Analysis of tensor approximation for compression-domain volume visualization

Abstract

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. Addi-tionally, 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 com-pression 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. AbstractAs 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 higherorder 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.

Tensor Approximation for Multidimensional and Multivariate Data

“…In scientific visualization, TA methods have first been introduced for interactive multiresolution and multiscale direct volume rendering [6][7][8][46][47][48]. Additionally, their compact representation power has been exploited for 3D volume data compression [4,6] with notable advantages over other approaches at extreme compression ratios [2]. In this work, we explore the multiscale feature expressiveness of TA methods for the first time on vector fields, i.e.…”

Quality assessment of volume compression approaches using isovalue clustering

“…For the purpose of analyzing the proposed VQA, we mea- performed with Tucker tensor rank truncation [40].…”

Simultaneous encryption and compression of medical images based on optimized tensor compressed sensing with 3D Lorenz

“…The higher-order singular value decomposition (HOSVD) provides a generalization of the low-rank approximation of matrices to the case of tensors [28–30]. To facilitate the distinction between scalars, vectors, matrices and higher dimensional tensors, the type of a given quantity will be reduced by its representation: scalars are denoted by lower-case letters (), vectors are written as capitals (), matrices corresponding to bold-face capitals () and tensors are written as calligraphic letters ().…”