A Distributed Algorithm for Content Based Indexing of Images by Projections on Ritz Primary Images

Abstract

Large collections of images can be indexed by their projections on a few “primary” images. The optimal primary images are the eigenvectors of a large covariance matrix. We address the problem of computing primary images when access to the images is expensive. This is the case when the images cannot be kept locally, but must be accessed through slow communication such as the Internet, or stored in a compressed form. A distributed algorithm that computes optimal approximations to the eigenvectors (known as Ritz vectors) in one pass through the image set is proposed. When iterated, the algorithm can recover the exact eigenvectors. The widely used SVD technique for computing the primary images of a small image set is a special case of the proposed algorithm. In applications to image libraries and learning, it is necessary to compute different primary images for several sub-categories of the image set. The proposed algorithm can compute these additional primary images “offline”, without the image data. Similar computation by other algorithms is impractical even when access to the images is inexpensive.