Review and classification of trajectory summarisation algorithms: From compression to segmentation

With the continuous development and cost reduction of positioning and tracking technologies, a large amount of trajectories are being exploited in multiple domains for knowledge extraction. A trajectory is formed by a large number of measurements, where many of them are unnecessary to describe the actual trajectory of the vehicle, or even harmful due to sensor noise. This not only consumes large amounts of memory, but also makes the extracting knowledge process more difficult. Trajectory summarisation techniques can solve this problem, generating a smaller and more manageable representation and even semantic segments. In this comprehensive review, we explain and classify techniques for the summarisation of trajectories according to their search strategy and point evaluation criteria, describing connections with the line simplification problem. We also explain several special concepts in trajectory summarisation problem. Finally, we outline the recent trends and best practices to continue the research in next summarisation algorithms.

Error Bounded Line Simplification Algorithms for Trajectory Compression: An Experimental Evaluation

Nowadays, various sensors are collecting, storing, and transmitting tremendous trajectory data, and it is well known that the storage, network bandwidth, and computing resources could be heavily wasted if raw trajectory data is directly adopted. Line simplification algorithms are effective approaches to attacking this issue by compressing a trajectory to a set of continuous line segments, and are commonly used in practice. In this article, we first classify the error bounded line simplification algorithms into different categories and review each category of algorithms. We then study the data aging problem of line simplification algorithms and distance metrics from the views of aging friendliness and aging errors. Finally, we present a systematic experimental evaluation of representative error bounded line simplification algorithms, including both compression optimal and sub-optimal methods, in terms of commonly adopted perpendicular Euclidean, synchronous Euclidean, and direction-aware distances. Using real-life trajectory datasets, we systematically evaluate and analyze the performance (compression ratio, average error, running time, aging friendliness, and query friendliness) of error bounded line simplification algorithms with respect to distance metrics, trajectory sizes, and error bounds. Our study provides a full picture of error bounded line simplification algorithms, which leads to guidelines on how to choose appropriate algorithms and distance metrics for practical applications.

Analysis of the effectiveness of constraining metrics of geometric simplification algorithms based on expert evaluation of line detail

The paper reveals dependencies between the character of the line shape and combination of constraining metrics that allows comparable reduction in detail by different geometric simplification algorithms. The study was conducted in a form of the expert survey. geometrically simplified versions of three coastline fragments were prepared using three different geometric simplification algorithms—Douglas-peucker, Visvalingam-Whyatt and Li-Openshaw. Simplification was constrained by similar value of modified hausdorff distance (linear offset) and similar reduction of number of line bends (compression of the number of detail elements). Respondents were asked to give a numerical estimate of the detail of each image, based on personal perception, using a scale from one to ten. The results of the survey showed that lines perceived by respondents as having similar detail can be obtained by different algorithms. however, the choice of the metric used as a constraint depends on the nature of the line. Simplification of lines that have a shallow hierarchy of small bends is most effectively constrained by linear offset. As the line complexity increases, the compression metric for the number of detail elements (bends) increases its influence in the perception of detail. For one of the three lines, the best result was consistently obtained with a weighted combination of the analyzed metrics as a constraint. None of the survey results showed that only reducing the number of bends can be used as an effective characteristic of similar reduction in detail. It was therefore found that the linear offset metric is more indicative when describing changes in line detail.

Articulated Trajectory Mapping for Reviewing Walking Tours

This paper addresses how to enrich a map-based representation for reviewing walking tours with the features of trajectory mapping and tracing animation. Generally, a trajectory generated by raw GPS data can often be difficult to browse through on a map. To resolve this issue, we first illustrated tangled trajectory lines, inaccurate indoor positioning, and unstable trajectory lines as problems encountered when mapping raw trajectory data. Then, we proposed a new framework that focuses on GPS horizontal accuracy to locate indoor location points and find stopping points on an accelerometer. We also applied a conventional line simplification algorithm to make the trajectory cleaner and then integrated the extracted points with the clean trajectory line. Furthermore, our experiments with some actual logs of walking tours demonstrated that articulated trajectory mapping, which comprises simplification and characterization methods, sufficiently reliable and effective for better reviewing experiences. The paper contributes to the research on cleaning up map-based displays and tracing animations of raw trajectory GPS data by using not only location data but also sensor data that smartphones can collect.

A Vector Line Simplification Algorithm Based on the Douglas–Peucker Algorithm, Monotonic Chains and Dichotomy

When using the traditional Douglas–Peucker (D–P) algorithm to simplify linear objects, it is easy to generate results containing self-intersecting errors, thus affecting the application of the D–P algorithm. To solve the problem of self-intersection, a new vector line simplification algorithm based on the D–P algorithm, monotonic chains and dichotomy, is proposed in this paper. First, the traditional D–P algorithm is used to simplify the original lines, and then the simplified lines are divided into several monotonic chains. Second, the dichotomy is used to search the intersection positions of monotonic chains effectively, and intersecting monotonic chains are processed, thus solving the self-intersection problems. Two groups of experimental data are selected based on large data sets. Results demonstrate that the proposed experimental method has advantages in algorithmic efficiency and accuracy when compared to the D–P algorithm and the Star-shaped algorithm.

A Novel Method for Plane Extraction from Low-Resolution Inhomogeneous Point Clouds and its Application to a Customized Low-Cost Mobile Mapping System

Over the last decade, increasing demands for building interior mapping have brought the challenge of effectively and efficiently acquiring geometric information. Most mobile mapping methods rely on the integration of Simultaneous Localization And Mapping (SLAM) and costly Inertial Measurement Units (IMUs). Meanwhile, the methods also suffer misalignment errors caused by the low-resolution inhomogeneous point clouds captured using multi-line Mobile Laser Scanners (MLSs). While point-based alignments between such point clouds are affected by the highly dynamic moving patterns of the platform, plane-based methods are limited by the poor quality of the planes extracted, which reduce the methods’ robustness, reliability, and applicability. To alleviate these issues, we proposed and developed a method for plane extraction from low-resolution inhomogeneous point clouds. Based on the definition of virtual scanlines and the Enhanced Line Simplification (ELS) algorithm, the method extracts feature points, generates line segments, forms patches, and merges multi-direction fractions to form planes. The proposed method reduces the over-segmentation fractions caused by measurement noise and scanline curvature. A dedicated plane-to-plane point cloud alignment workflow based on the proposed plane extraction method was created to demonstrate the method’s application. The implementation of the coarse-to-fine procedure and the shortest-path initialization strategy eliminates the necessity of IMUs in mobile mapping. A mobile mapping prototype was designed to test the performance of the proposed methods. The results show that the proposed workflow and hardware system achieves centimeter-level accuracy, which suggests that it can be applied to mobile mapping and sensor fusion.