Multilinear Analysis of Image Ensembles: TensorFaces

By M. Alex O. Vasilescu, Demetri Terzopoulos. European Conference on Computer Vision, 2002

961 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/048bfc88b9f54512304433bb2eeb68a3172159a8

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In Computational Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Image Denoising Using the Higher Order Singular Value Decomposition (2013, neutral): “Some pioneering and successful applications of the HOSVD in computer vision have been proposed in [35].”
Factorization strategies for third-order tensors (2011, methodology): “Applications involving operations with tensors include chemometrics [41], psychometrics [24], signal processing [9] [27] [39], computer vision [44] [46] [45], data mining [1] [38], graph analysis [21], neuroscience [3] [30] [31], and many more.”
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging (2013, background): “Third-order (and higher) tensors arise in a wide variety of application areas, including, but not limited to, chemometrics [24], psychometrics [13], and image and signal processing [5, 15, 23, 17, 8, 20, 29, 28, 30].”
Unsupervised Multiway Data Analysis: A Literature Survey (2009, background): “Nevertheless , it does give a good approximation of the data as shown in many applications, e.g., face recognition [38], [39].”
F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig on Minimal Subspaces in Tensor Representations on Minimal Subspaces in Tensor Representations (neutral): “It has been used in many areas such as psychometrics [22] [5], chemometrics [2], analysis of turbulent flows [3], image analysis and pattern recognition [24], data mining. . ..”
Tensor Decomposition for Signal Processing and Machine Learning (2016, background): “Tensor algebra has many similarities but also many striking differences with matrix algebra – e.g., low-rank tensor factorization is essentially unique under mild conditions; determining tensor rank is NP-hard, on the other hand, and the best lowrank approximation of a higher rank tensor may not…”
Automatic Analysis of Facial Affect: A Survey of Registration, Representation, and Recognition (2015, methodology): “One way to deal with head-pose variations is to design high-level representations that learn the appearance variation caused by head-pose variations using linear or nonlinear feature extraction techniques such as factor analysis [109], multilinear mapping with tensors [159] or manifold learning [148”
Face transfer with multilinear models (2005, methodology): “These techniques were successfully applied to multilinear analysis of images [Vasilescu and Terzopoulos 2002; Vasilescu and Terzopoulos 2004].”
Age Synthesis and Estimation via Faces: A Survey (2010, positive): “When face images show multiple facial attributes [172], such as identity, expression, gender, age, ethnicity, and pose, the tensor representation (multilinear analysis) [173] can be adopted to handle uncontrollable and personalized characteristics.”
Canonical Correlation Analysis of Video Volume Tensors for Action Categorization and Detection (2009, background): “2 Multilinear algebra and notations Following the notations in [24, 28], a video volume is a third-order tensor which is denoted by A = (A)ijk ∈ RI×J×K .”
Multilinear subspace analysis of image ensembles (2003, methodology): “Reference [13] discusses the attractive properties of this analysis, some of which we now summarize.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, positive): “We have shown that the Tucker/HOSVD decomposition may be considered as a multilinear extension of PCA [160]; it therefore generalizes signal subspace techniques and finds application in areas including multilinear blind source separation, classification, feature extraction, and subspace-based harmon”
Multilinear independent components analysis (2005, methodology): “Motivated by the reported outperformance in the face recognition literature of PCA by ICA in the linear case where only a single factor is allowed to vary, and the outperformance of PCA by TensorFaces when multiple factors are allowed to vary, it is natural to ask whether there a multilinear general”
Separating Self-Expression and Visual Content in Hashtag Supervision (2017, background): “In computer vision, prominent examples of tensor models include the modeling of style and content [25], the joint analysis of image ensembles [29], sparse image coding [21] and gait recognition [8, 28].”
Tensor Canonical Correlation Analysis for Action Classification (2007, background): “This section briefly introduces useful notations and concepts of multilinear algebra [10].”
Non-negative tensor factorization with applications to statistics and computer vision (2005, background): “In computer vision, 3-way tensor decompositions, treating the training images as a 3D cube, have been also proposed (Shashua & Levin, 2001; Vasilescu & Terzopoulos , 2002) with the idea of preserving certain features of the SVD.”
Efficient MATLAB Computations with Sparse and Factored Tensors (2007, positive): “More recently, these methods have been applied to signal processing [10, 11], image processing [52, 54, 57, 53], data mining [43, 46, 1, 45], scientific computing [6], and elsewhere [26, 36].”
Tensor Analyzers (2013, methodology): “Tucker decomposition was applied to a 5-mode array of face images in (Vasilescu & Terzopoulos, 2002), finding multilinear bases called TensorFaces.”