TTHRESH: Tensor Compression for Multidimensional Visual Data (original) (raw)

Compression of image ensembles using tensor decomposition

2013 Picture Coding Symposium (PCS), 2013

With the ever-growing trend of globalization, product design is often conducted collaboratively among several divisions, thus making it a huge challenge to transfer large CAE (Computer Aided Engineering) data between different locations. Our goal is to reduce the size of transfer data so that fast data transfer can be realized even when the network speed is slow. In this study, we have developed a data compression method based on TD (Tensor Decomposition). In this method, voxel simulation results data are represented as tensors and tensor decomposition based on HOOI (Higher-Order Orthogonal Iteration) algorithm is applied to the tensors. After tensor decompression, the original tensor is decomposed into a core tensor and a series of basis matrices, whose summed size is considerably smaller than that of the original tensor. As a result, a compression ratio of over 60:1 is achieved for steady flow simulation results data and the error is below 5%. A compression ratio of over 70:1 is achieved for unsteady flow simulation results data and the error is below 5%. We have confirmed that at 5% error, no significant information is lost during the data compression process. Tensor decomposition has been applied for image data compression, dimensionality reduction, and more recently for the compression of hexahedral mesh-based simulation result database. However, it is a first application of tensor decomposition to the data compression of voxel-based simulation results.

Interactive Multiscale Tensor Reconstruction for Multiresolution Volume Visualization

IEEE Transactions on Visualization and Computer Graphics, 2000

Large scale and structurally complex volume datasets from high-resolution 3D imaging devices or computational simulations pose a number of technical challenges for interactive visual analysis. In this paper, we present the first integration of a multiscale volume representation based on tensor approximation within a GPU-accelerated out-of-core multiresolution rendering framework. Specific contributions include (a) a hierarchical brick-tensor decomposition approach for pre-processing large volume data, (b) a GPU accelerated tensor reconstruction implementation exploiting CUDA capabilities, and (c) an effective tensor-specific quantization strategy for reducing data transfer bandwidth and out-of-core memory footprint. Our multiscale representation allows for the extraction, analysis and display of structural features at variable spatial scales, while adaptive level-of-detail rendering methods make it possible to interactively explore large datasets within a constrained memory footprint. The quality and performance of our prototype system is evaluated on large structurally complex datasets, including gigabyte-sized micro-tomographic volumes.

Visual Descriptors for Dense Tensor Fields in Computational Turbulent Combustion: A Case Study

Journal of Imaging Science and Technology, 2015

Simulation and modeling of turbulent flow, and of turbulent reacting flow in particular, involve solving for and analyzing time-dependent and spatially dense tensor quantities, such as turbulent stress tensors. The interactive visual exploration of these tensor quantities can effectively steer the computational modeling of combustion systems. In this article, the authors analyze the challenges in dense symmetric-tensor visualization as applied to turbulent combustion calculation; most notable among these challenges are the dataset size and density. They analyze, together with domain experts, the feasibility of using several established tensor visualization techniques in this application domain. They further examine and propose visual descriptors for volume rendering of the data. Of these novel descriptors, one is a density-gradient descriptor which results in Schlieren-style images, and another one is a classification descriptor inspired by machine-learning techniques. The result is a hybrid visual analysis tool to be utilized in the debugging, benchmarking and verification of models and solutions in turbulent combustion. The authors demonstrate this analysis tool on two example configurations, report feedback from combustion researchers, and summarize the design lessons learned.

Multiscale Tensor Approximation for Volume Data

2010

Advanced 3D microstructural analysis in natural sciences and engineering depends ever more on modern data acquisition and imaging technologies such as micro-computed or synchrotron tomography and interactive visualization. The acquired high-resolution volume data sets have sizes in the order of tens to hundreds of GBs, and typically exhibit spatially complex internal structures. Such large structural volume data sets represent a grand challenge to be explored, analyzed and interpreted by means of interactive visualization, since the amount of data to be rendered is typically far beyond the current performance limits of interactive graphics systems. As a new approach to tackle this bottleneck problem, we employ higher-order tensor approximations (TAs). We demonstrate the power of TA to represent, and focus on, structural features in volume data. We show that TA yields a high data reduction at competitive rate distortion and that, at the same time, it provides a natural means for mult...

Parallel Tensor Compression for Large-Scale Scientific Data

2015

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data, assuming double precision. By viewing the data as a dense five-way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 5000 on realworld data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed-memory parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.

Volume visualizing high-resolution turbulence computations

Theoretical and computational fluid …, 1998

Using several volume visualization packages including a new package we developed called Volsh, we investigate a 25 GB dataset from a 256 3 computation of decaying quasigeostrophic turbulence. We compare surface fitting and direct volume rendering approaches, as well as a number of techniques for producing feature-revealing spatial cues. We also study the pros and cons of using batch and interactive tools for visualizing the data and discuss the relative merits of using each approach. We find that each tool has its own advantages and disadvantages, and a combination of tools is most effective at exploring large four-dimensional scalar datasets. The resulting visualizations show several new phenomena in the dynamics of coherent vortices.

Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

Fluids

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurat...