degree and map scale change of multi-scale contour clusters are vital to the automation of map generalization. However, no method has been proposed to calculate the relations. This paper aims at filling the gap by proposing a new approach. It firstly constructed a directed contour tree by pre-processing of unclosed contours, and then developed a quantitative expression of topological relations of contour cluster based on directed contour tree. After this, it employed 108 groups of multi-scale contour clusters with different geomorphological types to explore the changing regularity of topological indices with map scale. Last, it used 416 points to calculate the quantitative relations between topological similarity degree and map scale change by curve fitting method. The results show that the quantitative expression of multi-scale topological indexes is closely related to the contour interval change, and power function is the best fit among the candidate functions.

Accessibility is an important issue in transport geography, land planning, and many other related fields. Accessibility problems become computationally demanding when involving high-resolution requirements. Using conventional methods, providing high-resolution accessibility analysis for real-time decision support remains a challenge. In this paper, we present a parallel processing model, named HiAccess, to solve the high-resolution accessibility analysis problems in real time. One feature of HiAccess is a fast road network construction method, in which the road network topology is determined by traversing the original road nodes only once. The parallel strategies of HiAccess are fully optimized with few repeated computations. Moreover, a simple, efficient, and highly effective map generalization method is proposed to reduce computation load without an accuracy loss. The flexibility of HiAccess enables it to work well when applied to different accessibility analysis models. To further demonstrate the applicability of HiAccess, a case study of settlement sites selection for poverty alleviation in Xiangxi, Central China, is carried out. The accessibility of jobs, health care, educational resources, and other public facilities are comprehensively analyzed for settlement sites selection. HiAccess demonstrates the striking performance of measuring highresolution (using 100 m × 100 m grids) accessibility of a city (in total over 250k grids, roads with 232k segments, and 40 facilities) in 1 sec without preprocessing, while ArcGIS takes nearly 1 h to achieve a less satisfactory result. In additional experiments, HiAccess is tested on much larger data sets with excellent performance.

Spatial conflicts can remain unresolved during map generalization if only displacement is used, especially for urban building maps. To solve all possible spatial conflicts during urban building map generalization, we propose a collaborative displacement method, combining aggregation, elimination, and constrained reshape. After applying an improved vector field-based displacement for solution of initial conflicts, two types of sequential conflicts are detected and evaluated to identify additional displacement solutions based on a trial and error strategy. If no displacement solution is available, aggregation, elimination, or constrained reshape are selected and applied for the unsolved sequential conflicts based on cartographic rules. For a more reasonable generalization result, an improved constrained reshape approach is also introduced for buildings in conflicts along roads. Two data sets with scales of 1:5000 and 1:25000 for urban building map were selected to validate this approach. The results indicate that it is reasonable and feasible to solve all defined spatial conflicts in urban building map generalization using our proposed method.

Aggregating areas into larger regions is a common problem in spatial planning, geographic information science, and cartography. The aim can be to group administrative areal units into electoral districts or sales territories, in which case the problem is known as districting. In other cases, area aggregation is seen as a generalization or visualization task, which aims to reveal spatial patterns in geographic data. Despite these different motivations, the heart of the problem is the same: given a planar partition, one wants to aggregate several elements of this partition to regions. These often must have or exceed a particular size, be homogeneous with respect to some attribute, contiguous, and geometrically compact. Even simple problem variants are known to be NP-hard, meaning that there is no reasonable hope for an efficient exact algorithm. Nevertheless, the problem has been attacked with heuristic and exact methods. In this article we present a new exact method for area aggregation and compare it with a state-of-the-art method for the same problem. Our method results in a substantial decrease of the running time and, in particular, allowed us to solve certain instances that the existing method could not solve within five days. Both our new method and the existing method use integer linear programming, which allows existing problem solvers to be applied. Other than the existing method, however, our method employs a cutting-plane method, which is an advanced constraint-handling approach. We discuss this approach in detail and present its application to the aggregation of areas in choropleth maps.

