Abstract Visualizing large‐scale, time‐varying volumetric data using direct volume rendering remains a significant challenge in scientific visualization, particularly as data sizes and resolutions continue to increase. One promising direction for addressing this challenge is the use of tensor decompositions, which have proven to be a useful tool for the compact representation of large, high‐dimensional data. However, their integration into time‐dependent interactive visualization pipelines remains limited. We introduce TT4D, a memory‐ and time‐efficient lossy compression and decompression technique for four‐dimensional (4D) time‐varying volume data based on the tensor train (TT) decomposition. Our approach employs efficient subsampling during decomposition to reduce memory consumption and computational cost, enabling the processing of large datasets while avoiding unnecessarily large intermediate matrices and tensors. Beyond compression, TT4D provides a GPU‐based, on‐the‐fly decoding scheme that avoids reconstructing the entire 4D volume, supporting interactive visualization. At equivalent error levels, TT4D outperforms other transform‐based compressors at random‐access decompression across datasets up to 64GB. Exploiting the structure of TT cores, our approach enables adaptive multiresolution rendering, fast spatio‐temporal data exploration, and interactive filtering. Together, these capabilities make TT4D a scalable solution for interactive visualization of high‐resolution, time‐varying volume data.

We present tntorch, a tensor learning framework that supports multiple decompositions (including Candecomp/Parafac, Tucker, and Tensor Train) under a unified interface. With our library, the user can learn and handle low-rank tensors with automatic differentiation, seamless GPU support, and the convenience of PyTorch's API. Besides decomposition algorithms, tntorch implements differentiable tensor algebra, rank truncation, cross-approximation, batch processing, comprehensive tensor arithmetics, and more.

We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs). The code is available at https://github.com/aelphy/c-pic.

Abstract Sobol's method is one of the most powerful and widely used frameworks for global sensitivity analysis, and it maps every possible combination of input variables to an associated Sobol index. However, these indices are often challenging to analyze in depth, due in part to the lack of suitable, flexible enough, and fast‐to‐query data access structures as well as visualization techniques. We propose a visualization tool that leverages tensor decomposition, a compressed data format that can quickly and approximately answer sophisticated queries over exponential‐sized sets of Sobol indices. This way, we are able to capture the complete global sensitivity information of high‐dimensional scalar models. Our application is based on a three‐stage visualization, to which variables to be analyzed can be added or removed interactively. It includes a novel hourglass‐like diagram presenting the relative importance for any single variable or combination of input variables with respect to any composition of the rest of the input variables. We showcase our visualization with a range of example models, whereby we demonstrate the high expressive power and analytical capability made possible with the proposed method.

Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy compression algorithm for multidimensional data over regular grids. It leverages the higher-order singular value decomposition (HOSVD), a generalization of the SVD to three dimensions and higher, together with bit-plane, run-length and arithmetic coding to compress the HOSVD transform coefficients. Our scheme degrades the data particularly smoothly and achieves lower mean squared error than other state-of-the-art algorithms at low-to-medium bit rates, as it is required in data archiving and management for visualization purposes. Further advantages of the proposed algorithm include very fine bit rate selection granularity and the ability to manipulate data at very small cost in the compression domain, for example to reconstruct filtered and/or subsampled versions of all (or selected parts) of the data set.

Abstract While color plays a fundamental role in film design and production, existing solutions for film analysis in the digital humanities address perceptual and spatial color information only tangentially. We introduce VIAN, a visual film annotation system centered on the semantic aspects of film color analysis. The tool enables expert‐assessed labeling, curation, visualization and Classification of color features based on their perceived context and aesthetic quality. It is the first of its kind that incorporates foreground‐background information made possible by modern deep learning segmentation methods. The proposed tool seamlessly integrates a multimedia data management system, so that films can undergo a full color‐oriented analysis pipeline.

Histograms are a fundamental tool for multidimensional data analysis and processing, and many applications in graphics and visualization rely on computing histograms over large regions of interest (ROI). Integral histograms (IH) greatly accelerate the calculation in the case of rectangular regions, but come at a large extra storage cost. Based on the tensor train decomposition model, we propose a new compression and approximate retrieval algorithm to reduce the overall IH memory usage by several orders of magnitude at a user-defined accuracy. To this end we propose an incremental tensor decomposition algorithm that allows us to compress integral histograms of hundreds of gigabytes. We then encode the borders of any desired rectangular ROI in the IH tensor-compressed domain and reconstruct the target histogram at a high speed which is independent of the region size. We furthermore generalize the algorithm to support regions of arbitrary shape rather than only rectangles, as well as histogram field computation, i.e., recovering many histograms at once. We test our method with several multidimensional data sets and demonstrate that it radically speeds up costly histogram queries while avoiding storing massive, uncompressed IHs.

Signal processing and filter operations are important tools for visual data processing and analysis. Due to GPU memory and bandwidth limitations, it is challenging to apply complex filter operators to large-scale volume data interactively. We propose a novel and fast multiscale compression-domain volume filtering approach integrated into an interactive multiresolution volume visualization framework. In our approach, the raw volume data is decomposed offline into a compact hierarchical multiresolution tensor approximation model. We then demonstrate how convolution filter operators can effectively be applied in the compressed tensor approximation domain. To prevent aliasing due to multiresolution filtering, our solution (a) filters accurately at the full spatial volume resolution at a very low cost in the compressed domain, and (b) reconstructs and displays the filtered result at variable level-of-detail. The proposed system is scalable, allowing interactive display and filtering of large volume datasets that may exceed the available GPU memory. The desired filter kernel mask and size can be modified online, producing immediate visual results.

Task period selection is often used to adjust the workload to the available computational resources. In this paper, we propose a model where each selected period is not restricted to be a natural number, but can be any rational number within a range. Under this generalization, we contribute a period selection algorithm that yields a much smaller hyperperiod than that of previous works: with respect to the largest period, the hyperperiod with integer constraints is exponentially bounded; with rational periods the worst case is only quadratic. By means of an integer approximation at each task activation, we show how our rational period approach can work under system clock granularity; it is thus compatible with scheduling analysis practice and implementation. Our finding has practical applications in several fields of real-time scheduling: lowering complexity in table driven schedulers, reducing search space in model checking analysis, generating synthetic workload for statistical analysis of real-time scheduling algorithms, etc.

In this paper a new task model with periods defined as ranges is proposed with the main goal of drastically reduce the hyperperiod of the task set. The model is focused to be applied in cyclic scheduling, where the length of the major cycle of the plan is determined by the hyperperiod. But it also can be applied in synthetic task sets generation, where having a small hyperperiod reduces complexity and simulation time. A new algorithm, which allows to calculate the minimum hyperperiod of such a set of tasks, is presented. This algorithm calculates the minimum value even with a large number of tasks, where exhaustive search becomes intractable.