Abstract Mining of GPS trajectories of moving vehicles and devices can provide valuable insights into urban systems, planning and operational applications. Understanding object motion often requires that the spatial-temporal matching of trajectories be invariant to shifting, scaling and rotation. To this end, Procrustes analysis enables to transform one data set of a trajectory to represent another set of data as closely as possible. We propose a novel shift-scale-rotation invariant Procrustes distance metric based on the Kabsch algorithm, which calculates the optimal rotation matrix by minimizing the root-mean squared deviation between two paired sets of points of trajectories or trajectory segments. We present two novel runtime efficient algorithms which are based on our proposed distance metric: 1) the sliding-shifting-scaling-Kabsch-rotation (S3KR) algorithm for detecting recurring short query patterns in longer motion trajectories and 2) a novel time series subsequence clustering algorithm to group GPS trajectory data and to discover prototypical patterns. We demonstrate the potential of our proposed sliding Procrustes analysis algorithms by applying it on real-world GPS trajectories collected in urban and rural areas from different transport modes, as well as on nautical GPS trajectories. We also demonstrate that our methods outperform the state of the art in accuracy and runtime on synthetic and real world data.

Data exploration is an essential task for gaining an understanding of the potential and limitations of novel datasets. This paper discusses the challenges related to exploring large Automatic Identification System (AIS) datasets. We address these challenges using trajectory-based analysis approaches implemented in distributed computing environments using Spark and GeoMesa. This approach enables the exploration of datasets that are too big to handle within conventional spatial database systems. We demonstrate our approach using a case study of 4 billion AIS records.

Temporal data visualization is used to analyze dependent variables that vary over time, with time being an independent variable. Visualizing temporal data is inherently difficult, due to the many aspects that need to be communicated to the users (e.g., time and variable changes). This is an important topic in visualization, and a wide range of visualization techniques dealing with different tasks have already been designed. In this paper we propose popup-plots, a novel concept where the common interaction of 3D rotation is used to navigate through the data. This allows the users to view the data from different perspectives without having to learn and adapt to new interaction concepts. Popup-plots are therefore a novel method for visualizing and interacting with dependent variables over time. We extend 2D plots with the temporal information by bending the space according to the time. The bending is calculated based on a spherical coordinates approach, which is continuously influenced by the viewing direction towards the plot. Hence, the plot can be viewed from various angles with seamless transitions in between, offering the possibility to analyze different aspects of the represented data. As the current viewing direction is inherently depicted by the shape of the data, the users are able to deduce which part of the data is currently viewed. The temporal information is encoded into the visualization itself, resembling annual rings of a tree. We demonstrate our method by applying it to data from two different domains, comprising measurements at spatial positions over time, and we also evaluated the usability of our solution.

We present a new method for analyzing data manifolds based on Weyl's tube theorem. The coefficients of the tube polynomial for a manifold provide geometric information such as the volume of the manifold or its Euler characteristic, thus providing bounds on the geometric nature of the manifold. We present an algorithm estimating the coefficients of the tube polynomial for a given manifold and demonstrate the features of our algorithm on artificial data sets. We apply the algorithm on a real-world traffic data set to determine the number and properties of clusters. We furthermore demonstrate that our algorithm can be used to determine image coverage of an object, giving hints on where a manifold is not sufficiently sampled.

Existing visual surveillance systems typically require that human operators observe video streams from different cameras, which becomes infeasible if the number of observed cameras is ever increasing. In this paper, we present a new surveillance system that combines automatic video analysis (i.e., single person tracking and crowd analysis) and interactive visualization. Our novel visualization takes advantage of a high resolution display and given 3D information to focus the operator's attention to interesting/ critical areas of the observed area. This is realized by embedding the results of automatic scene analysis techniques into the visualization. By providing different visualization modes, the user can easily switch between the different modes and can select the mode which provides most information. The system is demonstrated for a real setup on a university campus.

We present a crowd analysis approach computing a representation of the major pedestrian flows in complex scenes. It treats crowds as a set of moving particles and builds a spatio-temporal model of motion events. A Growing Neural Gas algorithm encodes optical flow particle trajectories as sequences of local motion events and learns a topology which is the base for trajectory distance computations. Trajectory prototypes are aligned with a two-open-ends version of Dynamic Time Warping to cope with fragmented trajectores. The trajectories are grouped into an automatically determined number of clusters with self-tuning spectral clustering. The clusters are compactly represented with the help of Principal Component Analysis, providing a technique for unusual motion detection based on residuals. We demonstrate results for a publicly available crowded video and a scene with volunteers moving according to defined origin-destination flows.

Video footage of real crowded scenes still poses severe challenges for automated surveillance. This paper evaluates clustering methods for finding independent dominant motion fields for an observation period based on a recently published real-time optical flow algorithm. We focus on self-tuning spectral clustering and Isomap combined with k-means. Several combinations of feature vector normalizations and distance measures (Euclidean, Mahanalobis and a general additive distance) are evaluated for four image sequences including three publicly available crowd datasets. Evaluation is based on mean accuracy obtained by comparison with a manually defined ground truth clustering. For every dataset at least one approach correctly classified more than 95% of the flow vectors without extra tuning of parameters, providing a basis for an automatic analysis after a view-dependent setup.

Commuters rely on realistic and real-time information in order to optimize the time spent on commuting between home and work. Delays in (urban) transport and congestion for individual motorized transport are a major issue for unnecessary long travel times. While some of these delays occur randomly,

This paper describes a vision based pedestrian detection and tracking system which is able to count people in very crowded situations like escalator entrances in underground stations. The proposed system uses motion to compute regions of interest and prediction of movements, extracts shape information from the video frames to detect individuals, and applies texture features to recognize people. A search strategy creates trajectories and new pedestrian hypotheses and then filters and combines those into accurate counting events. We show that counting accuracies up to 98 % can be achieved.

Addresses the problem of reliably fitting parametric and semi-parametric models to high density spot array images obtained in gene expression experiments. The goal is to measure the amount of genetic material at specific spot locations. Many spots can be modelled accurately by a Gaussian shape. In order to deal with highly overlapping spots the authors use robust M-estimators. When the parametric method fails, they use a novel, robust semi-parametric method which can handle spots of different shapes accurately. They present the results for real data and compare the complexity of the two methods.