Thoughtful consideration of the enumeration unit size in choropleth map design is important to ensure the correct communication of spatial information. However, the enumeration unit size and its influence on pattern conveying in choropleth maps have not yet been the subject of in-depth empirical studies. This research aims to address this gap. We focused on the issue concerning whether the ability to recognize spatial patterns on an Equal Area Unit Map is related to the hexagonal enumeration unit size, defined by the number of pixels. The aim is to indicate the range of the enumeration unit sizes, namely, at what point the upper and lower borders of the range where the spatial patterns start, and where the end is visible and recognizable by users. To address this problem, we conducted an empirical study with 488 users. The results show that the enumeration unit size has an impact on the users’ spatial pattern recognition abilities. Choropleth maps with enumeration unit sizes of 26, 52, and 104 pixels were, in the majority, indicated by participants as those most suitable for indicating spatial patterns. This was in contrast to choropleth maps with enumeration unit sizes of 1664 and 3328 pixels, which users indicated as not being useful. However, there were some exceptions to this general finding. Thus, determining the optimal enumeration unit size is a challenging task, and requires further insightful investigations.

The ditch pattern reflects the distribution characteristics of an agricultural drainage system and needs to be detected to enrich the data source before map generalization. Due to several breaks, the connectivity of the ditches is destroyed between ditches and rivers in map representation, making its structure complex. Previous studies have primarily focused on extracting parallel ditches, paying less attention to complex ditches with breaks. The pattern recognition of ditches does not merely involve the extraction of parallel relation. It involves the extraction of different level relations, which is a great challenge. Therefore, this study proposes a novel model to describe the complex structure of ditches. Our work consisted of the following three main contributions: (1) the collinear relation was defined to detect the groups of ditch segments separated by breaks, (2) the detection method of parallel relation was improved throughout the multi-parameter combined constraints, and (3) the main-tributary relation was proposed to build a connection between parallel groups and rivers. The experimental results showed that the proposed method was solved effectively in complex ditch pattern recognition.

In automatic map compilation, both the scale reduction and the geometric transformation of map features may give rise to spatial conflicts. Several generalization approaches have been established to resolve this problem, mainly for the displacement operator. This paper proposes one such approach that is based on the snake model and multiple agents. It focuses on the resolution of various spatial conflicts that emerge when generalizing the rural areas of medium density. In this approach, the map features are converted into map agent, object agent, group agent, and conflicting agent, and the spatial relationships between these features are managed by an auxiliary relationship agent. Each agent is assigned with tasks accordingly, and all agents collaborate with each other to complete the generalization. The snake-based algorithm is applied in the conflicting agent when it identifies a certain configuration. The experimental results indicate that the approach proposed in this paper can obtain good results.

Whatever the data source, or the capture process, the creation of a building footprint in a geographical dataset is error prone. Building footprints are designed with square angles, but once in a geographical dataset, the angles may not be exactly square. The almost-square angles blur the legibility of the footprints when displayed on maps, but might also be propagated in further applications based on the footprints, e.g., 3D city model construction. This paper proposes two new methods to square such buildings: a simple one, and a more complex one based on nonlinear least squares. The latter squares right and flat angles by iteratively moving vertices, while preserving the initial shape and position of the buildings. The methods are tested on real datasets and assessed against existing methods, proving the usefulness of the contribution. Direct applications of the squaring transformation, such as OpenStreetMap enhancement, or map generalization are presented.

Several algorithms have been developed to simplify buildings based on their local structure in past decades. However, different local structures are defined for certain purposes, and no algorithm can appropriately simplify all buildings. We propose a combined building simplification approach based on local structure classification and backtracking strategy. In this approach, local structures are classified and their based operations are defined by considering the buildings’ orthogonal and non-orthogonal features. Each building is simplified to target scale with a selected local-structure-based operation progressively scale-by-scale. Rules are built to support the selection of local-structure-based operations with a binary decision tree, and a backtracking strategy is used when an invalid operation is applied. When the building is too small or the evaluation shows that it cannot be simplified based on local structures, template matching or enlargement algorithms are applied to simplify the building. A dataset (1:10k) collected from the Ordnance Survey was used for the experiment and simplified scale of 1:25k. Results satisfied legibility constraints and the change in area, orientation and position of simplified buildings are controlled within certain range by comparing with the results generated based on other four simplification algorithms. Possible use of our approach for continuous scale transformation of buildings is also discussed.

