We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors.For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domainindependence. Our source code is available on GitHub 1 .Recently, a set of methods brought together under the term geometric deep learning [3] emerged, which aim to achieve this transfer by defining convolution operations for deep neural networks that can handle irregular input data. Existing work in this field can loosely be divided into two different subsets: the spectral and the spatial filtering approaches. The former is based on spectral graph theory [5], where eigenvalues of a graph's Laplacian matrix are interpreted as frequencies of node signals [22]. They are filtered in the spectral domain, analogously to Fourier domain filtering of traditional signals. The latter subset, the spatial approaches, perform convolution in local Euclidean neighborhoods w.r.t. local positional relations between points, represented for example as polar, spherical or Cartesian coordinates, as shown as examples in Figure 1.Contribution. We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured data. The main contribution is a trainable, spatial, continuous convolution kernel that leverages properties of B-spline bases to efficiently filter geometric input of arbitrary dimensionality. We show

Abstract:The Leap Motion Controller is a new device for hand gesture controlled user interfaces with declared sub-millimeter accuracy. However, up to this point its capabilities in real environments have not been analyzed. Therefore, this paper presents a first study of a Leap Motion Controller. The main focus of attention is on the evaluation of the accuracy and repeatability. For an appropriate evaluation, a novel experimental setup was developed making use of an industrial robot with a reference pen allowing a position accuracy of 0.2 mm. Thereby, a deviation between a desired 3D position and the average measured positions below 0.2 mm has been obtained for static setups and of 1.2 mm for dynamic setups. Using the conclusion of this analysis can improve the development of applications for the Leap Motion controller in the field of Human-Computer Interaction.

This paper presents a Fitts' law-based analysis of the user's performance in selection tasks with the Leap Motion Controller compared with a standard mouse device. The Leap Motion Controller (LMC) is a new contact-free input system for gesture-based human-computer interaction with declared sub-millimeter accuracy. Up to this point, there has hardly been any systematic evaluation of this new system available. With an error rate of 7.8 % for the LMC and 2.8% for the mouse device, movement times twice as large as for a mouse device and high overall effort ratings, the Leap Motion Controller's performance as an input device for everyday generic computer pointing tasks is rather limited, at least with regard to the selection recognition provided by the LMC.

Modern hardware and software development has led to an evolution of user interfaces from command-line to natural user interfaces for virtual immersive environments. Gestures imitating real-world interaction tasks increasingly replace classical two-dimensional interfaces based on Windows/Icons/Menus/Pointers (WIMP) or touch metaphors. Thus, the purpose of this paper is to survey the state-of-the-art Human-Computer Interaction (HCI) techniques with a focus on the special field of three-dimensional interaction. This includes an overview of currently available interaction devices, their applications of usage and underlying methods for gesture design and recognition. Focus is on interfaces based on the Leap Motion Controller (LMC) and corresponding methods of gesture design and recognition. Further, a review of evaluation methods for the proposed natural user interfaces is given.

Purpose With the coronavirus disease 2019 (COVID-19) pandemic spreading across the world, protective measures for containing the virus are essential, especially as long as no vaccine or effective treatment is available. One important measure is the so-called physical distancing or social distancing. Methods In this paper, we propose an agent-based numerical simulation of pedestrian dynamics in order to assess the behavior of pedestrians in public places in the context of contact transmission of infectious diseases like COVID-19, and to gather insights about exposure times and the overall effectiveness of distancing measures. Results To abide by the minimum distance of 1.5 m stipulated by the German government at an infection rate of 2%, our simulation results suggest that a density of one person per 16m2 or below is sufficient. Conclusions The results of this study give insight into how physical distancing as a protective measure can be carried out more efficiently to help reduce the spread of COVID-19.

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Abstract:The PAMONO-sensor (plasmon assisted microscopy of nano-objects) demonstrated an ability to detect and quantify individual viruses and virus-like particles. However, another group of biological vesicles-microvesicles (100-1000 nm)-also attracts growing interest as biomarkers of different pathologies and needs development of novel techniques for characterization. This work shows the applicability of a PAMONO-sensor for selective detection of microvesicles in aquatic samples. The sensor permits comparison of relative concentrations of microvesicles between samples. We also study a possibility of repeated use of a sensor chip after elution of the microvesicle capturing layer. Moreover, we improve the detection features of the PAMONO-sensor. The detection process utilizes novel machine learning techniques on the sensor image data to estimate particle size distributions of nano-particles in polydisperse samples. Altogether, our findings expand analytical features and the application field of the PAMONO-sensor. They can also serve for a maturation of diagnostic tools based on the PAMONO-sensor platform.