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.
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References
Abdi, H., Valentin, D., Edelman, B., and O'Toole, A. 1995. More about the difference between men and women: Evidence from linear neural networks and the principal component approach. Perception, 24:539–562.
Berry, M.W. 1992. Large-scale sparse singular value computations. The International Journal of Supercomputer Applications, 6(1):13–49.
Burl, M.C., Fayyad, U.M., Perona, P., Smyth, P., and Burl, M.P. 1994. Automating the hunt for volcanoes on venus. Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'94), pp. 302–309.
Champagne, B. 1994. Adaptive eigendecomposition of data covariance matrices based on first-order perturbations. IEEE Transactions on Signal Processing, 42(10):2758–2770.
Devijver, P.A. and Kittler, J. 1982. Pattern Recognition: A Statistical Approach. London: Prentice Hall.
Fukunaga, K. 1990. Introduction to Statistical Pattern Recognition (second edition). New York: Academic Press.
Golub, G.H. and Van-Loan, C.F. 1996. Matrix Computations (third edition). The Johns Hopkins University Press.
Hertz, J., Krogh, A., and Palmer, R. 1991. Introduction to the Theory of Neural Computation. Reading, Massachusetts: Addison-Wesley.
Jolliffe, I.T. 1986. Principal Component Analysis. Springer-Verlag.
Leonardis, A. and Bischof, H. 1996. Dealing with occlusions in the eigenspace approach. Proc. of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR'96). IEEE Computer Society Press, pp. 453–458.
Murakami, H. and Kumar, V. 1982. Efficient calculation of primary images from a set of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4(5):511–515.
Murase, H. and Nayar, S. 1994. Illumination planning for object recognition using parametric eigenspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(12):1219–1227.
Murase, H. and Lindenbaum, M. 1995. Partial eigenvalue decomposition of large images using spatial-temporal adaptive method. IEEE Transactions on Image Processing, 4(5):620–629.
Murase, H. and Nayar, S. 1995. Visual learning and recognition of 3D objects from appearance. International Journal of Computer Vision, 14:5–24.
Patel, N. and Sethi, I. 1997. Video segmentation for video data management. In The Handbook of Multimedia Information Management, W. Grosky, R. Jain, and R. Mehrotra (Eds.). Prentice Hall PTR, chap. 5, pp. 139–165.
Pentland, A., Picard, R.W., and Sclaroff, S. 1994. Photobook: Tools for content-base manipulation of image databases. Proc. SPIE Conf. on Storage and Retrieval of Image and Video Databases II, San Jose, CA, pp. 34–47.
Rosenfeld, A. and Kak, A.C. 1982. Digital Picture Processing (second edition). Academic Press.
Sanger, T.D. 1989. An optimality principle for unsupervised learning. In Advances in Neural Information Processing Systems, D.S. Touretzky (Ed.). San Mateo, 1989. (Denver 1988), Morgan Kaufmann, pp. 11–19.
Schweitzer, H. 1995. Occam algorithms for computing visual motion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(11):1033–1042.
Schweitzer, H. 1998a. Computing Ritz approximations to primary images. Proceedings of the Sixth International Conference on Computer Vision (ICCV'98), (in press).
Schweitzer, H. 1998b. Indexing images by trees of visual content. Proceedings of the Sixth International Conference on Computer Vision (ICCV'98), (in press).
Stewart, G.W. 1969. Accelerating the orthogonal iteration for the eigenvalues of a hermitian matrix. Numer. Math., 13:362–376.
Swets, D.L. and Weng, J. 1996. Using discriminant eigenfeatures for image retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(8):831–836.
Turk, M. and Pentland, A. 1991. Eigenfaces for recognition. Journal of Cognitive Neuroscience, 3(1):71–86.
Yang, X., Sarkar, T., and Arvas, E. 1989. A survey of conjugate gradient algorithms for solutions of extreme eigenproblems of a symmetric matrix. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(10):1550–1555.
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Schweitzer, H. A Distributed Algorithm for Content Based Indexing of Images by Projections on Ritz Primary Images. Data Mining and Knowledge Discovery 1, 375–390 (1997). https://doi.org/10.1023/A:1009725401947
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DOI: https://doi.org/10.1023/A:1009725401947