For the complex semantic features of objects in a geological map, maintaining a hierarchy between different geological objects is a big challenge when automatically generalizing the geological map. The typical methods focus on automation of geological map generalization or pay more attention to the hierarchical relation between geological objects, which reduces the accuracy of the geological map generalization result. Therefore, a conceptual framework that focuses on both the automated process and the geological objects is particularly important in developing an efficient software designed for automated generalization of geological maps. In this paper, we design a compound conceptual framework for automated generalization of geological maps based on multiple agents and workflow. In this framework, the process is divided into three stages: structure analysis, map generalization, and style standardization. The map objects in the source geological map are abstracted as diverse agents with different properties and behaviors, and the agents can communicate with each other when they are activated. Thus, the relationship of the map objects is coordinated in geological map generalization, avoiding the conflict between the different operation levels. The workflow technology is used to manage the automated process. We discuss the task, modeling method, and specific operation in every stage based on the current conceptual framework and the characteristics of a geological map. Finally, we use a simple geological map for experimental studies that verify the proposed conceptual framework. The result shows that it is advantageous to design the software for automated generalization of geological maps based on the proposed compound conceptual framework.

The Earth’s surface or any territory is a coherent whole or subwhole, in which the notion of “far more small things than large ones” recurs at different levels of scale ranging from the smallest of a couple of meters to the largest of the Earth’s surface or that of the territory. The coherent whole has the underlying character called wholeness or living structure, which is a physical phenomenon pervasively existing in our environment and can be defined mathematically under the new third view of space conceived and advocated by Christopher Alexander: space is neither lifeless nor neutral, but a living structure capable of being more alive or less alive. This paper argues that both the map and the territory are a living structure, and that it is the inherent hierarchy of “far more smalls than larges” that constitutes the foundation of maps and mapping. It is the underlying living structure of geographic space or geographic features that makes maps or mapping possible, i.e., larges to be retained, while smalls to be omitted in a recursive manner (Note: larges and smalls should be understood broadly and wisely, in terms of not only sizes, but also topological connectivity and semantic meaning). Thus, map making is largely an objective undertaking governed by the underlying living structure, and maps portray the truth of the living structure. Based on the notion of living structure, a map can be considered to be an iterative system, which means that the map is the map of the map of the map, and so on endlessly. The word endlessly means continuous map scales between two discrete ones, just as there are endless real numbers between 1 and 2. The iterated map system implies that each of the subsequent small-scale maps is a subset of the single large-scale map, not a simple subset but with various constraints to make all geographic features topologically correct.

As the coding of a dendritic river system can be used to represent the stream order and spatial-structure of a river network, it is always used in river selection, which is a key step in topographic map generalization. There are two categories of conventional hydrological coding systems, one is the top-down approach, and the other is the bottom-up approach. However, the former does not accurately reflect the hierarchies of a dendritic river network, which is produced by catchment relationships, and it is not appropriate for the stream selection of river networks with uniform distributions of tributaries. The latter cannot directly indicate the subtree depth of a stream, and it is not favorable to stream selection of river systems that have topologically deep structures. Therefore, a selection method for dendritic river networks based on hybrid coding is proposed in this paper. First, the dendritic river network is coded through classical top-down Horton coding. Second, directed topology trees are constructed to organize the river network data, and stroke connections are calculated to code the river network in the bottom-up approach. Third, the river network is marked through hybrid usage of the top-down approach and bottom-up approach, and based on the spatial characteristics of the river network, the river network is classified into three kinds of subtrees: deep branch, shallow branch and modest branch. Then, appropriate coding is assigned automatically to different subtrees to achieve river selection. Finally, actual topographic map data of a river system in a region of Hubei Province are used to comparatively validate the hybrid coding system against two existing isolated coding systems. The experimental results demonstrate that the hybrid coding method is very effective for river network selection, not only in highlighting hierarchies formed by catchment relationships but also in the uniform distribution of tributaries.

