Thematic maps allow for the visual analysis of spatial data. When comparing two map states, preserving the mental map of a user facilitates the comparison. One way to achieve this is to use animated transitions between the states. This work presents an algorithm for computing such animations, called morphs, between schematized map objects, a technique particularly pertinent in urban mobility scenarios where schematic maps improve map legibility. In schematic maps, abstraction is used to reduce the visual complexity while still conveying information on a selected phenomenon. Our method ensures that the morph has four favorable properties: (1) it is self-intersection-free, (2) it maintains the schematization of the input features, (3) it is self-contained, and (4) every segment moves at its own constant velocity. We present an efficient algorithm to compute vertex traces and the timing of the morph. We evaluate our approach on isochrones visualizing travel times and on different layouts of schematic transit networks. The results show that the additional constraints we induce on the morphing only have a minor influence on the optimization target while they reduce the complexity of the animation.

doi:10.1007/s41651-024-00198-w

@article{ForschKemna2024,
    abstract = {Thematic maps allow for the visual analysis of spatial data. When comparing two map states, preserving the mental map of a user facilitates the comparison. One way to achieve this is to use animated transitions between the states. This work presents an algorithm for computing such animations, called morphs, between schematized map objects, a technique particularly pertinent in urban mobility scenarios where schematic maps improve map legibility. In schematic maps, abstraction is used to reduce the visual complexity while still conveying information on a selected phenomenon. Our method ensures that the morph has four favorable properties: (1) it is self-intersection-free, (2) it maintains the schematization of the input features, (3) it is self-contained, and (4) every segment moves at its own constant velocity. We present an efficient algorithm to compute vertex traces and the timing of the morph. We evaluate our approach on isochrones visualizing travel times and on different layouts of schematic transit networks. The results show that the additional constraints we induce on the morphing only have a minor influence on the optimization target while they reduce the complexity of the animation.},
    author = {Forsch, Axel and Kemna, Ruben and Langetepe, Elmar and Haunert, Jan-Henrik},
    doi = {10.1007/s41651-024-00198-w},
    issue = {37},
    journal = {Journal of Geovisualization and Spatial Analysis},
    pages = {},
    title = {Polyline Morphing for Animated Schematic Maps},
    volume = {8},
    year = {2024}
}

With the ubiquity of mobile devices that are capable of tracking positions (be it via GPS or Wi-Fi/mobile network localization), there is a continuous stream of location data being generated every second. These location measurements are typically not considered individually but rather as sequences, each of which reflects the movement of one person or vehicle, which we call trajectory. This chapter presents new algorithmic approaches to process and visualize trajectories both in the network-constrained and the unconstrained case.

doi:10.1007/978-3-031-35374-1_3

@incollection{forsch2024volunteered,
    abstract = {With the ubiquity of mobile devices that are capable of tracking positions (be it via GPS or Wi-Fi/mobile network localization), there is a continuous stream of location data being generated every second. These location measurements are typically not considered individually but rather as sequences, each of which reflects the movement of one person or vehicle, which we call trajectory. This chapter presents new algorithmic approaches to process and visualize trajectories both in the network-constrained and the unconstrained case.},
    address = {Cham},
    author = {Forsch, Axel and Funke, Stefan and Haunert, Jan-Henrik and Storandt, Sabine},
    booktitle = {Volunteered Geographic Information: Interpretation, Visualization and Social Context},
    doi = {10.1007/978-3-031-35374-1_3},
    editor = {Burghardt, Dirk and Demidova, Elena and Keim, Daniel A.},
    isbn = {978-3-031-35374-1},
    pages = {43--77},
    publisher = {Springer Nature Switzerland},
    title = {Efficient Mining of Volunteered Trajectory Datasets},
    year = {2024}
}

Due to the global climate change and increasing traffic volumes in cities, a shift from individual to public and multimodal transport is aspired. Travel time is one of the most important aspects for many people when choosing their mode of trans- portation. This leads to the requirement that changes in travel times have to be considered when planning new public trans- port infrastructure. This research paper presents and compares different techniques for visualizing the impact of new lines in existing public transport networks on travel times. The general approach of simulating timetable data and calculating intermodal travel times considering public transport and walking is being applied to two current infrastructure projects in the city of Bonn and the surrounding region. The created maps generally aim to visualize the spread in travel times between existing and extended transportation networks discretized by different spatial units such as rectangles or postal code areas. In comparison to other common methods which typically require two maps for two different scenarios (e.g. in case of isochro- nes), our approach gives the opportunity to combine all relevant information within one map. It is also shown how to apply bivariate choropleth maps for displaying travel times and how to visualize improvements in the accessibility of multiple target points of interest at once.

