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Array Processing and Fast Optimization Algorithms for Distorted Circular Contour Retrieval


A specific formalism for virtual signal generation permits to transpose an image processing problem to an array processing problem. The existing method for straight-line characterization relies on the estimation of orientations and offsets of expected lines. This estimation is performed thanks to a subspace-based algorithm called subspace-based line detection (SLIDE). In this paper, we propose to retrieve circular and nearly circular contours in images. We estimate the radius of circles and we extend the estimation of circles to the retrieval of circular-like distorted contours. For this purpose we develop a new model for virtual signal generation; we simulate a circular antenna, so that a high-resolution method can be employed for radius estimation. An optimization method permits to extend circle fitting to the segmentation of objects which have any shape. We evaluate the performances of the proposed methods, on hand-made and real-world images, and we compare them with generalized Hough transform (GHT) and gradient vector flow (GVF).


  1. Crawford JF: A noniterative method for fitting circular arcs to measured points. Nuclear Instruments and Methods in Physics Research 1983,211(2):223-225.

    Article  Google Scholar 

  2. Karimäki V: Effective circle fitting for particle trajectories. Nuclear Instruments and Methods in Physics Research Section A 1991,305(1):187-191. 10.1016/0168-9002(91)90533-V

    Article  Google Scholar 

  3. Coath G, Musumeci P: Adaptive arc fitting for ball detection in robocup. Proceedings of APRS Workshop on Digital Image Computing (WDIC '03), February 2003, Brisbane, Australia 63–68.

    Google Scholar 

  4. Ballard DH: Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition 1981,13(2):111-122. 10.1016/0031-3203(81)90009-1

    Article  Google Scholar 

  5. Tisse CL, Martin L, Torres L, Robert M: Person identification technique using human iris recognition. International Conference on Vision Interface (VI '02), May 2002, Calgary, Canada 294–299.

    Google Scholar 

  6. Aghajan HK: Subspace techniques for image understanding and computer vision, Ph.D. dissertation.

    Google Scholar 

  7. Aghajan HK, Kailath T: Sensor array processing techniques for super resolution multi-line-fitting and straight edge detection. IEEE Transactions on Image Processing 1993,2(4):454-465. 10.1109/83.242355

    Article  Google Scholar 

  8. Xu C, Prince JL: Gradient vector flow: a new external force for snakes. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 1997, San Juan, Puerto Rico, USA 66–71.

    Google Scholar 

  9. Xie X, Mirmehdi M: RAGS: region-aided geometric snake. IEEE Transactions on Image Processing 2004,13(5):640-652. 10.1109/TIP.2004.826124

    Article  MathSciNet  Google Scholar 

  10. Bourennane S, Marot J: Contour estimation by array processing methods. EURASIP Journal on Applied Signal Processing 2006, 2006: 15 pages.

    MathSciNet  MATH  Google Scholar 

  11. Jones DR, Perttunen CD, Stuckman BE: Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory and Applications 1993,79(1):157-181. 10.1007/BF00941892

    Article  MathSciNet  Google Scholar 

  12. Bourennane S, Marot J: Optimization and interpolation for distorted contour estimation. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '06), May 2006, Toulouse, France 2: 717–720.

    MATH  Google Scholar 

  13. Aghajan HK, Kailath T: SLIDE: subspace-based line detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 1994,16(11):1057-1073. 10.1109/34.334386

    Article  Google Scholar 

  14. Roy R, Kailath T: ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(7):984-995. 10.1109/29.32276

    Article  Google Scholar 

  15. Aghajan HK, Khalaj BH, Kailath T: Estimation of multiple 2-D uniform motions by SLIDE: subspace-based line detection. IEEE Transactions on Image Processing 1999,8(4):517-526. 10.1109/83.753739

    Article  Google Scholar 

  16. Sheinvald J, Kiryati N: On the magic of SLIDE. Machine Vision and Applications 1997,9(5-6):251-261. 10.1007/s001380050046

    Article  Google Scholar 

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Correspondence to Julien Marot.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Marot, J., Bourennane, S. Array Processing and Fast Optimization Algorithms for Distorted Circular Contour Retrieval. EURASIP J. Adv. Signal Process. 2007, 057354 (2007).

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