Geological maps are an important information source used in the support of activities relating to mining, earth resources, hazards, and environmental studies. Owing to the complexity of this particular map type, the process of geological map generalization has not been comprehensively addressed, and thus a complete automated system for geological map generalization is not yet available. In particular, while in other areas of map generalization constraint-based techniques have become the prevailing approach in the past two decades, generalization methods for geological maps have rarely adopted this approach. This paper seeks to fill this gap by presenting a methodology for the automation of geological map generalization that builds on size constraints (i.e., constraints that deal with the minimum area and distance relations in individual or pairs of map features). The methodology starts by modeling relevant size constraints and then uses a workflow consisting of generalization operators that respond to violations of size constraints (elimination/selection, enlargement, aggregation, and displacement) as well as algorithms to implement these operators. We show that the automation of geological map generalization is possible using constraint-based modeling, leading to improved process control compared to current approaches. However, we also show the limitations of an approach that is solely based on size constraints and identify extensions for a more complete workflow.

As a result of the increasing popularity of indoor activities, many facilities and services are provided inside buildings; hence, there is a need to visualize points-of-interest (POIs) that can describe these indoor service facilities on indoor maps. Over the last few years, indoor mapping has been a rapidly developing area, with the emergence of many forms of indoor representation. In the design of indoor map applications, cartographical methodologies such as generalization and symbolization can make important contributions. In this study, a self-adaptive method is applied for the design of a multi-scale and personalized indoor map. Based on methods of map generalization and multi-scale representation, we adopt a scale-adaptive strategy to visualize the building structure and POI data on indoor maps. At smaller map scales, the general floor distribution and functional partitioning of each floor are represented, while the POI data are visualized by simple symbols. At larger map scales, the detailed room distribution is displayed, and the service information of the POIs is described by detailed symbols. Different strategies are used for the generalization of the background building structure and the foreground POI data to ensure that both can satisfy real-time performance requirements. In addition, for better personalization, different POI data, symbols or color schemes are shown to users in different age groups, with different genders or with different purposes for using the map. Because this indoor map is adaptive to both the scale and the user, each map scale can provide different map users with decision support from different perspectives.

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its generalized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

The road network is one of the key feature classes in topographic maps and databases. In the task of deriving road networks for products at smaller scales, road network selection forms a prerequisite for all other generalization operators, and is thus a fundamental operation in the overall process of topographic map and database production. The objective of this work was to develop an algorithm for automated road network selection from a large-scale (1:10,000) to a small-scale database (1:200,000). The project was pursued in collaboration with swisstopo, the national mapping agency of Switzerland, with generic mapping requirements in mind. Preliminary experiments suggested that a selection algorithm based on betweenness centrality performed best for this purpose, yet also exposed problems. The main contribution of this paper thus consists of four extensions that address deficiencies of the basic centrality-based algorithm and lead to a significant improvement of the results. The first two extensions improve the formation of strokes concatenating the road segments, which is crucial since strokes provide the foundation upon which the network centrality measure is computed. Thus, the first extension ensures that roundabouts are detected and collapsed, thus avoiding interruptions of strokes by roundabouts, while the second introduces additional semantics in the process of stroke formation, allowing longer and more plausible strokes to built. The third extension detects areas of high road density (i.e., urban areas) using density-based clustering and then locally increases the threshold of the centrality measure used to select road segments, such that more thinning takes place in those areas. Finally, since the basic algorithm tends to create dead-ends—which however are not tolerated in small-scale maps—the fourth extension reconnects these dead-ends to the main network, searching for the best path in the main heading of the dead-end.

Maps at different scales have different emphases on the information representation of point data. With a focus on large scales, this paper proposes an improved sequential displacement method. While existing approaches mostly use a fixed order to place points during displacement, the proposed method takes into consideration the spatial distribution characteristics, including the spatial structure and the holistic distance relations of a point group. This method first rapidly extracts feature points through a quadtree index to capture the spatial structure of a point group. Then, it uses map information content to determine the points to be processed. Finally, a global distance matrix for the above two sets of points is established. Overlapping of symbols is resolved by processing the global distance matrix. The algorithm is estimated by comparing with the latest strategy, which has overcome the position drift drawback of traditional sequential displacement methods and the results show that the proposed method can improve the effects of map expression and meet the requirements of real-time processing.

Extraction of the skeleton line of complex polygons is difficult, and a hot topic in map generalization study. Due to the irregularity and complexity of junctions, it is difficult for traditional methods to maintain main structure and extension characteristics when dealing with dense junction areas, so a skeleton line extraction method considering stroke features has been proposed in this paper. Firstly, we put forward a long-edge adaptive node densification algorithm, which is used to construct boundary-constrained Delaunay triangulation to uniformly divide the polygon and extract the initial skeleton line. Secondly, we defined the triangles with three adjacent triangles (Type III) as the basic unit of junctions, then obtained the segmented areas with dense junctions on the basis of local width characteristics and correlation relationships of each Type III triangle. Finally, we concatenated the segments into strokes and corrected the initial skeleton lines based on the extension direction features of each stroke. The actual water network data of Jiangsu Province in China were used to verify the method. Experimental results show that the proposed method can better identify the areas with dense junctions and that the extracted skeleton line is naturally smooth and well-connected, which accurately reflects the main structure and extension characteristics of these areas.

Cartographic generalization is a problem, which poses interesting challenges to automation. Whereas plenty of algorithms have been developed for the different sub-problems of generalization (e.g., simplification, displacement, aggregation), there are still cases, which are not generalized adequately or in a satisfactory way. The main problem is the interplay between different operators. In those cases the human operator is the benchmark, who is able to design an aesthetic and correct representation of the physical reality. Deep learning methods have shown tremendous success for interpretation problems for which algorithmic methods have deficits. A prominent example is the classification and interpretation of images, where deep learning approaches outperform traditional computer vision methods. In both domains-computer vision and cartography-humans are able to produce good solutions. A prerequisite for the application of deep learning is the availability of many representative training examples for the situation to be learned. As this is given in cartography (there are many existing map series), the idea in this paper is to employ deep convolutional neural networks (DCNNs) for cartographic generalizations tasks, especially for the task of building generalization. Three network architectures, namely U-net, residual U-net and generative adversarial network (GAN), are evaluated both quantitatively and qualitatively in this paper. They are compared based on their performance on this task at target map scales 1:10,000, 1:15,000 and 1:25,000, respectively. The results indicate that deep learning models can successfully learn cartographic generalization operations in one single model in an implicit way. The residual U-net outperforms the others and achieved the best generalization performance.

Points on maps that stand for geographic objects such as settlements are generally connected by road networks. However, in the existing algorithms for point cluster simplification, points are usually viewed as discrete objects or their distances are considered in Euclidean spaces, and therefore the point cluster generalization results obtained by these algorithms are sometimes unreasonable. To take roads into consideration so that point clusters can be simplified in appropriate ways, the network Voronoi diagram is used and a new algorithm is proposed in this paper. First, the weighted network Voronoi diagram is constructed taking into account the weights of the points and the properties of the related road segments. Second, the network Voronoi polygons are generated and two factors (i.e., the area of the network Voronoi polygon and the total length of the dilated road segments in the polygon) are considered as the basis for point simplification. Last, a Cartesian coordinate system is built based on the two factors and the point clusters are simplified by means of the “concentric quadrants„. Our experiments show that the algorithm can effectively and correctly transmit types of information in the process of point cluster simplification, and the results are more reasonable than that generated by the ordinary Voronoi-based algorithm and the weighted Voronoi-based algorithm.