doi:https://doi.org/10.1007/s42489-024-00167-9

@article{Baltzer2024,
    abstract = {Due to the global climate change and increasing traffic volumes in cities, a shift from individual to public and multimodal
transport is aspired. Travel time is one of the most important aspects for many people when choosing their mode of trans-
portation. This leads to the requirement that changes in travel times have to be considered when planning new public trans-
port infrastructure. This research paper presents and compares different techniques for visualizing the impact of new lines
in existing public transport networks on travel times. The general approach of simulating timetable data and calculating
intermodal travel times considering public transport and walking is being applied to two current infrastructure projects in
the city of Bonn and the surrounding region. The created maps generally aim to visualize the spread in travel times between
existing and extended transportation networks discretized by different spatial units such as rectangles or postal code areas. In
comparison to other common methods which typically require two maps for two different scenarios (e.g. in case of isochro-
nes), our approach gives the opportunity to combine all relevant information within one map. It is also shown how to apply
bivariate choropleth maps for displaying travel times and how to visualize improvements in the accessibility of multiple
target points of interest at once.},
    author = {Baltzer, Dorian and Haunert, Jan-Henrik and Forsch, Axel},
    doi = {https://doi.org/10.1007/s42489-024-00167-9},
    journal = {KN - Journal of Cartography and Geographic Information},
    publisher = {Springer},
    title = {Visualizing the Influence of New Public Transport Infrastructure on Travel Times},
    url = {https://link.springer.com/article/10.1007/s42489-024-00167-9},
    year = {2024}
}

doi:10.1080/00087041.2023.2284436

@article{ForschHaunert2024,
    author = {Axel Forsch and Jan-Henrik Haunert},
    doi = {10.1080/00087041.2023.2284436},
    issue = {4},
    journal = {The Cartographic Journal},
    pages = {383--401},
    title = {Metrochrones: Schematic Isochrones for Schematic Metro Maps},
    volume = {60},
    year = {2023}
}

doi:10.1145/3615899.3627931

@inproceedings{arzoumanidis2023catchment,
    address = {Hamburg, Germany},
    author = {Lukas Arzoumanidis and Axel Forsch and Jan-Henrik and Youness Dehbi},
    booktitle = {Proc. 1st ACM SIGSPATIAL Workshop on Sustainable Mobility},
    doi = {10.1145/3615899.3627931},
    title = {Catchment cell visualization for multi-modal public transportation networks},
    year = {2023}
}

The optimal path between two vertices in a graph depends on the optimization objective, which is often defined as a weighted sum of multiple criteria. When integrating two criteria, their relative importance is expressed with a balance factor α. We present a new approach for inferring α from trajectories. The core of our approach is a compression algorithm that requires a graph G representing a transportation network, two edge costs modeling routing criteria, and a path P in G representing the trajectory. It yields a minimum subsequence S of the sequence of vertices of P and a balance factor α, such that the path P can be fully reconstructed from S, G, its edge costs, and α. By minimizing the size of S over α, we learn the balance factor that corresponds best to the user's routing preferences. In an evaluation with crowd-sourced cycling trajectories, we weigh the usage of official signposted cycle routes against other routes. More than 50% of the trajectories can be segmented into five optimal sub-paths or less. Almost 40% of the trajectories indicate that the cyclist is willing to take a detour of 50% over the geodesic shortest path to use an official cycle path.

