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SLIDE: Subspace-Based Line Detection
November 1994 (vol. 16 no. 11)
pp. 1057-1073

An analogy is made between each straight line in an image and a planar propagating wavefront impinging on an array of sensors so as to obtain a mathematical model exploited in recent high resolution methods for direction-of-arrival estimation in sensor array processing. The new so-called SLIDE (subspace-based line detection) algorithm then exploits the spatial coherence between the contributions of each line in different rows of the image to enhance and distinguish a signal subspace that is defined by the desired line parameters. SLIDE yields closed-form and high resolution estimates for line parameters, and its computational complexity and storage requirements are far less than those of the standard method of the Hough transform. If unknown a priori, the number of lines is also estimated in the proposed technique. The signal representation employed in this formulation is also generalized to handle grey-scale images as well. The technique has also been generalized to fitting planes in 3-D images. Some practical issues of the proposed technique are given.

[1] H. K. Aghajan and T. Kailath, "A subspace fitting approach to super resolution multi-line fitting and straight edge detection," inProc. of IEEE ICASSP, San Fransisco, CA, 1992, pp. III:121-124.
[2] H. K. Aghajan and T. Kailath, "SLIDE: subspace-based line detection," inProc. IEEE ICASSP, Minneapolis, MN, 1993, pp. 89-92.
[3] H. K. Aghajan and T. Kailath, "Sensor array processing techniques for super resolution multi-line fitting and straight edge detection,"IEEE Trans. Image Processing, vol. 2, no. 4, pp. 454-465, 1993.
[4] E.R. Davies,Machine Vision: Theory, Algorithms, Practicalities. London: Academic Press, 1990.
[5] S. R. Deans,The Radon Transform and Some of Its Applications. New York: John Wiley&Sons, 1983.
[6] R.O. Duda and P.E. Hart, "Use of the Hough transformation to detect lines and curves in pictures,"Commun. Ass. Comput. Mach., vol. 15, no. 1, pp. 11-15, Jan. 1972.
[7] G. H. Golub and C. F. Van Loan,Matrix Computations. Baltimore, MD: Johns Hopkins University Press, 1984.
[8] S. Haykin,Adaptive Filter Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1991.
[9] P. Hough, "Method and means for recognizing complex patterns," U.S. Patent 3069654, 1962.
[10] A. Jain,Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[11] N. Kiryati and A. M. Bruckstein, "On navigation between friends and foes,"IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 6, pp. 602-606, 1991.
[12] W. Niblack and D. Petkovic, "On improving the accuracy of the Hough transform: Theory, simulations and experiments," inProc. IEEE Conf. CVPR'88, Ann Arbor, MI, June 1988, pp. 574-579.
[13] S. J. Orfanidis,Optimum Signal Processing, 2nd ed. New York: MacMillan, 1988.
[14] B. N. Parlett,The Symmetric Eigenvalue Problem. Englewood Cliffs, NJ: Prentice-Hall, 1980.
[15] A. Paulraj, R. Roy, and T. Kailath, "Estimation of signal parameters by rotational invariance techniques (ESPRIT)," inProc. 19th Asilomar Conf. Circuits, Systems and Comp., 1985.
[16] A. Paulraj, R. Roy, and T. Kailath, "A subspace rotation approach to signal parameter estimation,"Proc. IEEE, July 1986, pp. 1044-1045.
[17] R. Roy and T. Kailath, "ESPRIT: Estimation of signal parameters via rotational invariance techniques,"IEEE Trans. on ASSP, vol. 37, no. 7, pp. 984-995, 1989.
[18] R. O. Schmidt, "Multiple emitter location and signal parameter estimation,"IEEE Trans. Antenn. Propagat., vol. 34, no. 3, pp. 276-280, March 1986. First presented at RADC Spectrum Estimation Workshop, 1979, Griffiss AFB, NY.
[19] M. Viberg, B. Ottersten, and T. Kailath, "Detection and estimation in sensor arrays using weighted subspace fitting,"IEEE Trans. SP, vol. 39, no. 11, pp. 2436-2449, 1991.
[20] M. Wax and T. Kailath, "Detection of signals by information theoretic criteria,"IEEE Trans. ASSP, vol. 33, no. 2, pp. 387-392, 1985.
[21] M. Wax and I. Ziskind, "Detection of the number of coherent signals by the MDL principle,"IEEE Trans. ASSP, vol. 37, no. 8, pp. 1190-1196, 1989.
[22] G. Xu and T. Kailath, "A fast algorithm for signal subspace decomposition and its performance analysis," inProc. IEEE ICASSP, Toronto, Canada, 1991, pp. 3069-3072.

Index Terms:
edge detection; object recognition; array signal processing; computational complexity; curve fitting; parameter estimation; SLIDE; subspace-based line detection; direction-of-arrival estimation; sensor array processing; straight lines; line parameter estimation; computational complexity; Hough transform; signal representation; grey-scale images; 3D images
Citation:
H.K. Aghajan, T. Kailath, "SLIDE: Subspace-Based Line Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 11, pp. 1057-1073, Nov. 1994, doi:10.1109/34.334386
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