A computer application designed to generalize linear elements in a vector formatted cartographic set by means of two of the most contrasted line generalization algorithms, Douglas-Peucker simplification and Bézier curves based smoothing, is presented in this paper. Regarding codification, the simultaneous treatment of different lineal geometry entity classes and the conservation of their original topological relationships among them are considered. It is recommended in processes that produce small scale reductions (in a 1:2 relationship or similar). The application allows changing the characteristic parameters of the referred algorithms and proposes a report of the results obtained after every transformation. That way it supplies an additional facility as a trial tool to choose the parameters that give the best results in every process

Map generalization utilizes transformation operations to derive smaller-scale maps from larger-scale maps, and is a key procedure for the modelling and understanding of geographic space. Studies to date have largely applied a fixed tolerance to aggregate clustered buildings into a single object, resulting in the loss of details that meet cartographic constraints and may be of importance for users. This study aims to develop a method that amalgamates clustered buildings gradually without significant modification of geometry, while preserving the map details as much as possible under cartographic constraints. The amalgamation process consists of three key steps. First, individual buildings are grouped into distinct clusters by using the graph-based spatial clustering application with random forest (GSCARF) method. Second, building clusters are decomposed into scaling subgroups according to homogeneity with regard to the mean distance of subgroups. Thus, hierarchies of building clusters can be derived based on scaling subgroups. Finally, an amalgamation operation is progressively performed from the bottom-level subgroups to the top-level subgroups using the maximum distance of each subgroup as the amalgamating tolerance instead of using a fixed tolerance. As a consequence of this step, generalized intermediate scaling results are available, which can form the multi-scale representation of buildings. The experimental results show that the proposed method can generate amalgams with correct details, statistical area balance and orthogonal shape while satisfying cartographic constraints (e.g., minimum distance and minimum area).

The author first discusses the various ways of classifying cartographic generalization techniques, and then analyzes the course of the generalization process during the creation of a 1:50 000 topographic map on the basis of a 1:10 000 map. Using this analysis as a foundation, the author identifies, discusses and illustrates with examples the five types of cartographic generalization.

A critical problem in mapping data is the frequent updating of large data sets. To solve this problem, the updating of small-scale data based on large-scale data is very effective. Various map generalization techniques, such as simplification, displacement, typification, elimination, and aggregation, must therefore be applied. In this study, we focused on the elimination and aggregation of the building layer, for which each building in a large scale was classified as “0-eliminated,” “1-retained,” or “2-aggregated.” Machine-learning classification algorithms were then used for classifying the buildings. The data of 1:1000 scale and 1:25,000 scale digital maps obtained from the National Geographic Information Institute were used. We applied to these data various machine-learning classification algorithms, including naive Bayes (NB), decision tree (DT), k-nearest neighbor (k-NN), and support vector machine (SVM). The overall accuracies of each algorithm were satisfactory: DT, 88.96%; k-NN, 88.27%; SVM, 87.57%; and NB, 79.50%. Although elimination is a direct part of the proposed process, generalization operations, such as simplification and aggregation of polygons, must still be performed for buildings classified as retained and aggregated. Thus, these algorithms can be used for building classification and can serve as preparatory steps for building generalization.

This study proposes a template matching simplification method from the perspective of shape cognition based on the typical template characteristics of building distributions and representations. The method first formulates a series of templates to abstract the building shape by generalizing their polygons and analyzing their symbolic meanings, then conducts the simplification by searching and matching the most similar template that can be used later to replace the original building. On the premise of satisfying the individual geometric accuracy on a smaller scale, the proposed method can enhance the impression of well-known landmarks and reflect the pattern in mapping areas by the symbolic template. The turning function that describes shape by measuring the changes of the tangent-angle as a function of the arc-length is employed to obtain the similar distance between buildings and template polygons, and the least squares model is used to control the geometry matching of the candidate template. Experiments on real datasets are carried out to assess the usefulness of this method and compare it with two existing methods. The experiments suggest that our method can preserve the main structure of building shapes and geometric accuracy.

