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Keywords = cartographic symbolization

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24 pages, 4249 KB  
Article
Religious Cartography as a Segment of Thematic Cartography: A Case Study of the Archdiocese of Đakovo–Osijek
by Stanislav Frangeš, Brankica Malić and Robert Župan
Heritage 2025, 8(9), 356; https://doi.org/10.3390/heritage8090356 - 2 Sep 2025
Viewed by 743
Abstract
This research presents the development of a thematic map of the Archdiocese of Đakovo–Osijek, one of five Roman Catholic archdioceses in the Republic of Croatia. The map delineates contemporary ecclesiastical boundaries and key religious sites, while drawing on both historical and modern geospatial [...] Read more.
This research presents the development of a thematic map of the Archdiocese of Đakovo–Osijek, one of five Roman Catholic archdioceses in the Republic of Croatia. The map delineates contemporary ecclesiastical boundaries and key religious sites, while drawing on both historical and modern geospatial datasets. In addition to the final cartographic product, this paper emphasizes the methodological process of map creation, including data acquisition, historical georeferencing, symbol design, and GIS integration. The workflow is structured within a Historical GIS framework to ensure positional and semantic accuracy. The aim is not only to present a high-quality spatial representation but also to propose a reproducible methodology adaptable to other religious cartographic projects. Full article
(This article belongs to the Section Cultural Heritage)
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27 pages, 5349 KB  
Article
Proportional Symbol Maps: Value-Scale Types, Online Value-Scale Generator and User Perspectives
by Radek Barvir, Martin Holub and Alena Vondrakova
ISPRS Int. J. Geo-Inf. 2025, 14(9), 340; https://doi.org/10.3390/ijgi14090340 - 1 Sep 2025
Viewed by 1510
Abstract
Proportional symbol maps are a frequently used method of thematic cartography. Using an intuitive principle—the larger, the more—provides a simple and precise way of visualizing quantity in maps using geographic information systems (GIS). However, none of the current GIS software provides a proper [...] Read more.
Proportional symbol maps are a frequently used method of thematic cartography. Using an intuitive principle—the larger, the more—provides a simple and precise way of visualizing quantity in maps using geographic information systems (GIS). However, none of the current GIS software provides a proper map legend that could be used to interpret exact phenomenon quantity values from the map in reverse. Cartographers have been designing value scales manually for such a possibility of interpretation. Eventually, they preferred to resign to the accuracy of the interpretation and use the legend offered by the software. The paper describes the development of an easy-to-use online value scale generator for static maps, aiming to eliminate the time-consuming process to make map design more efficient while preserving the precision of cartographic visualization and its subsequent interpretation. The tool consists of a free web platform performing all necessary calculations and rendering an appropriate value scale based on user-defined input parameters. This functionality is performed for most typically used symbol shapes as well as for custom-design shapes provided by the user in SVG vector graphics. The output is then returned in a vector SVG and PDF file format to be used directly in a map legend or possibly edited in graphic software before such a step. The presented tool is therefore independent of which software was used for map design. Within the research, two user experiments were performed to compare generated value scales with simple legends generated in GIS and to gather insights from cartography experts. Full article
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45 pages, 54599 KB  
Article
Reintegrating Marginalized Rural Heritage: The Adaptive Potential of Barn Districts in Central Europe’s Cultural Landscapes
by Elżbieta Komarzyńska-Świeściak and Anna Alicja Wancel
Sustainability 2025, 17(15), 7166; https://doi.org/10.3390/su17157166 - 7 Aug 2025
Viewed by 1102
Abstract
Barn districts—ensembles of agricultural buildings situated at the edges of rural settlements—once played a key role in the spatial and economic organization of agrarian communities in Central Europe. Today, many of these structures remain marginalized and underexplored in contemporary landscape and heritage planning. [...] Read more.
