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:
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)