Abstract
This paper presents an MCMC stochastic gradient algorithm for finding representations with optimal retrieval performance on given image datasets. For linear subspaces in the image space and the spectral space, the problem is formulated as that of optimization on a Grassmann manifold. By exploiting the underlying geometry of the manifold, a computationally effective algorithm is developed. The feasibility and effectiveness of the proposed algorithm are demonstrated through extensive experimental results.
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References
P.N. Belhumeur, J. P. Hepanha, and D. J. Kriegman, “Eigenfaces vs. fisherfaces: Recognition using class specific linear projection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19(7), pp. 711–720, 1997.
W.M. Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, Academic Press, 2003.
S. Geman and C.-R. Hwang, “Diffusions for global optimization,” SIAM J. Control and Optimization, vol. 24(24), pp. 1031–1043, 1987.
U. Grenander and M. I. Miller, “Representations of knowledge in complex systems,” Journal of the Royal Statistical Society, vol. 56(3), pp. 549–603, 1994.
U. Helmke and J. B. Moore, Optimization and Dynamical Systmes, Springer, 1996.
A. Hyvarinen, “Fast and robust fixed-point algorithm for independent component analysis,” IEEE Transactions on Neural Networks, vol. 10, pp. 626–634, 1999.
X. Liu and L. Cheng, “Independent spectral representations of images for recognition,” Journal of the Optical Society of America A, in press, 2003.
X. Liu and A. Srivastava, “Stochastic search for optimal linear representations of images on spaces with orthogonality constraints,” in Proceedings of the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, 2003.
X. Liu, A. Srivastava, and Kyle Gallivan, “Optimal linear representations of images for object recognition,” IEEE Transactions on Pattern Recognition and Machine Intelligence, under review, 2003 (Available at http://www.stat.fsu.eud/~anuj).
X. Liu and D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Research, vol. 42, no. 23, pp. 2617–2634, 2002.
H. Muller, W. Muller, D. M. Squire, S. Marchand-Maillet, and T. Pun, “Performance evaluation in content-based image retrieval: overview and proposals,” Pattern Recognition Letters, vol. 22, pp. 593–601, 2001.
C.P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, 1999.
Y. Rui, T. S. Huang, “Image retrieval: Current techniques, promising directions and open issues,” Journal of Visual Communication and Image Representation, vol. 10, pp. 39–62, 1999.
A.W. M. Smeulders, M. Worring, S. Santini, A. Gupta, and R. Jain, “Contentbased image retrieval at the end of the early years,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, pp. 1–32, 2000.
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Liu, X., Srivastava, A., Sun, D. (2003). Learning Optimal Representations for Image Retrieval Applications. In: Bakker, E.M., Lew, M.S., Huang, T.S., Sebe, N., Zhou, X.S. (eds) Image and Video Retrieval. CIVR 2003. Lecture Notes in Computer Science, vol 2728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45113-7_6
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DOI: https://doi.org/10.1007/3-540-45113-7_6
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