Barn districts—ensembles of agricultural buildings situated at the edges of rural settlements—once played a key role in the spatial and economic organization of agrarian communities in Central Europe. Today, many of these structures remain marginalized and underexplored in contemporary landscape and heritage planning. This paper presents a comparative study of six barn districts in Poland’s Kraków-Częstochowa Upland, where vernacular construction, ecological adaptation, and local tradition shaped distinctive rural–urban interfaces. We applied a mixed-methods approach combining cartographic and archival analysis, field surveys, and interviews with residents and experts. The research reveals consistent patterns of landscape transformation, functional decline, and latent adaptive potential across varied morphological and material typologies. Despite differing levels of preservation, barn districts retain symbolic, spatial, and socio-cultural value for communities and local landscapes. The study emphasizes the importance of reintegrating these marginal heritage structures through adaptive reuse strategies rooted in the values of the New European Bauhaus—sustainability, aesthetics, and inclusion. The findings contribute to broader discussions on rural socio-ecological resilience and landscape-based development, highlighting how place-based strategies can bridge past identities with future-oriented spatial planning. Full article
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17 pages, 886 KB  
Article
Predicting Cartographic Symbol Location with Eye-Tracking Data and Machine Learning Approach
by Paweł Cybulski
J. Eye Mov. Res. 2025, 18(4), 35; https://doi.org/10.3390/jemr18040035 - 7 Aug 2025
Viewed by 539
Abstract
Visual search is a core component of map reading, influenced by both cartographic design and human perceptual processes. This study investigates whether the location of a target cartographic symbol—central or peripheral—can be predicted using eye-tracking data and machine learning techniques. Two datasets were [...] Read more.
Visual search is a core component of map reading, influenced by both cartographic design and human perceptual processes. This study investigates whether the location of a target cartographic symbol—central or peripheral—can be predicted using eye-tracking data and machine learning techniques. Two datasets were analyzed, each derived from separate studies involving visual search tasks with varying map characteristics. A comprehensive set of eye movement features, including fixation duration, saccade amplitude, and gaze dispersion, were extracted and standardized. Feature selection and polynomial interaction terms were applied to enhance model performance. Twelve supervised classification algorithms were tested, including Random Forest, Gradient Boosting, and Support Vector Machines. The models were evaluated using accuracy, precision, recall, F1-score, and ROC-AUC. Results show that models trained on the first dataset achieved higher accuracy and class separation, with AdaBoost and Gradient Boosting performing best (accuracy = 0.822; ROC-AUC > 0.86). In contrast, the second dataset presented greater classification challenges, despite high recall in some models. Feature importance analysis revealed that fixation standard deviation as a proxy for gaze dispersion, particularly along the vertical axis, was the most predictive metric. These findings suggest that gaze behavior can reliably indicate the spatial focus of visual search, providing valuable insight for the development of adaptive, gaze-aware cartographic interfaces. Full article
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19 pages, 4722 KB  
Article
Effect of Dynamic Point Symbol Visual Coding on User Search Performance in Map-Based Visualizations
by Weijia Ge, Jing Zhang, Xingjian Shi, Wenzhe Tang and Longlong Qian
ISPRS Int. J. Geo-Inf. 2025, 14(8), 305; https://doi.org/10.3390/ijgi14080305 - 5 Aug 2025
Viewed by 812
Abstract
As geographic information visualization continues to gain prominence, dynamic symbols are increasingly employed in map-based applications. However, the optimal visual coding for dynamic point symbols—particularly concerning encoding type, animation rate, and modulation area—remains underexplored. This study examines how these factors influence user performance [...] Read more.
As geographic information visualization continues to gain prominence, dynamic symbols are increasingly employed in map-based applications. However, the optimal visual coding for dynamic point symbols—particularly concerning encoding type, animation rate, and modulation area—remains underexplored. This study examines how these factors influence user performance in visual search tasks through two eye-tracking experiments. Experiment 1 investigated the effects of two visual coding factors: encoding types (flashing, pulsation, and lightness modulation) and animation rates (low, medium, and high). Experiment 2 focused on the interaction between encoding types and modulation areas (fill, contour, and entire symbol) under a fixed animation rate condition. The results revealed that search performance deteriorates as the animation rate of the fastest target symbol exceeds 10 fps. Flashing and lightness modulation outperformed pulsation, and modulation areas significantly impacted efficiency and accuracy, with notable interaction effects. Based on the experimental results, three visual coding strategies are recommended for optimal performance in map-based interfaces: contour pulsation, contour flashing, and entire symbol lightness modulation. These findings provide valuable insights for optimizing the design of dynamic point symbols, contributing to improved user engagement and task performance in cartographic and geovisual applications. Full article
(This article belongs to the Topic Theories and Applications of Human-Computer Interaction)
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22 pages, 6495 KB  
Article
Automated Icon Extraction from Tourism Maps: A Synergistic Approach Integrating YOLOv8x and SAM
by Di Cao, Xinran Yan, Jingjing Li, Jiayao Li and Lili Wu
ISPRS Int. J. Geo-Inf. 2025, 14(2), 55; https://doi.org/10.3390/ijgi14020055 - 30 Jan 2025
Cited by 2 | Viewed by 1400
Abstract
Map symbols play a crucial role in cartographic representation. Among these symbols, icons are particularly valued for their vivid and intuitive designs, making them widely utilized in tourist maps. However, the diversity and complexity of these symbols present significant challenges to cartographic workflows. [...] Read more.
