This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Custom-Built Moments for Edge Location
April 2006 (vol. 28 no. 4)
pp. 637-642
We present a general construction of functions whose moments serve to locate and parametrize step edges within an image. Previous use of moments to locate edges was limited to functions supported on a circular region, but our method allows the use of "custom-designed” functions supported on circles, rectangles, or any desired shape, and with graphs whose shape may be chosen with great freedom. We present analyses of the sensitivity of our method to pixelization errors or discrepancy between the image and an idealized edge model. The parametric edge description yielded by our method makes it especially suitable as a component of wedgelet image coding.

[1] M. Wertheimer, “Untersuchungen zur Lehre der Gestalt, II,” Psychologische Forschung, vol. 4, pp. 301-350, 1923.
[2] A.P. Reeves, M.L. Akey, and O.R. Mitchell, “A Moment Based Two-Dimensional Edge Operator,” Proc. IEEE CS Symp. Computer Vision and Pattern Recognition, pp. 312-317, 1983.
[3] J.F. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, 1986.
[4] E.P. Lyvers, O.R. Mitchell, M.L. Akey, and A.P. Reeves, “Subpixel Measurements Using a Moment-Based Edge Operator,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1293-1309, Dec. 1989.
[5] S. Ghosal and R. Mehrotra, “Orthogonal Moment Operators for Subpixel Edge Detection,” Pattern Recognition, vol. 26, no. 2, pp. 295-306, 1993.
[6] S.X. Liao and M. Pawlak, “On Image Analysis by Moments,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 254-266, Mar. 1996.
[7] S. Ghosal and R. Mehrotra, “A Moment-Based Unified Approach to Image Feature Detection,” IEEE Trans. Image Processing, vol. 6, no. 6, pp. 781-793, 1997.
[8] D.L. Donoho, “Wedgelets: Nearly Minimax Estimations of Edges,” Annals of Statistics, vol. 27, no. 3, pp. 859-897, 1999.
[9] R. Mukundan, S.H. Ong, and P.A. Lee, “Image Analysis by Tchebichef Moments,” IEEE Trans. Image Processing, vol. 10, no. 9, pp. 1357-1364, 2001.
[10] I. Popovici and W.D. Withers, Research Proposal Naval Academy Research Council, Nov. 2003.
[11] X. Huo, “JBEAM: Multiscale Curve Coding via Beamlets,” IPAM presentation, Sept. 2004.
[12] H. Führ, L. Demaret, and F. Friedrich, “Beyond Wavelets: New Image Representation Paradigms,” (preprint).
[13] L. Demaret, H. Führ, and F. Friedrich, “A Quick Guide to Wedgelets,” (preprint).
[14] I. Popovici and W.D. Withers, “Locating Edges and Removing Ringing Artifacts in JPEG Images by Frequency-Domain Analysis,” (preprint).
[15] J.K. Romberg, M.B. Wakin, R.G. Baraniuk, Multiscale Geometric Image Processing. (preprint).

Index Terms:
Edge detection, moments, step edge, Radon transform, wedgelets.
Citation:
Irina Popovici, William Douglas Withers, "Custom-Built Moments for Edge Location," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 637-642, April 2006, doi:10.1109/TPAMI.2006.75
Usage of this product signifies your acceptance of the Terms of Use.