Abstract
A multidimensional Hough transform is used in conjunction with continuous wavelet transforms to aid in solving a parameterized inverse problem. The inverse problem under consideration is the characterization of distributed scatterers by means of active wideband remote sensing. Wavelet transforms are used to obtain estimates of distributed scatterers in the delay/scale plane. From a noisy wavelet transform estimate, the Hough transform is used to estimate a support region which is directly related to the physical parameters describing the distributed object.
Similar content being viewed by others
References
T.L. Dixon and L.H. Sibul, “A Wavelet Transform Approach to Parameter Estimation of a Distributed Object,”Proceedings of the 28th Annual Conference on Information Sciences and Systems, March 1994.
T.L. Dixon, “Wideband Imaging of Distributed Objects Using Wavelet Transforms and Generalized Inverse Theory,” Ph.D. Thesis, Department of Electrical Engineering, The Pennsylvania State University, PA, August 1994.
P.V.C. Hough, “Method and Means for Recognizing Complex Patterns,” U.S. Patent 3,069,654, Dec. 18, 1962.
A. Rosenfeld,Picture Processing by Computer, New York: Academic Press, 1969.
R.O. Duda and P.E. Hart, “Use of the Hough Transformation to Detect Lines and Curves in Pictures,”Communications of the ACM, Vol. 15, 1972, pp. 11–15.
S.D. Shapiro, “Transformations for the Computer Detection of Curves in Noisy Pictures,”Computer Graphics and Image Processing, Vol. 4, 1975, pp. 328–338.
C. Kimme, D. Ballard, and J. Sklansky, “Finding Circles by an Array of Accumulators,”Communications of the ACM, Vol. 18, February 1975, pp. 120–122.
A. Iannino and S.D. Shapiro, “A Survey of the Hough Transform and its Extensions for Curve Detection,”Proceedings of the IEEE Computer Society Conference on Pattern Recognition and Image Processing, Chicago, June 1978.
J. Illingworth and J. Kittler, “A Survey of the Hough Transform,”Computer Vision, Graphics, and Image Processing, Vol. 44, No. 1, October 1988, pp. 87–116.
F. O'Gorman and M.B. Clowes, “Finding Picture Edges Through Colinearity of Feature Points,”IEEE Transactions on Computers, Vol. C-25, No. 4, April 1976, pp. 449–456.
L. Feng and Y. Fainman, “Detection of a General Ellipse by an Optical Hough Transform,”Applied Optics, Vol. 31, No. 17, July 10, 1992, p. 3259.
S.M. Bhandarkar and M. Suk, “Qualitative Features and the Generalized Hough Transform,”Pattern Recognition, Vol. 25, No. 9, 1992, p. 987.
R.K.K. Yip, P.K.S. Tam, and D.N.K. Leung, “Modification of the Hough Transform for Circle and Ellipse Detection Using a 2-Dimensional Array,”Pattern Recognition, Vol. 25, No. 9, 1992, p. 1007.
M.E. Brummer, “Hough Transform Detection of the Longitudinal Fissure in Tomographic Head Images,”IEEE Transactions on Medical Imaging, Vol. 10, No. 1, March 1, 1991, p. 74.
W.E.L. Grimson, “On the Sensitivity of the Hough Transform for Object Recognition”,IEEE Transactions on Pattern Analysis and Machines, Vol. 12, No. 3, March 1, 1990, p. 255.
H.K. Yuen, “Comparative Study of Hough Transform Methods for Circle Finding,”Image and Vision Computing, Vol. 8, No. 1, February 1, 1990, p. 71.
P.M. Lapsa, “Efficient Multi-dimensional Transformation from Data Space to Parameter Space,”Pattern Recognition Letters, Vol. 13, 1992, pp. 63–72.
H. Wechsler and J. Sklansky, “Automatic Detection of Ribs in Chest Radiographs,”Pattern Recognition, Vol. 9, January 1975, p. 21.
T.L. Dixon and L.H. Sibul, “Wideband Imaging of the Rotating Sphere: A Wavelet Transform Approach,”Proceedings of the 27th Annual Asilomar Conference on Signals, Systems, and Computers, Nov. 1993.
C.W. Groetsch,Generalized Inverses of Linear Operators: Representation and Approximation, New York: Dekker, 1977.
I. Daubechies, “The Wavelet Transform, Time-Frequency Localization, and Signal Analysis,”IEEE Transactions on Information Theory, Vol. 36, No. 5, September 1990, pp. 961–1005.
H.L. Naparst, “Dense Target Signal Processing,”IEEE Trans. on Info. Theory, Vol. 37, No. 2, March 1991, pp. 317–327.
P. Maass, “Wideband Approximation and Wavelet Transform,” inRadar and Sonar, Part II, New York: Springer-Verlag, 1992, pp. 83–88.
M.J.D. Powell,Computer Journal, Vol. 7, pp. 155–160, 1969.
M. Hestenes,Conjugate Direction Methods in Optimization, New York: Springer-Verlag, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dixon, T.L., Sibul, L.H. A parameterized hough transform approach for estimating the support of the wideband spreading function of a distributed object. Multidim Syst Sign Process 7, 75–86 (1996). https://doi.org/10.1007/BF02106108
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02106108