Road selection is a critical component of road network generalization that directly affects its accuracy. However, most conventional selection methods are based solely on either a linear or an areal representation mode, often resulting in low selection accuracy and biased structural selection. In this paper we propose an improved hybrid method combining the linear and areal representation modes to increase the accuracy of road selection. The proposed method offers two primary advantages. First, it improves the stroke generation algorithm in a linear representation mode by using an ordinary least square (OLS) model to consider overall information for the roads to be connected. Second, by taking advantage of the areal representation mode, the proposed method partitions road networks and calculates road density based on weighted Voronoi diagrams. Roads were selected using stroke importance and a density threshold. Finally, experiments were conducted comparing the proposed technique with conventional single representation methods. Results demonstrate the increased stroke generation accuracy and improved road selection achieved by this method.

Computational Ecology and Software ISSN 2220-721X URL: http://www.iaees.org/publications/journals/ces/online-version.asp RSS: http://www.iaees.org/publications/journals/ces/rss.xml E-mail: ces@iaees.org Editor-in-Chief: WenJun Zhang Aims and Scope COMPUTATIONAL ECOLOGY AND SOFTWARE (ISSN 2220-721X) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of computational ecology. It is the transactions of the International Society of Computational Ecology. The journal is concerned with the ecological researches, constructions and applications of theories and methods of computational sciences including computational mathematics, computational statistics and computer science. It features the simulation, approximation, prediction, recognition, and classification of ecological issues. Intensive computation is one of the major stresses of the journal. The journal welcomes research articles, short communications, review articles, perspectives, and book reviews. The journal also supports the activities of the International Society of Computational Ecology. The topics to be covered by CES include, but are not limited to: •Computation intensive methods, numerical and optimization methods, differential and difference equation modeling and simulation, prediction, recognition, classification, statistical computation (Bayesian computing, randomization, bootstrapping, Monte Carlo techniques, stochastic process, etc.), agent-based modeling, individual-based modeling, artificial neural networks, knowledge based systems, machine learning, genetic algorithms, data exploration, network analysis and computation, databases, ecological modeling and computation using Geographical Information Systems, satellite imagery, and other computation intensive theories and methods. •Artificial ecosystems, artificial life, complexity of ecosystems and virtual reality. •The development, evaluation and validation of software and algorithms for computational ecology. The development and evaluation of apparatus, instruments and machines for ecological and environmental analysis, investigation and monitoring based on the software of computational ecology. •Methodological applications of computational ecology in the researches of ecology and environmental sciences. Authors can submit their works to the email box of this journal, ces@iaees.org. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts. In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue.

Computational Ecology and Software ISSN 2220-721X URL: http://www.iaees.org/publications/journals/ces/online-version.asp RSS: http://www.iaees.org/publications/journals/ces/rss.xml E-mail: ces@iaees.org Editor-in-Chief: WenJun Zhang Aims and Scope COMPUTATIONAL ECOLOGY AND SOFTWARE (ISSN 2220-721X) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of computational ecology. It is the transactions of the International Society of Computational Ecology. The journal is concerned with the ecological researches, constructions and applications of theories and methods of computational sciences including computational mathematics, computational statistics and computer science. It features the simulation, approximation, prediction, recognition, and classification of ecological issues. Intensive computation is one of the major stresses of the journal. The journal welcomes research articles, short communications, review articles, perspectives, and book reviews. The journal also supports the activities of the International Society of Computational Ecology. The topics to be covered by CES include, but are not limited to: •Computation intensive methods, numerical and optimization methods, differential and difference equation modeling and simulation, prediction, recognition, classification, statistical computation (Bayesian computing, randomization, bootstrapping, Monte Carlo techniques, stochastic process, etc.), agent-based modeling, individual-based modeling, artificial neural networks, knowledge based systems, machine learning, genetic algorithms, data exploration, network analysis and computation, databases, ecological modeling and computation using Geographical Information Systems, satellite imagery, and other computation intensive theories and methods. •Artificial ecosystems, artificial life, complexity of ecosystems and virtual reality. •The development, evaluation and validation of software and algorithms for computational ecology. The development and evaluation of apparatus, instruments and machines for ecological and environmental analysis, investigation and monitoring based on the software of computational ecology. •Methodological applications of computational ecology in the researches of ecology and environmental sciences. Authors can submit their works to the email box of this journal, ces@iaees.org. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts. In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue.