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.
authors.affiliation: Department of Computer Science, Cornell University, Ithaca, NY 14850, USA. cponce@cs.cornell.edu
authors.forename: Colin
authors.initials: C
authors.lastname: Ponce
authors.forename: Amit
authors.initials: A
authors.lastname: Singer
mesh_terms: D000465:Algorithms; D020285:Cryoelectron Microscopy; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D025341:Principal Component Analysis