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Item Massively Parallel Batch Neural Gas for Bounding Volume Hierarchy Construction(The Eurographics Association, 2014) Weller, René; Mainzer, David; Srinivas, Abhishek; Teschner, Matthias; Zachmann, Gabriel; Jan Bender and Christian Duriez and Fabrice Jaillet and Gabriel ZachmannOrdinary bounding volume hierarchy (BVH) construction algorithms create BVHs that approximate the boundary of the objects. In this paper, we present a BVH construction that instead approximates the volume of the objects with successively finer levels. It is based on Batch Neural Gas (BNG), a clustering algorithm that is known from machine learning. Additionally, we present a novel massively parallel version of this BNG-based hierarchy construction that runs completely on the GPU. It reduces the theoretical complexity of the sequential algorithm from O(nlogn) to O(log2 n) and also our CUDA implementation outperforms the CPU version significantly in practice.Item Location-dependent Generalization of Road Networks Based on Equivalent Destinations(The Eurographics Association and John Wiley & Sons Ltd., 2016) Dijk, Thomas C. van; Haunert, Jan-Henrik; Oehrlein, Johannes; Kwan-Liu Ma and Giuseppe Santucci and Jarke van WijkSuppose a user located at a certain vertex in a road network wants to plan a route using a wayfinding map. The user's exact destination may be irrelevant for planning most of the route, because many destinations will be equivalent in the sense that they allow the user to choose almost the same paths. We propose a method to find such groups of destinations automatically and to contract the resulting clusters in a detailed map to achieve a simplified visualization. We model the problem as a clustering problem in rooted, edge-weighted trees. Two vertices are allowed to be in the same cluster if and only if they share at least a given fraction of their path to the root. We analyze some properties of these clusterings and give a linear-time algorithm to compute the minimum-cardinality clustering. This algorithm may have various other applications in network visualization and graph drawing, but in this paper we apply it specifically to focus-and-context map generalization. When contracting shortestpath trees in a geographic network, the computed clustering additionally provides a constant-factor bound on the detour that results from routing using the generalized network instead of the full network. This is a desirable property for wayfinding maps.Item Using K-Means Clustering for a Spatial Analysis of Multivariate and Time-Varying Microclimate Data(The Eurographics Association, 2013) Häb, Kathrin; Middel, Ariane; Hagen, Hans; O. Kolditz and K. Rink and G. ScheuermannIn this study, we propose a k-means clustering algorithm combined with glyph-based encoding method to analyze the spatial distribution and dependence of multivariate, time-varying 3D microclimate data. We obtained five climate variables, i.e. air and surface temperature, specific humidity, direct shortwave radiation and sensible heat flux, from an ENVI-met R simulation of a residential neighborhood in Phoenix, AZ. In a preprocessing step, we aggregated the 3D gridded simulation data by adding up value differences between two consecutive time steps for each grid cell over the entire simulation time to get a highly compressed view of the data without losing the spatial context. K-means clustering was then conducted in coordinate space by weighting each grid cell based on its difference to the spatial mean of temporal value differences. To reduce occlusion and to encode additional cluster member information, the visualization focused on the k-means cluster centroids. Resulting images show that the applied technique is suitable to provide a first insight into the spatial relationship of features based on their temporal variability.Item Visual Analysis of Confocal Raman Spectroscopy Data using Cascaded Transfer Function Design(The Eurographics Association and John Wiley & Sons Ltd., 2017) Schikora, Christoph Markus; Plack, Markus; Bornemann, Rainer; Bolívar, Peter Haring; Kolb, Andreas; Heer, Jeffrey and Ropinski, Timo and van Wijk, Jarke2D Confocal Raman Microscopy (CRM) data consist of high dimensional per-pixel spectral data of 1000 bands and allows for complex spectral and spatial-spectral analysis tasks, i.e., in material discrimination, material thickness, and spatial material distributions. Currently, simple integral methods are commonly applied as visual analysis solutions to CRM data which exhibit restricted discrimination power in various regards. In this paper we present a novel approach for the visual analysis of 2D multispectral CRM data using multi-variate visualization techniques. Due to the large amount of data and the demand of an explorative approach without a-priori restriction, our system allows for arbitrary interactive (de)selection of varaibles w/o limitation and an unrestricted online definition/construction of new, combined properties. Our approach integrates CRM specific quantitative measures and handles material-related features for mixed materials in a quantitative manner. Technically, we realize the online definition/construction of new, combined properties as semi-automatic, cascaded, 1D and 2D multidimensional transfer functions (MD-TFs). By interactively incorporating new (raw or derived) properties, the dimensionality of the MD-TF space grows during the exploration procedure and is virtually unlimited. The final visualization is achieved by an enhanced color mixing step which improves saturation and contrast.Item Vector Field k-Means: Clustering Trajectories by Fitting Multiple Vector Fields(The Eurographics Association and Blackwell Publishing Ltd., 2013) Ferreira, Nivan; Klosowski, James T.; Scheidegger, Carlos E.; Silva, Cláudio T.; B. Preim, P. Rheingans, and H. TheiselScientists study trajectory data to understand trends in movement patterns, such as human mobility for traffic analysis and urban planning. In this paper, we introduce a novel trajectory clustering technique whose central idea is to use vector fields to induce a notion of similarity between trajectories, letting the vector fields themselves define and represent each cluster. We present an efficient algorithm to find a locally optimal clustering of trajectories into vector fields, and demonstrate how vector-field k-means can find patterns missed by previous methods. We present experimental evidence of its effectiveness and efficiency using several datasets, including historical hurricane data, GPS tracks of people and vehicles, and anonymous cellular radio handoffs from a large service provider.