Tensor Decomposition Methods in Visual Computing

Tutorial held at the IEEE VIS 2016 conference.

Lecturers:

• Renato Pajarola , Professor, Visualization and MultiMedia Lab, University of Zürich
• Rafael Ballester-Ripoll, PhD Student, Visualization and MultiMedia Lab, University of Zürich

Slides:

• Section 1 (PDF, 46 MB)
• Section 2 (PDF, 37 MB)

Links:

• Background theory on tensor decomposition (PDF, 9 MB)
• MicroCT volume datasets
• BTF datasets
• Tensor decomposition software
• vmmlib library

References:

Basic Theory and Models

• [LMV00a] "A Multilinear Singular Value Decomposition" (L. de Lathauwer et al.)
• [LMV00b] "On the Best Rank-1 and Rank-(R1,...,RN) Approximation of Higher-Order Tensors" (L. de Lathauwer et al.)
• [KB09] "Tensor Decompositions and Applications" (T. Kolda, B. Bader)
• [O10a] "Tensor-Train Decomposition" (I. V. Oseledets)
• [S13] "Tensor Approximation in Visualization and Graphics: Background Theory" (S. Suter) (PDF, 9 MB)

Volume Compression and Visualization

• [WXC+08] "Hierarchical Tensor Approximation of Multidimensional Visual Data" (Q. Wu et al.)
• [SGM+11] "Interactive Multiscale Tensor Reconstruction for Multiresolution Volume Visualization" (S. Suter et al.)
• [TMP13] "TAMRESH: Tensor Approximation Multiresolution Hierarchy for Interactive Volume Visualization" (S. Suter et al.)
• [BSP15] "Analysis of Tensor Approximation for Compression-Domain Volume Visualization" (R. Ballester-Ripoll et al.)
• [BP15] "Lossy Volume Compression Using Tucker Truncation and Thresholding" (R. Ballester-Ripoll, R. Pajarola)

Bidirectional Texture Functions

• [TS06] "All-Frequency Precomputed Radiance Transfer using Spherical Radial Basis Functions and Clustered Tensor Approximation" (Y.-T. Tsai, Z.-C. Shih)
• [RK09] "BTF Compression via Sparse Tensor Decomposition" (R. Ruiters, R. Klein)
• [T12] "K-clustered Tensor Approximation: A Sparse Multilinear Model for Real-time Rendering" (Y.-T. Tsai)
• [T15] "Multiway K-Clustered Tensor Approximation: Toward High-Performance Photorealistic Data-Driven Rendering" (Y.-T. Tsai)
• [BP16] "Compressing Bidirectional Texture Functions via Tensor Train Decomposition" (R. Ballester-Ripoll, R. Pajarola) (to appear)

Tensor Completion and Synthesis

• [CSS08] "Higher Order SVD Analysis for Dynamic Texture Synthesis" (R. Costantini et al.)
• [KSV13] "Low-Rank Tensor Completion by Riemannian Optimization" (D. Kressner et al.)
• [CHL14] "Simultaneous Tensor Decomposition and Completion Using Factor Priors" (Y.-L. Chen et al.)
• [FJ15] "Tucker Factorization with Missing Data with Application to Low-n-Rank Tensor Completion" (M. Filipovic, A. Jukic)

Adaptive Sampling

• [HPB07] "Matrix Row-Column Sampling for the Many-Light Problem" (M. Hasan et al.)
• [OST08] "Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time" (I. V. Oseledets et al.)
• [CC10] "Generalizing the Column-Row Matrix Decomposition to Multi-Way Arrays" (C. Caiafa, A. Cichocki)
• [O10b] "TT-Cross Approximation for Multidimensional Arrays" (I. V. Oseledets)
• [S11] "Fast Adaptive Interpolation of Multi-Dimensional Arrays in Tensor Train Format" (D. Savostyanov and I. V. Oseledets)
• [BPP16] "A Surrogate Visualization Model Using the Tensor Train Format" (R. Ballester-Ripoll et al.) (to appear)