Map symbols play a crucial role in cartographic representation. Among these symbols, icons are particularly valued for their vivid and intuitive designs, making them widely utilized in tourist maps. However, the diversity and complexity of these symbols present significant challenges to cartographic workflows. Icon design often relies on manual drawing, which is not only time-consuming but also heavily dependent on specialized skills. Automating the extraction of symbols from existing maps could greatly enhance the map symbol database, offering a valuable resource to support both symbol design and map production. Nevertheless, the intricate shapes and dense distribution of symbols in tourist maps complicate the accurate and efficient detection and extraction using existing methods. Previous studies have shown that You Only Look Once (YOLO) series models demonstrate strong performance in object detection, offering high accuracy and speed. However, these models are less effective in fine-grained boundary segmentation. To address this limitation, this article proposes integrating YOLO models with the Segment Anything Model (SAM) to tackle the challenges of combining efficient detection with precise segmentation. This article developed a dataset consisting of both paper-based and digital tourist maps, with annotations for five main categories of symbols: human landscapes, natural sceneries, humans, animals, and cultural elements. The performance of various YOLO model variants was systematically evaluated using this dataset. Additionally, a user interaction mechanism was incorporated to review and refine detection results, which were subsequently used as prompts for the SAM to perform precise symbol segmentation. The results indicate that the YOLOv8x model achieved excellent performance on the tourist map dataset, with an average detection accuracy of 94.4% across the five symbol categories, fully meeting the requirements for symbol detection tasks. The inclusion of a user interaction mechanism enhanced the reliability and flexibility of detection outcomes, while the integration of the SAM significantly improved the precision of symbol boundary extraction. In conclusion, the integration of YOLOv8x and SAM provides a robust and effective solution for automating the extraction of map symbols. This approach not only reduces the manual workload involved in dataset annotation, but also offers valuable theoretical and practical insights for enhancing cartographic efficiency. Full article
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24 pages, 6475 KB  
Article
Towards AI-Assisted Mapmaking: Assessing the Capabilities of GPT-4o in Cartographic Design
by Abdulkadir Memduhoğlu
ISPRS Int. J. Geo-Inf. 2025, 14(1), 35; https://doi.org/10.3390/ijgi14010035 - 17 Jan 2025
Cited by 4 | Viewed by 3646
Abstract
Cartographic design is fundamental to effective mapmaking, requiring adherence to principles such as visual hierarchy, symbolization, and color theory to convey spatial information accurately and intuitively, while Artificial Intelligence (AI) and Large Language Models (LLMs) have transformed various fields, their application in cartographic [...] Read more.
Cartographic design is fundamental to effective mapmaking, requiring adherence to principles such as visual hierarchy, symbolization, and color theory to convey spatial information accurately and intuitively, while Artificial Intelligence (AI) and Large Language Models (LLMs) have transformed various fields, their application in cartographic design remains underexplored. This study assesses the capabilities of a multimodal advanced LLM, GPT-4o, in understanding and suggesting cartographic design elements, focusing on adherence to established cartographic principles. Two assessments were conducted: a text-to-text evaluation and an image-to-text evaluation. In the text-to-text assessment, GPT-4o was presented with 15 queries derived from key concepts in cartography, covering classification, symbolization, visual hierarchy, color theory, and typography. Each query was posed multiple times under different temperature settings to evaluate consistency and variability. In the image-to-text evaluation, GPT-4o analyzed maps containing deliberate cartographic errors to assess its ability to identify issues and suggest improvements. The results indicate that GPT-4o demonstrates general reliability in text-based tasks, with variability influenced by temperature settings. The model showed proficiency in classification and symbolization tasks but occasionally deviated from theoretical expectations. In visual hierarchy and layout, the model performed consistently, suggesting appropriate design choices. In the image-to-text assessment, GPT-4o effectively identified critical design flaws such as inappropriate color schemes, poor contrast and misuse of shape and size variables, offering actionable suggestions for improvement. However, limitations include dependency on input quality and challenges in interpreting nuanced spatial relationships. The study concludes that LLMs like GPT-4o have significant potential in cartographic design, particularly for tasks involving creative exploration and routine design support. Their ability to critique and generate cartographic elements positions them as valuable tools for enhancing human expertise. Further research is recommended to enhance their spatial reasoning capabilities and expand their use of visual variables beyond color, thereby improving their applicability in professional cartographic workflows. Full article
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19 pages, 4203 KB  
Article
Exploring Cartographic Differences in Web Map Applications: Evaluating Design, Scale, and Usability
by Jakub Zejdlik and Vit Vozenilek
ISPRS Int. J. Geo-Inf. 2025, 14(1), 9; https://doi.org/10.3390/ijgi14010009 - 31 Dec 2024
Viewed by 3107
Abstract
Although there are many articles dealing with web map applications, they often focus on just one or a few applications. Several articles deal with the technical solution of the applications, but relatively few are focused on the cartographic aspects of these applications. This [...] Read more.
