Mahmuda Ahmed

A comparison and evaluation of map construction algorithms using vehicle tracking data

Map construction methods automatically produce and/or update street map datasets using vehicle tracking data. Enabled by the ubiquitous generation of geo-referenced tracking data, there has been a recent surge in map construction algorithms coming from different computer science domains. A cross-comparison of the various algorithms is still very rare, since (i) algorithms and constructed maps are generally not publicly available and (ii) there is no standard approach to assess the result quality, given the lack of benchmark data and quantitative evaluation methods. This work represents a first comprehensive attempt to benchmark such map construction algorithms. We provide an evaluation and comparison of seven algorithms using four datasets and four different evaluation measures. In addition to this comprehensive comparison, we make our datasets, source code of map construction algorithms and evaluation measures publicly available on http://mapconstruction.org.. This site has been established as a repository for map construction data and algorithms and we invite other researchers to contribute by uploading code and benchmark data supporting their contributions to map construction algorithms.

Constructing street networks from GPS trajectories

We consider the problem of constructing street networks from geo-referenced trajectory data: Given a set of trajectories in the plane, compute a street network that represents all trajectories in the set. We present a simple and practical incremental algorithm that is based on partial matching of the trajectories to the graph. We use minimumlink paths to reduce the complexity of the reconstructed graph. We provide quality guarantees and experimental results based on both real and synthetic data. For the partial matching we introduce a new variant of partial Frechet distance.

Local persistent homology based distance between maps

We define a topology-based distance metric between road networks embedded in the plane. This distance measure is based on local persistent homology, and employs a local distance signature that enables identification and visualization of local differences between the road networks. This paper is motivated by the need to recognize changes in road networks over time and to assess the quality of different map construction algorithms. One particular challenge is evaluating the results when no ground truth is known. However, we demonstrate that we can overcome this hurdle by using a statistical technique known as the bootstrap.

A Path-Based Distance for Street Map Comparison

Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ. However, the majority of current graph comparison algorithms are based on structural properties of graphs, such as their degree distribution or their local connectivity properties, and do not consider their spatial embedding. This ignores a key property of road networks since the similarity of travel over two road networks is intimately tied to the specific spatial embedding. Likewise, many current algorithms specific to street map comparison either do not provide quality guarantees or focus on spatial embeddings only. Motivated by road network comparison, we propose a new path-based distance measure between two planar geometric graphs that is based on comparing sets of travel paths generated over the graphs. Surprisingly, we are able to show that using paths of bounded link-length, we can capture global structural and spatial differences between the graphs. We show how to utilize our distance measure as a local signature in order to identify and visualize portions of high similarity in the maps. Finally, we present an experimental evaluation of our distance measure and its local signature on street map data from Berlin, Germany and Athens, Greece.

Map Construction Algorithms

The book provides an overview of the state-of-the-art of map construction algorithms, which use tracking data in the form of trajectories to generate vector maps. The most common trajectory type is GPS-based trajectories. It introduces three emerging algorithmic categories, outlines their general algorithmic ideas, and discusses three representative algorithms in greater detail. To quantify map construction algorithms, the authors include specific datasets and evaluation measures. The datasets, source code of map construction algorithms and evaluation measures are publicly available on http://www.mapconstruction.org. The web site serves as a repository for map construction data and algorithms and researchers can contribute by uploading their own code and benchmark data. Map Construction Algorithms is an excellent resource for professionals working in computational geometry, spatial databases, and GIS. Advanced-level students studying computer science, geography and mathematics will also find this book a useful tool.

Choosing thresholds for density-based map construction algorithms

Due to the ubiquitous use of various positioning technologies in smart phones and other devices, geospatial tracking data has become a routine data source. One of its uses that has gained recent popularity is the construction of street maps from vehicular tracking data. Due to the inherent noise in the data, many map construction algorithms are based on thresholding a density function. While kernel density estimation provides a firm theoretical foundation for computing the density from the measurements, the thresholds are generally picked in a heuristic, and often brute-force way, which results in slow algorithms with no guarantees on the map construction quality. In this paper, we formalize the selection of thresholds in a density-based street map construction algorithm. We propose a new thresholding technique that uses persistent homology combined with statistical analysis to determine a small set of thresholds that captures all relevant topological features. We formally prove that when the samples are drawn uniformly from the street map, a constant number of thresholds suffices to recover the street map. We also provide algorithms to compute the thresholds for different sampling assumptions. Finally, we show the effectiveness of our algorithms in several experiments on artificially generated data and on real GPS trajectory data.

On maximum weight objects decomposable into based rectilinear convex objects

Our main concern is the following variant of the image segmentation problem: given a weighted grid graph and a set of vertical and/or horizontal base lines crossing through the grid, compute a maximum-weight object which can be decomposed into based rectilinear convex objects with respect to the base lines. Our polynomial-time algorithm reduces the problem to solving a polynomial number of instances of the maximum flow problem.

Probabilistic street-intersection reconstruction from GPS trajectories: approaches and challenges

Analyzing and mining geo-referenced trajectory data has different aspects to researchers from different communities. For example, animal location data provides ecologists live points of contact between ecologies and the species. And by studying movements of individual animals, they have gained insight into population distributions, important resources, dispersal settings, social interaction or general patterns of how the space was used in an ecological system. Similarly, geologists and environmentalists use earthquake positional data for predicting the location of the next earthquake. Intelligent Transportation Systems and GIS communities use heuristic algorithms on vehicle trajectory data sets to construct or update digital street-maps that represent the data set. Recently, the Computational Geometry community started to give attention to the street-map construction problems as well, applying different approaches and providing quality guarantees. Although different communities use different types or aspects of the GPS data, they face one challenge in common: how to model or incorporate the impreciseness of the input data in their output. In this paper we discuss specifically the impact of spatial inaccuracy of GPS trajectory data on street-map reconstruction algorithms. In particular, we discuss approaches and challenges to associate that impreciseness with the reconstructed street-intersections.

Analysis of Minimum-energy Path-preserving Graphs for Ad-hoc Wireless Networks *

We consider ad-hoc wireless networks and the topology control problem defined as minimizing the amount of power needed to maintain connectivity. The issue boils down to selecting the optimum transmission power level at each node based on the position information of reachable nodes. Local decisions regarding the transmission power level induce a subgraph of the maximum powered graph G max in which edges represent direct reachability at maximum power. In this paper we propose an analysis for constructing minimum-energy path-preserving subgraphs of G max, i.e. subgraphs minimizing the energy consumption between node pairs. We also propose an algorithm for constructing subgraph of G max based on one-hop neighbor information. By presenting experimental results we show the effectiveness of our proposed algorithm.

TraceBundle Map Construction Algorithm

This chapter presents the TraceBundle algorithm, which is a representative of the intersection linking category of map construction algorithms . The main approach is to first detect intersection nodes, then “bundle” trajectories around them in order to construct edges. Changes in movement direction and speed are used as turn indicators, and similar turns are combined to form intersection nodes. In an improved version of the algorithm the hierarchical nature of the road network is considered and different road categories are taken into account. By segmenting the trajectories based on speed, hierarchical road network layers are derived which are then combined into a single network. Segmentation also addresses the challenges imposed by noisy, low-sampling rate trajectories and provides for a mechanism for accommodating incremental map updates.