Computing steerable principal components of a large set of images and their rotations

IEEE Transactions on Image Processing

Volumn 20, Issue 11, 2011, Pages 3051-3062

  Ponce, Colin ^a   Singer, Amit ^b  

^a Department of Computer Science and School of Operations Research and Information Engineering   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

EDICS Category: TEC PRC image and video processing techniques

Indexed keywords

BLOCK CIRCULANT; CRYO-ELECTRON MICROSCOPY; EFFICIENT ALGORITHM; IMAGE AND VIDEO PROCESSING; LARGE IMAGES; NUMERICAL EXPERIMENTS; PRINCIPAL COMPONENTS;

ALGORITHMS; COVARIANCE MATRIX; ELECTRON MICROSCOPES; ROTATION;

PRINCIPAL COMPONENT ANALYSIS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; CRYOELECTRON MICROSCOPY; IMAGE ENHANCEMENT; METHODOLOGY; PRINCIPAL COMPONENT ANALYSIS;

ALGORITHMS; CRYOELECTRON MICROSCOPY; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; PRINCIPAL COMPONENT ANALYSIS;

EID: 80054799154     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2011.2147323     Document Type: Article

References (22)

1. L. Borland and M. van Heel, "Classification of image data in conjugate representation spaces," J. Opt. Soc. Amer. A, vol. 7, no. 4, pp. 601-610, 1990.
2. A. Dutt and V. Rokhlin, "Fast Fourier transorms for nonequispaced data," SIAM J. Sci. Comput., vol. 14, no. 6, pp. 1368-1393, 1993.
3. J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State, 2nd ed. New York: Oxford Univ. Press, 2006.
4. D. G. Gardner, J. C. Gardner, G. Lausch, and W. W. Meinke, "Method for the analysis of multi-component exponential decays," J. Chem. Phys., vol. 31, p. 987, 1959.
5. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ., 1996.
6. L. Greengard and J.-Y. Lee, "Accelerating the nonuniform fast Fourier transform," SIAM Rev., vol. 46, no. 3, pp. 443-454, 2004.
7. M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields," J. Opt. Soc. Amer. A, vol. 21, pp. 53-58, 2004.
8. R. Hilai and J. Rubinstein, "Recognition of rotated images by invariant Karhunen-Loeve expansion," J. Opt. Soc. Amer. A, vol. 11, pp. 1610-1618, 1994.
9. M. Jogan, E. Zagar, and A. Leonardis, "Karhunen-Loéve expansion of a set of rotated templates," IEEE Trans. Image Process., vol. 12, no. 7, pp. 817-825, Jul. 2003.
10. A. Khotanzad and J. H. Lu, "Object recognition using a neural network and invariant Zernike features," in Proc. IEEE Conf. Vis. Pattern Recognit., 1989, pp. 200-205.
11. F. Natterer, The Mathematics of Computerized Tomography. Philadelphia, PA: SIAM, 2001.
12. R. Park, "Correspondence," IEEE Trans. Image Process., vol. 11, no. 3, pp. 332-334, Mar. 2002.
13. P. A. Penczek, J. Zhu, and J. Frank, "A common-lines based method for determining orientations for N > 3 particle projections simultaneously," Ultramicroscopy, vol. 63, pp. 205-218, 1996.
14. P. Perona, "Deformable kernels for early vision," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 5, pp. 488-499, May 1995.
15. A. E. Siegmann, "Quasi fast Hankel transform," Opt. Lett., vol. 1, pp. 13-15, 1977.
16. F. J. Sigworth, "Classical detection theory and the Cryo-EM particle selection problem," J. Structural Biol., vol. 145, pp. 111-122, 2004.
17. A. Singer, Z. Zhao, Y. Shkolnisky, and R. Hadani, "Viewing angle classification of cryo-electron microscopy images using eigenvectors," SIAM J. Imag. Sci., vol. 4, no. 2, pp. 723-759, 2011.
18. A. Singer and Z. Zhao, In Preparation.
19. M. R. Teague, "Image analysis via the general theory of moments," J. Opt. Soc. Amer., vol. 70, pp. 920-930, 1980.
20. M. Uenohara and T. Kanade, "Optimal approximation of uniformly rotated images: Relationship between Karhunen-Loeve expansion and discrete cosine transform," IEEE Trans. Image Process., vol. 7, no. 1, pp. 116-119, Jan. 1998.
21. M. van Heel and J. Frank, "Use of multivariate statistics in analysing the images of biological macromolecules," Ultramicroscopy, vol. 6, pp. 187-194, 1981.
22. M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, and A. Patwardhan, "Single-particle electron cryo-microscopy: Towards atomic resolution," Quarterly Rev. Biophys., vol. 33, no. 4, pp. 307-369, 2000.