Although there are many articles dealing with web map applications, they often focus on just one or a few applications. Several articles deal with the technical solution of the applications, but relatively few are focused on the cartographic aspects of these applications. This article evaluates eight web mapping applications based on six cartographic aspects: map key, map scale, map layout, navigation elements, labels, and analytical tools. The objective is to identify differences in the presentation of geographic information and propose improvements for cartographic quality and user-friendliness. The methodology involved visual analysis at two scales. The comparison included applications such as Mapy.cz, OpenStreetMap, Google Maps, Bing Maps, HERE Maps, MapQuest, ViaMichelin, and Locus Map. The results revealed significant differences among the applications that may impact user orientation and experience. For instance, Google Maps does not display forest symbols on its default map, which can reduce clarity, whereas Mapy.cz offers the most comprehensive range of analytical tools. Advertisements in applications like MapQuest and ViaMichelin disrupt the user experience, and some applications lack essential functions, such as distance measurement. The paper identifies strengths and weaknesses in the cartographic design of these applications. Findings reveal that while each application possesses unique characteristics, they share common features. An interesting feature is the absence of cartographic symbols and labels of some elements in some applications. The study recommends the unification of cartographic principles and further user testing to optimize the layout and functionality of web mapping applications. Full article
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18 pages, 11676 KB  
Article
Mapping Localization Preferences for Residential Buildings
by Jacek Jabłoński, Łukasz Wielebski and Beata Medyńska-Gulij
ISPRS Int. J. Geo-Inf. 2024, 13(9), 329; https://doi.org/10.3390/ijgi13090329 - 15 Sep 2024
Viewed by 1685
Abstract
In this study, we tried to gauge the trends of localization preferences for residential buildings among young adults. The pragmatic dimension of these studies is important in the process of real estate investment, where a location can be expressed using indicators and statistical [...] Read more.
In this study, we tried to gauge the trends of localization preferences for residential buildings among young adults. The pragmatic dimension of these studies is important in the process of real estate investment, where a location can be expressed using indicators and statistical data and then, using maps, indicate preferred areas for living in a small town. The aim of our research was to examine and visualize the preferences of young people for living locations in relation to access to services. We conducted an online survey using a Likert scale to determine which services and amenities are most important for young residents. Using multi-criteria evaluation (MCE) methods and their formulas, we calculated the attractiveness coefficient of the location of residential buildings, which we propose to call the RBLAF (Residential Building’s Localization Attractiveness Factor). The results of this research are maps: qualitative–quantitative with point symbols for the structure of services and quantitative isochromatics showing the preferences of potential future investors in real estate. Full article
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24 pages, 33997 KB  
Article
The Symbolization of Regional Elements Based on Local-Chronicle Text Mining and Image-Feature Extraction
by Lili Wu, Di Cao, Jinjin Yang, Ruoyi Zhang and Xinran Yan
ISPRS Int. J. Geo-Inf. 2024, 13(9), 299; https://doi.org/10.3390/ijgi13090299 - 23 Aug 2024
Viewed by 1749
Abstract
In the context of the information age, the symbolization of regional elements has become a crucial component in modern cartographic practice. The targeted identification of regional elements and the design of map symbols are prerequisites for realizing the symbolization of regional elements. Therefore, [...] Read more.