doi:10.5311/JOSIS.2023.26.256

@article{forsch2023inferring,
    abstract = {The optimal path between two vertices in a graph depends on the optimization objective, which is often defined as a weighted sum of multiple criteria. When integrating two criteria, their relative importance is expressed with a balance factor α. We present a new approach for inferring α from trajectories. The core of our approach is a compression algorithm that requires a graph G representing a transportation network, two edge costs modeling routing criteria, and a path P in G representing the trajectory. It yields a minimum subsequence S of the sequence of vertices of P and a balance factor α, such that the path P can be fully reconstructed from S, G, its edge costs, and α. By minimizing the size of S over α, we learn the balance factor that corresponds best to the user's routing preferences. In an evaluation with crowd-sourced cycling trajectories, we weigh the usage of official signposted cycle routes against other routes. More than 50% of the trajectories can be segmented into five optimal sub-paths or less. Almost 40% of the trajectories indicate that the cyclist is willing to take a detour of 50% over the geodesic shortest path to use an official cycle path.},
    author = {Axel Forsch and Johannes Oehrlein and Benjamin Niedermann and Jan-Henrik Haunert},
    doi = {10.5311/JOSIS.2023.26.256},
    journal = {Journal of Spatial Information Science},
    number = {5},
    pages = {99--124},
    title = {Inferring routing preferences from user-generated trajectories using a compression criterion},
    volume = {26},
    year = {2023}
}

doi:10.5194/ica-abs-5-89-2022

@article{korir2022modalsplit,
    address = {Vienna},
    author = {Korir, Victor and Forsch, Axel and Dehbi, Youness and Haunert, Jan-Henrik},
    doi = {10.5194/ica-abs-5-89-2022},
    journal = {Abstracts of the ICA},
    month = {sep},
    pages = {89},
    title = {Visualizing the Modal Split in Public Transportation Networks},
    volume = {5},
    year = {2022}
}

Ever since location-based services and mobile applications collecting data gathered through Global Navigation Satellite System (GNSS) positioning have become popular, concerns about location privacy have been expressed. Research has shown that human trajectory repositories containing sequences of observed locations ordered in time constitute a rich source for analyzing movement patterns, but they can also reveal sensitive personal information, such as a person’s home address. In this paper, we present a mechanism that protects visits to sensitive locations by suppressing revealing parts of trajectories. Our attack model acknowledges that the course of a trajectory, combined with spatial context information, can facilitate privacy breaches even if sensitive locations have been concealed. Thus, we introduce the concept of k-site-unidentifiability, a specialization of k-anonymity, under which a sensitive location cannot be singled out from a group of at least k sites that the trajectory could have visited. In an experimental study, we show that our method is utility-preserving and protects sensitive locations reliably even in sparsely built environments. As it can process each trajectory independently, individuals may also use our mechanism to enhance their privacy before publishing their trajectories.

doi:10.1080/13658816.2022.2081694

@article{brauer2022myhome,
    abstract = {Ever since location-based services and mobile applications collecting data gathered through Global Navigation Satellite System (GNSS) positioning have become popular, concerns about location privacy have been expressed. Research has shown that human trajectory repositories containing sequences of observed locations ordered in time constitute a rich source for analyzing movement patterns, but they can also reveal sensitive personal information, such as a person’s home address. In this paper, we present a mechanism that protects visits to sensitive locations by suppressing revealing parts of trajectories. Our attack model acknowledges that the course of a trajectory, combined with spatial context information, can facilitate privacy breaches even if sensitive locations have been concealed. Thus, we introduce the concept of k-site-unidentifiability, a specialization of k-anonymity, under which a sensitive location cannot be singled out from a group of at least k sites that the trajectory could have visited. In an experimental study, we show that our method is utility-preserving and protects sensitive locations reliably even in sparsely built environments. As it can process each trajectory independently, individuals may also use our mechanism to enhance their privacy before publishing their trajectories.},
    author = {Anna Brauer and Ville M\"{a}kinen and Axel Forsch and Juha Oksanen and Jan-Henrik Haunert},
    doi = {10.1080/13658816.2022.2081694},
    eprint = {https://doi.org/10.1080/13658816.2022.2081694},
    journal = {International Journal of Geographical Information Science},
    number = {12},
    pages = {2496--2524},
    publisher = {Taylor \& Francis},
    title = {My home is my secret: concealing sensitive locations by context-aware trajectory truncation},
    url = {https://doi.org/10.1080/13658816.2022.2081694},
    volume = {36},
    year = {2022}
}

In the context of volunteered geographic information, large sets of trajectories of humans and animals are collected. Analyzing these trajectories visually is often complicated due to limited display sizes. For instance, when a user chooses a large map scale to inspect the details of a trajectory, only a small part of the trajectory is visible in the map. Therefore, in this article, we present an approach for visualizing the off-screen evolution of trajectories, i.e., their continuation outside of the displayed map. We propose visual cues in the form of glyphs that are displayed at the map's boundary and that consist of one or multiple disk sectors of varying size and opening angle. These glyphs indicate the direction and variability of direction of a trajectory's continuation outside the map frame. We present an algorithm for computing the glyphs efficiently and evaluate them in a user study. The results show that the glyphs are intuitive to understand even without explanation. We further present suggestions for improving the glyph design based on the results.

doi:10.1007/s42489-022-00106-6

@article{forsch2022offscreen,
    abstract = {In the context of volunteered geographic information, large sets of trajectories of humans and animals are collected. Analyzing these trajectories visually is often complicated due to limited display sizes. For instance, when a user chooses a large map scale to inspect the details of a trajectory, only a small part of the trajectory is visible in the map. Therefore, in this article, we present an approach for visualizing the off-screen evolution of trajectories, i.e., their continuation outside of the displayed map. We propose visual cues in the form of glyphs that are displayed at the map's boundary and that consist of one or multiple disk sectors of varying size and opening angle. These glyphs indicate the direction and variability of direction of a trajectory's continuation outside the map frame. We present an algorithm for computing the glyphs efficiently and evaluate them in a user study. The results show that the glyphs are intuitive to understand even without explanation. We further present suggestions for improving the glyph design based on the results.},
    author = {Forsch, Axel and Amann, Friederike and Haunert, Jan-Henrik},
    day = {18},
    doi = {10.1007/s42489-022-00106-6},
    issn = {2524-4965},
    journal = {KN - Journal of Cartography and Geographic Information},
    month = {May},
    number = {3},
    pages = {201--212},
    title = {Visualizing the Off-Screen Evolution of Trajectories},
    volume = {72},
    year = {2022}
}

Travel-time maps are an important tool for analyzing the efficacy of public transportation systems. These maps display one or multiple isochrones. An isochrone is a line of equal travel time, which means that reaching any point on it from a given starting point requires the same amount of time. As timetables are usually very irregular over the course of a week, travel-time maps are highly variant with respect to the starting time. Thus, for an extensive analysis of the network, this variance has to be visualized appropriately. One way of doing this is by using a digital map with animated transitions between different isochrones, so called morphs. In this work, we present an algorithm for computing such morphs between isochrones, particularly targeting schematized travel-time maps as they are often used for visualization in the context of public transportation. In our current research, we are optimizing the morphing between two given polygonal lines. In future research we plan to extend the approach to finding the correct polygon correspondences in the given isochrones.

@inproceedings{forsch2022morphing,
    abstract = {Travel-time maps are an important tool for analyzing the efficacy of public transportation systems. These maps display one or multiple isochrones. An isochrone is a line of equal travel time, which means that reaching any point on it from a given starting point requires the same amount of time. As timetables are usually very irregular over the course of a week, travel-time maps are highly variant with respect to the starting time. Thus, for an extensive analysis of the network, this variance has to be visualized appropriately. One way of doing this is by using a digital map with animated transitions between different isochrones, so called morphs. In this work, we present an algorithm for computing such morphs between isochrones, particularly targeting schematized travel-time maps as they are often used for visualization in the context of public transportation. In our current research, we are optimizing the morphing between two given polygonal lines. In future research we plan to extend the approach to finding the correct polygon correspondences in the given isochrones.},
    address = {Bochum},
    author = {Forsch, Axel and Kemna, Ruben and Langetepe, Elmar and Haunert, Jan-Henrik},
    booktitle = {3rd Schematic Mapping Workshop},
    month = {apr},
    note = {Poster abstract. Available at: https://www.ruhr-uni-bochum.de/schematicmapping/papers/smw-fklh.pdf},
    title = {Morphing of Schematized Polygons for Animated Travel-Time Maps},
    year = {2022}
}

We consider the problem of matching trajectories to a road map, giving particular consideration to trajectories that do not exclusively follow the underlying network. Such trajectories arise, for example, when a person walks through the inner part of a city, crossing market squares or parking lots. We call such trajectories semi-restricted. Sensible map matching of semi-restricted trajectories requires the ability to differentiate between restricted and unrestricted movement. We develop in this paper an approach that efficiently and reliably computes concise representations of such trajectories that maintain their semantic characteristics. Our approach utilizes OpenStreetMap data to not only extract the network but also areas that allow for free movement (as e.g. parks) as well as obstacles (as e.g. buildings). We discuss in detail how to incorporate this information in the map matching process, and demonstrate the applicability of our method in an experimental evaluation on real pedestrian and bicycle trajectories.

