Computing steerable principal components of a large set of images and their rotations

Colin Ponce; Amit Singer

doi:10.1109/TIP.2011.2147323

Computing steerable principal components of a large set of images and their rotations

Colin Ponce, Amit Singer

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.

Original language	English (US)
Article number	5759743
Pages (from-to)	3051-3062
Number of pages	12
Journal	IEEE Transactions on Image Processing
Volume	20
Issue number	11
DOIs	https://doi.org/10.1109/TIP.2011.2147323
State	Published - Nov 2011

All Science Journal Classification (ASJC) codes

Software
Computer Graphics and Computer-Aided Design

Keywords

EDICS Category: TEC-PRC image and video processing techniques

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10.1109/TIP.2011.2147323

Cite this

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title = "Computing steerable principal components of a large set of images and their rotations",

abstract = "We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.",

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author = "Colin Ponce and Amit Singer",

note = "Funding Information: Manuscript received April 12, 2010; revised December 06, 2010; accepted April 07, 2011. Date of publication May 02, 2011; date of current version October 19, 2011 This work was supported by the National Institute of General Medical Sciences under Award R01GM090200. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Hsueh-Ming Hang.",

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AB - We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.

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Computing steerable principal components of a large set of images and their rotations

Abstract

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