In the context of the information age, the symbolization of regional elements has become a crucial component in modern cartographic practice. The targeted identification of regional elements and the design of map symbols are prerequisites for realizing the symbolization of regional elements. Therefore, we propose a method to symbolize regional elements by combining textual analysis and image processing. Firstly, local chronicles are used as the textual information source, and regional elements are extracted through textual data mining. Second, the real image data of the elements are selected, and the image segmentation algorithm, clustering algorithm, etc., are used to extract contours and colors from the images and carry out corresponding symbol simplification and color matching, to create highly recognizable symbols. Finally, we apply the symbols to two map types: the thematic map and the tourist map, and design a questionnaire to evaluate the outcomes of the symbol design. After a thorough review, it has been found that the method is superior to related symbolization studies in terms of data source authority, symbol generation efficiency, and symbol information carrying. In conclusion, guided by interdisciplinary thinking, this study effectively combines theoretical analysis and design practice, proposes a new idea of symbolization, and opens up a new way for geographic information visualization. Full article
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18 pages, 8018 KB  
Article
Collaborative Methods of Resolving Road Graphic Conflicts Based on Cartographic Rules and Generalization Operations
by Chuanbang Zheng, Qingsheng Guo, Lin Wang, Yuangang Liu and Jianfeng Jiang
ISPRS Int. J. Geo-Inf. 2024, 13(5), 154; https://doi.org/10.3390/ijgi13050154 - 6 May 2024
Cited by 1 | Viewed by 1675
Abstract
The resolution of road graphic conflicts is a key aspect of map generalization, which involves both scale reduction and the symbolization of map features. This study proposes collaborative methods of road graphic conflict resolution considering different road characteristics. These methods consider both geometric [...] Read more.
The resolution of road graphic conflicts is a key aspect of map generalization, which involves both scale reduction and the symbolization of map features. This study proposes collaborative methods of road graphic conflict resolution considering different road characteristics. These methods consider both geometric and semantic characteristics, and they incorporate the bend characteristics of roads, the road symbol size, and road semantics. Constrained Delaunay triangulation skeleton lines are used to categorize road graphic conflicts, which are made up of four independent conflict types and four group conflict types. Based on their characteristics, three collaborative methods are designed to deal with the different types of road graphic conflicts: collaboration between deletion and the snake displacement model, collaboration between the snake displacement model and collinearity, and collaboration among simplification, smoothing, and the beam displacement model. Two types of independent conflicts can be processed using only one simple operation. This study summarizes the cartographic rules for resolving road graphic conflicts, and these are used along with geometric features to drive the collaborative methods or one simple operation presented here. The experimental results indicate that the method proposed in this study can effectively resolve road graphic conflicts. Full article
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15 pages, 6373 KB  
Article
Animating Cartographic Meaning: Unveiling the Impact of Pictorial Symbol Motion Speed in Preattentive Processing
by Paweł Cybulski
ISPRS Int. J. Geo-Inf. 2024, 13(4), 118; https://doi.org/10.3390/ijgi13040118 - 3 Apr 2024
Cited by 3 | Viewed by 2452
Abstract
The primary objective of this study is to assess how the motion of dynamic point symbols impacts preattentive processing on a map. Specifically, it involves identifying the motion velocity parameters for cartographic animated pictorial symbols that contribute to the preattentive perception of the [...] Read more.
The primary objective of this study is to assess how the motion of dynamic point symbols impacts preattentive processing on a map. Specifically, it involves identifying the motion velocity parameters for cartographic animated pictorial symbols that contribute to the preattentive perception of the target symbols. We created five pictorial symbols, each accompanied by a unique animation tailored to convey the meaning associated with each symbol. The animation dynamics of symbols on the administrative map were distributed across arithmetic, logarithmic, and exponential scales. Eye-tracking technology was utilized to explain the user’s visual attention. The key findings reveal that, although movement does not uniformly hold the same designation in cartographic communication, it could guide user attention to identify the value peaks in quantitative map visualization. Motion velocity enhances the salience of animated symbols, making them stand out, not only against static elements but also against other animated distractors. Additionally, motion distributions between symbol classes based on exponential or arithmetic scales were identified as the most successful. Nevertheless, certain types of motion, such as rotational, do not perform well with pictorial symbols, even on the most effective motion distribution scale. Full article
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17 pages, 3383 KB  
Article
Measuring Efficiency and Accuracy in Locating Symbols on Mobile Maps Using Eye Tracking
by Wojciech Rymarkiewicz, Paweł Cybulski and Tymoteusz Horbiński
ISPRS Int. J. Geo-Inf. 2024, 13(2), 42; https://doi.org/10.3390/ijgi13020042 - 30 Jan 2024
Cited by 1 | Viewed by 2868
Abstract
This study investigated the impact of smartphone usage frequency on the effectiveness and accuracy of symbol location in a variety of spatial contexts on mobile maps using eye-tracking technology while utilizing the example of Mapy.cz. The scanning speed and symbol detection were also [...] Read more.
