TT4D: Tensor-Train-based 4D Time-Dependent Volume Rendering

Abstract

Visualizing large-scale, time-varying volumetric data using direct volume rendering remains a significant challenge in scien-tific visualization, particularly as data sizes and resolutions continue to increase. One promising direction for addressing thischallenge 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. Weintroduce 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 duringdecomposition to reduce memory consumption and computational cost, enabling the processing of large datasets while avoidingunnecessarily large intermediate matrices and tensors. Beyond compression, TT4D provides a GPU-based, on-the-fly decodingscheme that avoids reconstructing the entire 4D volume, supporting interactive visualization. At equivalent error levels, TT4Doutperforms other transform-based compressors at random-access decompression across datasets up to 64GB. Exploiting thestructure of TT cores, our approach enables adaptive multiresolution rendering, fast spatio-temporal data exploration, andinteractive filtering. Together, these capabilities make TT4D a scalable solution for interactive visualization of high-resolution, time-varying volume data.