doi:10.4230/LIPIcs.GIScience.2021.II.12

@inproceedings{behr2021matching,
    abstract = {We consider the problem of matching trajectories to a road map, giving particular consideration to trajectories that do not exclusively follow the underlying network. Such trajectories arise, for example, when a person walks through the inner part of a city, crossing market squares or parking lots. We call such trajectories semi-restricted. Sensible map matching of semi-restricted trajectories requires the ability to differentiate between restricted and unrestricted movement. We develop in this paper an approach that efficiently and reliably computes concise representations of such trajectories that maintain their semantic characteristics. Our approach utilizes OpenStreetMap data to not only extract the network but also areas that allow for free movement (as e.g. parks) as well as obstacles (as e.g. buildings). We discuss in detail how to incorporate this information in the map matching process, and demonstrate the applicability of our method in an experimental evaluation on real pedestrian and bicycle trajectories.},
    address = {Dagstuhl, Germany},
    annote = {Keywords: map matching, OpenStreetMap, GPS, trajectory, road network},
    author = {Behr, Timon and van Dijk, Thomas C. and Forsch, Axel and Haunert, Jan-Henrik and Storandt, Sabine},
    booktitle = {Proc. 11th International Conference on Geographic Information Science (GIScience '21) - Part II},
    doi = {10.4230/LIPIcs.GIScience.2021.II.12},
    editor = {Janowicz, Krzysztof and Verstegen, Judith A.},
    isbn = {978-3-95977-208-2},
    issn = {1868-8969},
    pages = {12:1--12:16},
    publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
    series = {Leibniz International Proceedings in Informatics (LIPIcs)},
    title = {{Map Matching for Semi-Restricted Trajectories}},
    url = {https://drops.dagstuhl.de/opus/volltexte/2021/14771},
    urn = {urn:nbn:de:0030-drops-147717},
    volume = {208},
    year = {2021}
}

The automatic generation of travel-time maps is a prerequisite for many fields of application such as tourist assistance and spatial decision support systems. The task is to determine outlines of zones that are reachable from a user's location in a given amount of time. In this work, we focus on travel-time maps with a formally guaranteed separation property in the sense that a zone exactly contains the part of the road network that is reachable within a pre-defined time from a given starting point and start time. In contrast to other automated methods, our approach generates schematized travel-time maps that reduce the visual complexity by representing each zone by an octilinear polygon. We aim at octilinear polygons with a small number of bends to further optimize the legibility of the map. The reachable parts of the road network are determined by the integration of timetable information for different modes of public transportation and pedestrian walkways based on a multi-modal time-expanded network. Moreover, the generated travel-time maps visualize multiple travel times using a map overlay of different time zones. In experiments on real-world data we compare our schematic visualizations to travel-time maps created with other visualization techniques.

doi:10.1111/tgis.12821

@article{forsch2021isochrones,
    abstract = {The automatic generation of travel-time maps is a prerequisite for many fields of application such as tourist assistance and spatial decision support systems. The task is to determine outlines of zones that are reachable from a user's location in a given amount of time. In this work, we focus on travel-time maps with a formally guaranteed separation property in the sense that a zone exactly contains the part of the road network that is reachable within a pre-defined time from a given starting point and start time. In contrast to other automated methods, our approach generates schematized travel-time maps that reduce the visual complexity by representing each zone by an octilinear polygon. We aim at octilinear polygons with a small number of bends to further optimize the legibility of the map. The reachable parts of the road network are determined by the integration of timetable information for different modes of public transportation and pedestrian walkways based on a multi-modal time-expanded network. Moreover, the generated travel-time maps visualize multiple travel times using a map overlay of different time zones. In experiments on real-world data we compare our schematic visualizations to travel-time maps created with other visualization techniques.},
    author = {Forsch, Axel and Dehbi, Youness and Niedermann, Benjamin and Oehrlein, Johannes and Rottmann, Peter and Haunert, Jan-Henrik},
    doi = {10.1111/tgis.12821},
    journal = {Transactions in GIS},
    number = {6},
    pages = {3233--3256},
    title = {Multimodal Travel-Time Maps with Formally Correct and Schematic Isochrones},
    volume = {25},
    year = {2021}
}