This study investigated the impact of smartphone usage frequency on the effectiveness and accuracy of symbol location in a variety of spatial contexts on mobile maps using eye-tracking technology while utilizing the example of Mapy.cz. The scanning speed and symbol detection were also considered. The use of mobile applications for navigation is discussed, emphasizing their popularity and convenience of use. The importance of eye tracking as a valuable tool for testing the usability of cartographic products, enabling the assessment of users’ visual strategies and their ability to memorize information, was highlighted. The frequency of smartphone use has been shown to be an important factor in users’ ability to locate symbols in different spatial contexts. Everyday smartphone users have shown higher accuracy and efficiency in image processing, suggesting a potential link between habitual smartphone use and increased efficiency in mapping tasks. Participants who were dissatisfied with the legibility of a map looked longer at the symbols, suggesting that they put extra cognitive effort into decoding the symbols. In the present study, gender differences in pupil size were also observed during the study. Women consistently showed a larger pupil diameter, potentially indicating greater cognitive load on the participants. Full article
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14 pages, 4142 KB  
Article
Motion Velocity as a Preattentive Feature in Cartographic Symbolization
by Paweł Cybulski and Vassilios Krassanakis
J. Eye Mov. Res. 2023, 16(4), 1-14; https://doi.org/10.16910/jemr.16.4.1 - 14 Sep 2023
Cited by 9 | Viewed by 1240
Abstract
The presented study aims to examine the process of preattentive processing of dynamic point symbols used in cartographic symbology. More specifically, we explore different motion types of geometric symbols on a map together with various motion velocity distribution scales. The main hypothesis is [...] Read more.
The presented study aims to examine the process of preattentive processing of dynamic point symbols used in cartographic symbology. More specifically, we explore different motion types of geometric symbols on a map together with various motion velocity distribution scales. The main hypothesis is that, in specific cases, motion velocity of dynamic point symbols is the feature that could be perceived preattentively on a map. In a controlled laboratory experiment, with 103 participants and eye tracking methods, we used administrative border maps with animated symbols. Participants’ task was to find and precisely identify the fastest changing symbol. It turned out that not every type of motion could be perceived preattentively even though the motion distribution scale did not change. The same applied to symbols’ shape. Eye movement analysis revealed that successful detection was closely related to the fixation on the target after initial preattentive vision. This confirms a significant role of the motion velocity distribution and the usage of symbols’ shape in cartographic design of animated maps. Full article
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17 pages, 322336 KB  
Article
Metric and Color Modifications for the Automated Construction of Map Symbols
by Xinyu Gong, Tian Lan and Peng Ti
ISPRS Int. J. Geo-Inf. 2023, 12(8), 331; https://doi.org/10.3390/ijgi12080331 - 8 Aug 2023
Cited by 2 | Viewed by 2246
Abstract
Personalized mappings become popular among the public with the support of data diversity and device diversity. To develop personalized maps, constructing map symbols through automated ways is beneficial. The formal representation of map symbols (i.e., expressing map symbols by mathematical operators) is fundamental [...] Read more.
Personalized mappings become popular among the public with the support of data diversity and device diversity. To develop personalized maps, constructing map symbols through automated ways is beneficial. The formal representation of map symbols (i.e., expressing map symbols by mathematical operators) is fundamental to the automated construction of map symbols. A previous study to evaluate the feasibility of structures of Chinese characters for representing map symbols shows that 77.5% of map symbols can be represented by them, although there are imperfections in some cases. It means that: (1) the other 22.5% of symbols should be formally represented by other mathematical solutions, and (2) those imperfect cases should be made perfect through some modification or refinements. In this study, we solve the representation problems of these two types of map symbols (i.e., the map symbol did not or imperfectly fit the structures of Chinese characters) by employing additional basic operators and proposing some metric and color modifications. To validate these proposed solutions, experiments have been carried out by using eight sets of symbols that are publicly available (e.g., Google Icons). The results indicated that almost all the map symbols can be formally represented with additional operators and metric and color modifications. The percentages of map symbols that did not fit structures of Chinese characters solved by these operators and modifications are 2.4% and 20.1%, respectively. The percentages of map symbols that imperfectly fit them solved by these operators and modifications are 8.7% and 8%, respectively. This work could not only enrich cartographic theory but also prompt the mathematization of map symbol construction. Full article
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