Matthias Plaue

Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras

We offer a formal investigation of the measurement principle of time-of-flight 3-D cameras using correlation of amplitude-modulated continuous-wave signals. These sensors can provide both depth maps and IR intensity pictures simultaneously and in real time. We examine the theory of the data acquisition in detail. The variance of the range measurements is derived in a concise way and we show that the computed range follows an offset normal distribution. The impact of quantization of that distribution is discussed. All theoretically investigated errors like the behavior of the variance, depth bias, saturation and quantization effects are supported by experimental results.

Trajectory extraction and density analysis of intersecting pedestrian flows from video recordings

Empirical data of human crowd behaviors are indispensable for the further understanding of pedestrian dynamics. In this paper, we describe a technique for the semi-automatic extraction of pedestrian trajectories from video recordings of human crowds. This method works on data obtained from an arbitrary observation angle and does not require additional information like the heights of the pedestrians etc. It is thus suitable for the analysis of data that have not been specifically prepared for this purpose, such as surveillance videos. We employ this method to analyze video recordings from a series of experiments that we conducted last year to reproduce pedestrian flows under controlled conditions. From these data we also estimate the continuous density of these pedestrian flows via a nearest-neighbor kernel density method which we argue is particularly suited for particle densities in general and human crowds consisting of multiple populations in particular.

Denoising of continuous-wave time-of-flight depth images using confidence measures

Time-of-flight range sensors with on-chip continuous-wave correlation of radio frequency-modulated signals are increasingly popu- lar. They simultaneously deliver depth maps and intensity images with noise and systematic errors that are unique for this particular kind of data. Based on recent theoretical findings on the dominating noise pro- cesses, we propose specific variants of normalized convolution and me- dian filtering, both adaptive and nonadaptive, to the denoising of the range images. We examine the proposed filters on real-world depth maps with varying reflectivity, structure, overexposure, and illumination. The best results are obtained by adaptive filters that locally adjust the level of smoothing using the estimated modulation amplitude as a mea-

Getting Out of the Way: Collision-Avoiding Pedestrian Models Compared to the RealWorld

Numerical simulation of human crowds is a challenging task and a number of models to simulate pedestrian dynamics on a microscopic level have been established. One aim of those models is to reproduce a realistic, and in particular collision-free, movement of crowds in complex environments. This work investigates three approaches on their capability to reproduce a collision-free movement of pedestrian crowds in complex dynamic environments. The baseline model is the well-known social force model. While in the social force model pedestrians do not explicitly avoid each other, the second model extends the social force model to avoid collisions explicitly. The observed collision-avoiding behavior produced by the third model is reached by calculating velocity obstacles. These are obstacles in the velocity space, meaning that if a pedestrian chooses a velocity that lies inside the velocity obstacle, then a collision occur at some time. This work discusses the models and their integration in a multi-agent simulation framework. The models are tested on data from a real-world experiment conducted at Technische Universitat Berlin. In this experiment, two pedestrian flows intersected at an angle of 90∘. The models’ performance with regard to the reproduction of a realistic crowds movement and their computational complexity are discussed in this work.

On Measuring Pedestrian Density and Flow Fields in Dense as well as Sparse Crowds

In the framework of macroscopic human crowd models, pedestrian dynamics are described via local density and flow fields. In theory at least, these density and flow fields are often required to have a certain degree of regularity such as being smooth. In this paper, we describe a new method for the calculation of spatio-temporally smooth, locally defined density and flow fields from pedestrian trajectories. This method is based on kernel density estimation with variable bandwidth and—for a large range of scale—yields spatially averaged values close to the density or flow defined in the standard way.

Methods for Modeling and Simulation of Multi-destination Pedestrian Crowds

In this paper we present an overview of the four parts of a research project concerning pedestrian flow modeling. In retrospect, rapid growth in the volume of public transport in the last 20 years has urged efficient planning and optimal construction of public facilities. At the same time, the modeling of transport and pedestrian behaviors has become an important research topic as well. In the study of pedestrian behaviors, whereas evacuation scenarios (in which pedestrians all target a definite destination) and multi-agent systems (in which pedestrians are treated as heterogeneous individuals) have attracted much attention as two specific problems, comparatively little attention has been paid to pedestrian crowd behaviors in situations of multiple destinations. The objective of the present study is to investigate pedestrian behaviors in such a context. Our primary focus is the modeling of intersecting pedestrian streams. To address the problem from a practical perspective, we applied simple but realistic geometric configurations in our study, which could be independently extended, if necessary.

Study on three-dimensional face recognition with continuous-wave time-of-flight range cameras

For a number of different security and industrial applications, there is the need for reliable person identification methods. Among these methods, face recognition has a number of advantages such as being noninvasive and potentially covert. Other advantages of conventional two-dimensional face recognition, in particular, are its low data capture duration and its low cost. However, the recent introduction of fast and comparatively inexpensive time-of-flight cameras for the recording of 2.5D range data in real time calls for a closer look at three-dimentional face recognition in this context. One major disadvantage, however, is the low quality of the data acquired with this type of camera. In this paper, we investigate the feasibility of face recognition systems based on such range images.

On a particular type of product manifolds and shear-free cosmological models

Shear-free flows or observer fields are important objects of study in general relativity; stationary or rigid observers are important examples of shear-free reference frames. In this paper, we introduce a geometric structure based on a local coordinate expression of metrics admitting a shear-free reference frame. Furthermore, we investigate a large sub-class of these models (‘tilted’ warped products) that includes the Robertson–Walker spacetime, the G¨ odel spacetime and other models of G¨ odel type. We present a novel example of a rotating and expanding cosmological model that is contained in this class. Finally, we describe the geodesic barotropic perfect fluid solutions.

Modeling and Numerical Simulation of Multi-destination Pedestrian Crowds

In this paper we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning has made the description and modeling of transport and pedestrian behaviors an important research topic in the last twenty years. Comparatively little attention has been paid to the problem of pedestrian crowd behaviors in geometries with multiple destinations: each of the possibly many pedestrians moves to one out of a number of destinations. The objective of the present study is to investigate pedestrian behaviors in such a context. The central problem is the modeling of crossing pedestrian streams. In view of a desirable practical relevance, realistic, i.e. rather complex geometries are studied in this context.

An Intensive Course in Mathematics for Engineers: Experiences and Prospects

One main concern – especially after the implementation of the bachelor program in Germany – is how to manage the great number of lectures and how to give above-average students (but not only for them!) the opportunity to complete their course of studies quickly, but without loss of content or quality of teachings. In order to attack these problems we started an intensive course for selected students in order to offer them a unique learning experience by employing a special teaching concept, with appropriate training and exercises.