Pose estimation from a single image using tensor decomposition and an algebra of circulants

Hoover,; Braman,; Hao,

doi:10.1109/iros.2011.6048087

Cited by 4 publications

(15 citation statements)

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“…In this section, we provide a brief overview of the tensor definitions and mathematical operations required to keep this work self contained, extended details may be found in [8][9][10][11][12][13][14].…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…In this section we provide an overview of our prior work on multilinear Tensor PCA as outlined in [8][9][10] and illustrate some of the shortcomings of such an approach. We then turn our attention to extensions of our prior work combined with the work of [6,7] to capitalize on correlations in both the rowand column-dimensions of the image set.…”

Section: Proposed 2dtpca Approachmentioning

confidence: 99%

“…To keep the current work self-contained, we present a brief overview of our work on Tensor PCA outlined in [8][9][10] that capitalizes on the definitions outlined in Section 2. As shown in Fig.…”

Section: Overview Of Tensor Pcamentioning

confidence: 99%

“…Most notably was a reduced order feature space in the row-pixels, referred to as 2DPCA [6] that was later extended to both the rowand column-pixels referred to as (2D) 2 PCA [7]. Finally, the author's show in [8][9][10] that an alternate approach to multilinear PCA (referred to as Tensor PCA) can be performed based on a recently defined multiplication operator for third order tensors [11][12][13][14], referred to as the t-product and resulting t-SVD (as outlined in Section 2). This operator is advantageous in that it allows for a tensor singular value decomposition to be defined that is analogous to its matrix counterpart, i.e., it decomposes a third-order tensor into three third-order tensors with similar orthogonality and diagonal structures.…”

Section: Introductionmentioning

confidence: 99%

“…The current paper builds on our prior work in [8][9][10] while capitalizing on the developments of both 2DPCA as well as (2D) 2 PCA as outlined in [6,7]. In particular, we illustrate that through the t-product and resulting t-SVD, (2D) 2 PCA can be re-formulated into a multilinear framework that decomposes both the rowand column-pixels into reduced dimensional tensor models of order three (i.e., reduced dimensional 3-mode tensors) referred to as 2D Tensor PCA (2DTPCA).…”

Section: Introductionmentioning

confidence: 99%

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2DTPCA: A New Framework for Multilinear Principal Component Analysis

Ozdemir¹,

Hoover

Caudle

2021

2021 IEEE International Conference on Image Processing (ICIP)

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Two-directional two-dimensional principal component analysis ((2D) 2 PCA) has shown promising results for it's ability to both represent and recognize facial images. The current paper extends these results into a multilinear framework (referred to as two-directional Tensor PCA or 2DTPCA for short) using a recently defined tensor operator for 3 rd -order tensors. The approach proceeds by first computing a low-dimensional projection tensor for the row-space of the image data (generally referred to as mode-1) and then subsequently computing a low-dimensional projection tensor for the column space of the image data (generally referred to as mode-3). Experimental results are presented on the ORL, extended Yale-B, COIL-100, and MNIST data sets that show the proposed approach outperforms traditional "tensor-based" PCA approaches with a much smaller subspace dimension in terms of recognition rates.

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Section: Mathematical Preliminariesmentioning

confidence: 99%

Section: Proposed 2dtpca Approachmentioning

confidence: 99%

Section: Overview Of Tensor Pcamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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2DTPCA: A New Framework for Multilinear Principal Component Analysis

Ozdemir¹,

Hoover

Caudle

2021

2021 IEEE International Conference on Image Processing (ICIP)

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A New Approach to Multilinear Dynamical Systems and Control

Hoover¹,

Caudle²,

Braman³

2021

Preprint

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The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown that under the right tensor multiplication operator, a third order tensor can be written as a product of third order tensors that is analogous to a traditional matrix eigenvalue decomposition where the "eigenvectors" become eigenmatrices and the "eigenvalues" become eigen-tuples. This new development allows for a proper tensor eigenvalue decomposition to be defined and has natural extension to linear systems theory through a tensor-exponential. Through this framework we extend many of traditional techniques used in linear system theory to their multilinear counterpart.

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High-Order Multilinear Discriminant Analysis via Order-$\textit{n}$ Tensor Eigendecomposition

Ozdemir¹,

Hoover²,

Caudle³

et al. 2022

Preprint

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Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data structures while keeping the natural representation of the data samples. In the past decade, great efforts have been made to extend the classic linear discriminant analysis for higherorder data classification generally referred to as multilinear discriminant analysis (MDA). Most of the existing approaches are based on the Tucker decomposition and n-mode tensormatrix products. The current paper presents a new approach to tensor-based multilinear discriminant analysis referred to as High-Order Multilinear Discriminant Analysis (HOMLDA). This approach is based upon the tensor decomposition where an ordern tensor can be written as a product of order-n tensors and has a natural extension to traditional linear discriminant analysis (LDA). Furthermore, the resulting framework, HOMLDA, might produce a within-class scatter tensor that is close to singular. Thus, computing the inverse inaccurately may distort the discriminant analysis. To address this problem, an improved method referred to as Robust High-Order Multilinear Discriminant Analysis (RHOMLDA) is introduced. Experimental results on multiple data sets illustrate that our proposed approach provides improved classification performance with respect to the current Tucker decomposition-based supervised learning methods.

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Pose estimation from a single image using tensor decomposition and an algebra of circulants

Cited by 4 publications

References 0 publications

2DTPCA: A New Framework for Multilinear Principal Component Analysis

2DTPCA: A New Framework for Multilinear Principal Component Analysis

A New Approach to Multilinear Dynamical Systems and Control

High-Order Multilinear Discriminant Analysis via Order-$\textit{n}$ Tensor Eigendecomposition

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