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Analysis of tensor approximation for compression-domain volume visualization


Ballester-Ripoll, Rafael; Suter, Susanne K; Pajarola, Renato (2015). Analysis of tensor approximation for compression-domain volume visualization. Computers & Graphics, 47:34-47.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Informatics
Dewey Decimal Classification:000 Computer science, knowledge & systems
Uncontrolled Keywords:visualization, tensor approximation, multiresolution, volume rendering, level-of-detail
Language:English
Date:April 2015
Deposited On:30 Oct 2015 07:27
Last Modified:14 Feb 2018 09:36
Publisher:Elsevier
ISSN:0097-8493
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.cag.2014.10.002
Other Identification Number:merlin-id:10254

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