On the efficient update of the Singular Value Decomposition

Stange, Peter

doi:10.1002/pamm.200810827

Cited by 22 publications

(21 citation statements)

References 4 publications

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“…Multiplying VC yields the right singular vectors ofWA. This can be done efficiently by exploiting the Cauchy structure iñ C [16]. The cost of this rank-one update is O(m 2 log 2 m).…”

Section: Efficient Learning For Image Stitchingmentioning

confidence: 99%

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As-Projective-As-Possible Image Stitching with Moving DLT

Zaragoza

Chin

Brown

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

455

482

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We investigate projective estimation under model inadequacies, i.e., when the underpinning assumptions of the projective model are not fully satisfied by the data. We focus on the task of image stitching which is customarily solved by estimating a projective warp -a model that is justified when the scene is planar or when the views differ purely by rotation. Such conditions are easily violated in practice, and this yields stitching results with ghosting artefacts that necessitate the usage of deghosting algorithms. To this end we propose as-projective-as-possible warps, i.e., warps that aim to be globally projective, yet allow local non-projective deviations to account for violations to the assumed imaging conditions. Based on a novel estimation technique called Moving Direct Linear Transformation (Moving DLT), our method seamlessly bridges image regions that are inconsistent with the projective model. The result is highly accurate image stitching, with significantly reduced ghosting effects, thus lowering the dependency on post hoc deghosting.

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“…Multiplying VC yields the right singular vectors ofWA. This can be done efficiently by exploiting the Cauchy structure iñ C [16]. The cost of this rank-one update is O(m 2 log 2 m).…”

Section: Efficient Learning For Image Stitchingmentioning

confidence: 99%

“…can be done efficiently using secular equations [16]. Multiplying VC yields the right singular vectors ofWA.…”

Section: Efficient Learning For Image Stitchingmentioning

confidence: 99%

As-Projective-As-Possible Image Stitching with Moving DLT

Zaragoza

Chin

Brown

et al. 2013

2013 IEEE Conference on Computer Vision and Pattern Recognition

455

482

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show abstract

“…This is due to the fact that singular vectors are expressed through singular values as Theorem 1 states. There are no any other error measures in the papers [19] [23] [24] which are related to SVD update.…”

Section: Methodsmentioning

confidence: 99%

“…There are methods which utilize the previously computed SVD decomposition and use it to compute the SVD for an extended matrix [19], [23] [24]. Below, we summarize the theoretical considerations behind those methods.…”

Section: Svd Update Theorymentioning

confidence: 99%

Singular Value Decomposition update and its application to (Inc)-OP-ELM

et al. 2016

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“…Here, we work with the eigenvalue decomposition (EVD) square root. Denoting the full EVD of as , or alternatively as the triplet , the full EVD of can be found via a rank-1 update to the (scaled) EVD of [53], [54]. We denote this as , where is a rank-1 matrix.…”

Section: B Online Transform Learningmentioning

confidence: 99%

Online Sparsifying Transform Learning—Part I: Algorithms

Ravishankar

Wen

Bresler

2015

IEEE J. Sel. Top. Signal Process.

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Techniques exploiting the sparsity of signals in a transform domain or dictionary have been popular in signal processing. Adaptive synthesis dictionaries have been shown to be useful in applications such as signal denoising, and medical image reconstruction. More recently, the learning of sparsifying transforms for data has received interest. The sparsifying transform model allows for cheap and exact computations. In this paper, we develop a methodology for online learning of square sparsifying transforms. Such online learning can be particularly useful when dealing with big data, and for signal processing applications such as real-time sparse representation and denoising. The proposed transform learning algorithms are shown to have a much lower computational cost than online synthesis dictionary learning. In practice, the sequential learning of a sparsifying transform typically converges faster than batch mode transform learning. Preliminary experiments show the usefulness of the proposed schemes for sparse representation, and denoising.

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On the efficient update of the Singular Value Decomposition

Cited by 22 publications

References 4 publications

As-Projective-As-Possible Image Stitching with Moving DLT

As-Projective-As-Possible Image Stitching with Moving DLT

Singular Value Decomposition update and its application to (Inc)-OP-ELM

Online Sparsifying Transform Learning—Part I: Algorithms

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