- Research Article
- Open Access
Array Processing and Fast Optimization Algorithms for Distorted Circular Contour Retrieval
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 057354 (2007)
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).
Crawford JF: A noniterative method for fitting circular arcs to measured points. Nuclear Instruments and Methods in Physics Research 1983,211(2):223-225.
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
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.
Ballard DH: Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition 1981,13(2):111-122. 10.1016/0031-3203(81)90009-1
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.
Aghajan HK: Subspace techniques for image understanding and computer vision, Ph.D. dissertation.
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
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.
Xie X, Mirmehdi M: RAGS: region-aided geometric snake. IEEE Transactions on Image Processing 2004,13(5):640-652. 10.1109/TIP.2004.826124
Bourennane S, Marot J: Contour estimation by array processing methods. EURASIP Journal on Applied Signal Processing 2006, 2006: 15 pages.
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
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.
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
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
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
Sheinvald J, Kiryati N: On the magic of SLIDE. Machine Vision and Applications 1997,9(5-6):251-261. 10.1007/s001380050046