Computing Steerable Principal Components of a Large Set of Images and Their Rotations

Authors:
Colin Ponce;Amit Singer
Affiliations:
Department of Computer Science, Cornell University, Ithaca, NY, USA;Department of Mathematics and PACM, Princeton University, Princeton, NJ, USA
Venue:
IEEE Transactions on Image Processing
Year:
2011

Citing 0
Cited 3

Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors

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An Algorithm for the Principal Component Analysis of Large Data Sets

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Rotation-Invariant HOG Descriptors Using Fourier Analysis in Polar and Spherical Coordinates

International Journal of Computer Vision

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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.