计算一大组图像及其旋转的可引导主成分。
Computing steerable principal components of a large set of images and their rotations.
机构信息
Department of Computer Science, Cornell University, Ithaca, NY 14850, USA.
出版信息
IEEE Trans Image Process. 2011 Nov;20(11):3051-62. doi: 10.1109/TIP.2011.2147323. Epub 2011 May 2.
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.
摘要
我们在此提出一种高效算法，可计算由大量图像及其在平面内的均匀旋转集组成的图像集的主成分分析 (PCA)。我们通过指出协方差矩阵的块循环结构并利用该结构来计算其特征向量来实现这一点。我们还通过数值实验展示了该算法相对于类似算法的优势。尽管它在许多情况下都很有用，但我们将算法的具体应用示例说明为低温电子显微镜问题。
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