Rafael Ballester-Ripoll

Lossy volume compression using Tucker truncation and thresholding

Tensor decompositions, in particular the Tucker model, are a powerful family of techniques for dimensionality reduction and are being increasingly used for compactly encoding large multidimensional arrays, images and other visual data sets. In interactive applications, volume data often needs to be decompressed and manipulated dynamically; when designing data reduction and reconstruction methods, several parameters must be taken into account, such as the achievable compression ratio, approximation error and reconstruction speed. Weighing these variables in an effective way is challenging, and here we present two main contributions to solve this issue for Tucker tensor decompositions. First, we provide algorithms to efficiently compute, store and retrieve good choices of tensor rank selection and decompression parameters in order to optimize memory usage, approximation quality and computational costs. Second, we propose a Tucker compression alternative based on coefficient thresholding and zigzag traversal, followed by logarithmic quantization on both the transformed tensor core and its factor matrices. In terms of approximation accuracy, this approach is theoretically and empirically better than the commonly used tensor rank truncation method.

Analysis of tensor approximation for compression-domain volume visualization

As modern high-resolution imaging devices allow to acquire increasingly large and complex volume data sets, their effective and compact representation for visualization becomes a challenging task. The Tucker decomposition has already confirmed higher-order tensor approximation (TA) as a viable technique for compressed volume representation; however, alternative decomposition approaches exist. In this work, we review the main TA models proposed in the literature on multiway data analysis and study their application in a visualization context, where reconstruction performance is emphasized along with reduced data representation costs. Progressive and selective detail reconstruction is a main goal for such representations and can efficiently be achieved by truncating an existing decomposition. To this end, we explore alternative incremental variations of the CANDECOMP/PARAFAC and Tucker models. We give theoretical time and space complexity estimates for every discussed approach and variant. Additionally, their empirical decomposition and reconstruction times and approximation quality are tested in both C++ and MATLAB implementations. Several scanned real-life exemplar volumes are used varying data sizes, initialization methods, degree of compression and truncation. As a result of this, we demonstrate the superiority of the Tucker model for most visualization purposes, while canonical-based models offer benefits only in limited situations. Graphical abstractDisplay Omitted HighlightsWe explore tensor decomposition techniques in the field of volume visualization.We contribute and compare alternative incremental variants.We provide time and space complexity estimates for these approaches and variants.We demonstrate the superiority of the Tucker model in most 3D visualization purposes.

A surrogate visualization model using the tensor train format

Complex simulations and numerical experiments typically rely on a number of parameters and have an associated score function, e.g. with the goal of maximizing accuracy or minimizing computation time. However, the influence of each individual parameter is often poorly understood a priori and the joint parameter space can be difficult to explore, visualize and optimize. We model this space as an N-dimensional black-box tensor and apply a cross approximation strategy to sample it. Upon learning and compactly expressing this space as a surrogate visualization model, informative subspaces are interactively reconstructed and navigated in the form of charts, images, surface plots, etc. By exploiting efficient operations in the tensor train format, we are able to produce diagrams such as parallel coordinates, bivariate projections and dimensional stacking out of highly-compressed parameter spaces. We demonstrate the proposed framework with several scientific simulations that contain up to 6 parameters and billions of tensor grid points.

Tensor Algorithms for Advanced Sensitivity Metrics

Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature, including the effective and mean dimensions, the dimension distribution, and the Shapley values. Such metrics combine up to exponential numbers of SI in different ways and can be of great aid in uncertainty quantification and model interpretation tasks, but are computationally challenging. We focus on surrogate-based sensitivity analysis for independently distributed variables, namely, via the tensor train (TT) decomposition. This format permits flexible and scalable surrogate modeling and can efficiently extract all SI at once in a compressed TT representation of their own. Based on this, we contribute a range of novel algorithms that compute more advanced sensitivity metrics by selecting and aggregating certain subsets of SI in the tensor compressed domain. Drawing on an interpretation of the ...

Multiresolution Volume Filtering in the Tensor Compressed Domain

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.