Particle-based models play a central role in many simulation techniques used for example in thermodynamics, molecular biology, material sciences, or astrophysics. Such simulations are carried out by directly calculating interactions on a set of individual particles over many time steps. Clusters of particles form higher-order structures like drops or waves. The interactive visual inspection of particle datasets allows gaining in-depth insight, especially for initial exploration tasks. However, their visualization is challenging in many ways. Visualizations are required to convey structures and dynamics on multiple levels, such as per-particle or per-structure. Structures are typically dense and highly dynamic over time and are thus likely subject to heavy occlusion. Furthermore, since simulation systems become increasingly powerful, the number of particles per time step increases steadily, reaching data set sizes of trillions of particles. This enormous amount of data is challenging not only from a computational perspective but also concerning comprehensibility. In this work, the idea of Focus+Context is applied to particle visualizations. Focus+Context is based on presenting a selection of the data – the focus – in high detail, while the remaining data – the context – is shown in reduced detail within the same image. This enables efficient and scalable visualizations that retain as much relevant information as possible while still being comprehensible for a human researcher. Based on the formulation of the most critical challenges, various novel methods for the visualization of static and dynamic 3D and nD particle data are introduced. A new approach that builds on global illumination and extended transparency allows to visualize otherwise occluded structures and steer visual saliency towards selected elements. To address the time-dependent nature of particle data, Focus+Context is then extended to time. By using an illustration-inspired visualization, the researcher is supported in assessing the dynamics of higher-order particle structures. To understand correlations and high dimensional structures in higher dimensional data, a new method is presented, based on the idea of depth of field.

A substantial number of works have aimed at modeling the receptive field properties of the primary visual cortex (V1). Their evaluation criterion is usually the similarity of the model response properties to the recorded responses from biological organisms. However, as several algorithms were able to demonstrate some degree of similarity to biological data based on the existing criteria, we focus on the robustness against loss of information in the form of occlusions as an additional constraint for better understanding the algorithmic level of early vision in the brain. We try to investigate the influence of competition mechanisms on the robustness. Therefore, we compared four methods employing different competition mechanisms, namely, independent component analysis, non-negative matrix factorization with sparseness constraint, predictive coding/biased competition, and a Hebbian neural network with lateral inhibitory connections. Each of those methods is known to be capable of developing receptive fields comparable to those of V1 simple-cells. Since measuring the robustness of methods having simple-cell like receptive fields against occlusion is difficult, we measure the robustness using the classification accuracy on the MNIST hand written digit dataset. For this we trained all methods on the training set of the MNIST hand written digits dataset and tested them on a MNIST test set with different levels of occlusions. We observe that methods which employ competitive mechanisms have higher robustness against loss of information. Also the kind of the competition mechanisms plays an important role in robustness. Global feedback inhibition as employed in predictive coding/biased competition has an advantage compared to local lateral inhibition learned by an anti-Hebb rule.

A substantial number of works have aimed at modeling the receptive field properties of the primary visual cortex (V1). Their evaluation criterion is usually the similarity of the model response properties to the recorded responses from biological organisms. However, as several algorithms were able to demonstrate some degree of similarity to biological data based on the existing criteria, we focus on the robustness against loss of information in the form of occlusions as an additional constraint for better understanding the algorithmic level of early vision in the brain. We try to investigate the influence of competition mechanisms on the robustness. Therefore, we compared four methods employing different competition mechanisms, namely, independent component analysis, non-negative matrix factorization with sparseness constraint, predictive coding/biased competition, and a Hebbian neural network with lateral inhibitory connections. Each of those methods is known to be capable of developing receptive fields comparable to those of V1 simple-cells. Since measuring the robustness of methods having simple-cell like receptive fields against occlusion is difficult, we measure the robustness using the classification accuracy on the MNIST hand written digit dataset. For this we trained all methods on the training set of the MNIST hand written digits dataset and tested them on a MNIST test set with different levels of occlusions. We observe that methods which employ competitive mechanisms have higher robustness against loss of information. Also the kind of the competition mechanisms plays an important role in robustness. Global feedback inhibition as employed in predictive coding/biased competition has an advantage compared to local lateral inhibition learned by an anti-Hebb rule.