We present a machine learning-based approach for detecting and visualizing complex behavior in spatiotemporal volumes. For this, we train models to predict future data values at a given position based on the past values in its neighborhood, capturing common temporal behavior in the data. We then evaluate the model's prediction on the same data. High prediction error means that the local behavior was too complex, unique or uncertain to be accurately captured during training, indicating spatiotemporal regions with interesting behavior. By training several models of varying capacity, we are able to detect spatiotemporal regions of various complexities. We aggregate the obtained prediction errors into a time series or spatial volumes and visualize them together to highlight regions of unpredictable behavior and how they differ between the models. We demonstrate two further volumetric applications: adaptive timestep selection and analysis of ensemble dissimilarity. We apply our technique to datasets from multiple application domains and demonstrate that we are able to produce meaningful results while making minimal assumptions about the underlying data.

We present a novel scheme for progressive rendering in interactive visualization. Static settings with respect to a certain image quality or frame rate are inherently incapable of delivering both high frame rates for rapid changes and high image quality for detailed investigation. Our novel technique flexibly adapts by steering the visualization process in three major degrees of freedom: when to terminate the refinement of a frame in the background and start a new one, when to display a frame currently computed, and how much resources to consume. We base these decisions on the correlation of the errors due to insufficient sampling and response delay, which we estimate separately using fast yet expressive heuristics. To automate the configuration of the steering behavior, we employ offline video quality analysis. We provide an efficient implementation of our scheme for the application of volume raycasting, featuring integrated GPU-accelerated image reconstruction and error estimation. Our implementation performs an integral handling of the changes due to camera transforms, transfer function adaptations, as well as the progression of the data to in time. Finally, the overall technique is evaluated with an expert study.

This paper presents a visualization approach for detecting and exploring similarity in the temporal variation of field data. We provide an interactive technique for extracting correlations from similarity matrices which capture temporal similarity of univariate functions. We make use of the concept to extract periodic and quasiperiodic behavior at single (spatial) points as well as similarity between different locations within a field and also between different data sets. The obtained correlations are utilized for visual exploration of both temporal and spatial relationships in terms of temporal similarity. Our entire pipeline offers visual interaction and inspection, allowing for the flexibility that in particular time-dependent data analysis techniques require. We demonstrate the utility and versatility of our approach by applying our implementation to data from both simulation and measurement.

We present a novel technique to generate transformations between arbitrary volumes, providing both expressive distances and smooth interpolates. In contrast to conventional morphing or warping approaches, our technique requires no user guidance, intermediate representations (like extracted features), or blending, and imposes no restrictions regarding shape or structure. Our technique operates directly on the volumetric data representation, and while linear programming approaches could solve the underlying problem optimally, their polynomial complexity makes them infeasible for high-resolution volumes. We therefore propose a progressive refinement approach designed for parallel execution that is able to quickly deliver approximate results that are iteratively improved toward the optimum. On this basis, we further present a new approach for the streaming selection of time steps in temporal data that allows for the reconstruction of the full sequence with a user-specified error bound. We finally demonstrate the utility of our technique for different applications, compare our approach against alternatives, and evaluate its characteristics with a variety of different data sets.

This paper introduces an optimization approach for generating grid layouts from large data collections such that they are amenable to level‐of‐detail presentation and exploration. Classic (flat) grid layouts visually do not scale to large collections, yielding overwhelming numbers of tiny member representations. The proposed local search‐based progressive optimization scheme generates hierarchical grids: leaves correspond to one grid cell and represent one member, while inner nodes cover a quadratic range of cells and convey an aggregate of contained members. The scheme is solely based on pairwise distances and jointly optimizes for homogeneity within inner nodes and across grid neighbors. The generated grids allow to present and flexibly explore the whole data collection with arbitrary local granularity. Diverse use cases featuring large data collections exemplify the application: stock market predictions from a Black‐Scholes model, channel structures in soil from Markov chain Monte Carlo, and image collections with feature vectors from neural network classification models. The paper presents feedback by a domain scientist, compares against previous approaches, and demonstrates visual and computational scalability to a million members, surpassing classic grid layout techniques by orders of magnitude.