This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Design of Multiparameter Steerable Functions Using Cascade Basis Reduction
June 1999 (vol. 21 no. 6)
pp. 552-556

Abstract—An efficient method of computing the least-squares optimal basis functions to steer any function locally is presented. The method combines the Lie group-theoretic and the singular value decomposition approaches. Its efficiency is demonstrated with the design of basis functions to steer a Gabor function under the four-parameter linear transformation group.

[1] W.T. Freeman and E.H. Adelson, "The Design and Use of Steerable Filters," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 891-906, 1991.
[2] E.P. Simoncelli, W.T. Freeman, E.H. Adelson, and D.J. Heeger, “Shiftable Multi-Scale Transforms,” IEEE Trans. Information Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
[3] P. Perona, "Deformable Kernels for Early Vision," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 488-499, May 1995.
[4] E. Simoncelli and H. Farid, “Steerable Wedge Filters,” Proc. Int'l Conf. Computer Vision, pp. 189-194, Boston, 1995.
[5] R. Manduchi and P. Perona, “Pyramidal Implementation of Deformable Kernels,” Proc. IEEE Int'l Conf. Image Processing, pp. 378-381, 1995.
[6] E. Adelson and J. Bergen, “Spatiotemporal Energy Models for the Perception of Motion,” J. Optimal Soc. of America A, vol. 2, no. 2, pp. 284-299, Feb. 1985.
[7] A. Watson and A. Ahumada, “Model of Human Visual-Motion Sensing,” J. Optimal Soc. of America A, vol. 2, no. 2, pp. 322-342, Feb. 1985.
[8] G.H. Granlund and H. Knuttson, Signal Processing for Computer Vision. Kluwer, 1995.
[9] R. Manmatha, "A Framework for Recovering Affine Transforms Using Points, Lines, or Image Brightnesses," Proc. Conf. Computer Vision and Pattern Recognition, pp. 141-146, 1994.
[10] Y. Xiong and S. Shafer, “Moment and Hypergeometric Filters for High Precision Computation of Focus, Stereo and Optical Flow,” Technical Report CMU-RI-TR-94-28, Carnegie Mellon Univ., 1994.
[11] H. Liu, T. Hong, M. Herman, and R. Chellappa, “A Reliable Optical Flow Algorithm Using 3D Hermite Polynomials,” Technical Report CS-TR-3291, Univ. of Maryland, 1994.
[12] D.J. Fleet and A.D. Jepson, “Computation of Component Image Velocity from Local Phase Information,” Int'l J. Computer Vision, vol. 5, no. 1, pp. 77-104, 1990.
[13] J. Weng, “Image Matching Using the Windowed Fourier Phase,” Int'l J. Computer Vision, vol. 11, no. 3, pp. 211-236, 1993.
[14] C. Gotsman, “Constant-Time Filtering by Singular Value Decomposition,” Computer Graphics Forum, vol. 13, no. 2, pp. 153-163, 1994.
[15] J. Nimeroff, E. Simoncelli, and J. Dorsey, “Efficient Re-Rendering of Naturally Illuminated Environments,” Fifth Eurographics Workshop on Rendering, 1994.
[16] D.J. Heeger and J.R. Bergen, “Pyramid-Based Texture Analysis/Synthesis,” SIGGRAPH 95 Conf. Proc., R.L. Cook, ed., pp. 229-238, Aug. 1995.
[17] M. Michaelis and G. Sommer, “A Lie Group-Approach to Steerable Functions,” Pattern Recognition Letters, vol. 16, no. 11, pp. 1,165-1,174, Nov. 1995.
[18] Y. Hel-Or and P. Teo, “Canonical Decomposition of Steerable Functions,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 809-816, San Francisco, 1996.
[19] R. Lenz, Group Theoretical Methods in Image Processing. New York: Springer-Verlag, 1990.

Index Terms:
Steerable filters, filter design, low-levelvision, pattern analysis.
Citation:
Patrick C. Teo, Yacov Hel-Or, "Design of Multiparameter Steerable Functions Using Cascade Basis Reduction," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 6, pp. 552-556, June 1999, doi:10.1109/34.771325
Usage of this product signifies your acceptance of the Terms of Use.