Subscribe
Issue No.02 - February (2011 vol.33)
pp: 382-393
Ricard Delgado-Gonzalo , École polytechnique fédérale de Lausanne (EPFL), Lausanne
Philippe Thévenaz , École polytechnique fédérale de Lausanne (EPFL), Lausanne
ABSTRACT
We propose an active contour (a.k.a. snake) that takes the shape of an ellipse. Its evolution is driven by surface terms made of two contributions: the integral of the data over an inner ellipse, counterbalanced by the integral of the data over an outer elliptical shell. We iteratively adapt the active contour to maximize the contrast between the two domains, which results in a snake that seeks elliptical bright blobs. We provide analytic expressions for the gradient of the snake with respect to its defining parameters, which allows for the use of efficient optimizers. An important contribution here is the parameterization of the ellipse which we define in such a way that all parameters have equal importance; this creates a favorable landscape for the proceedings of the optimizer. We validate our construct with synthetic data and illustrate its use on real data as well.
INDEX TERMS
Snakuscule, snake, dynamic contour, ellipse.
CITATION
Ricard Delgado-Gonzalo, Philippe Thévenaz, "The Ovuscule", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 2, pp. 382-393, February 2011, doi:10.1109/TPAMI.2010.112
REFERENCES
[1] P. Thévenaz and M. Unser, "Snakuscules," IEEE Trans. Image Processing, vol. 17, no. 4, pp. 585-593, Apr. 2008.
[2] S. Tsuji and F. Matsumoto, "Detection of Ellipses by a Modified Hough Transformation," IEEE Trans. Computers, vol. 27, no. 8, pp. 777-781, Aug. 1978.
[3] R. McLaughlin and M. Alder, "The Hough Transform versus the UpWrite," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 4, pp. 396-400, Apr. 1998.
[4] N. Bennett, R. Burridge, and N. Saito, "A Method to Detect and Characterize Ellipses Using the Hough Transform," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 652-657, July 1999.
[5] A. Garrido and N. Pérez de la Blanca, "Applying Deformable Templates for Cell Image Segmentation," Pattern Recognition, vol. 33, no. 5, pp. 821-832, May 2000.
[6] J. Blokland, A. Vossepoel, A. Bakker, and E. Pauwels, "Delineating Elliptical Objects with an Application to Cardiac Scintigrams," IEEE Trans. Medical Imaging, vol. 6, no. 1, pp. 57-66, Mar. 1987.
[7] D. Bright and E. Steel, "Two-Dimensional Top Hat Filter for Extracting Spots and Spheres from Digital Images," J. Microscopy, vol. 146, no. 2, pp. 191-200, May 1987.
[8] P. Lipson, A. Yuille, D. O'Keeffe, J. Cavanaugh, J. Taaffe, and D. Rosenthal, "Deformable Templates for Feature Extraction from Medical Images," Proc. First European Conf. Computer Vision, pp. 413-417, Apr. 1990.
[9] F. Escolano, M. Cazorla, D. Gallardo, and R. Rizo, "Deformable Templates for Tracking and Analysis of Intravascular Ultrasound Sequences," Proc. Int'l Workshop Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 521-534, May 1997.
[10] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active Contour Models," Proc. First IEEE Int'l Conf. Computer Vision, pp. 259-268, June 1987.
[11] B. Bascle and R. Deriche, "Features Extraction Using Parametric Snakes," Proc. 11th Int'l Conf. Pattern Recognition, pp. 659-662, Aug.-Sept. 1992.
[12] Y.-L. Fok, C. Chan, and T. Chin, "Automated Analysis of Nerve-Cell Images Using Active Contour Models," IEEE Trans. Medical Imaging, vol. 15, no. 3, pp. 353-368, June 1996.
[13] J. Cabrera and P. Meer, "Unbiased Estimation of Ellipses by Bootstrapping," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 7, pp. 752-756, July 1996.
[14] A. Fitzgibbon, M. Pilu, and R. Fisher, "Direct Least Square Fitting of Ellipses," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, May 1999.
[15] K. Voss and H. Suesse, "A New One-Parametric Fitting Method for Planar Objects," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 646-651, July 1999.
[16] J. Guerrero, S. Salcudean, J. McEwen, B. Masri, and S. Nicolaou, "Real-Time Vessel Segmentation and Tracking for Ultrasound Imaging Applications," IEEE Trans. Medical Imaging, vol. 28, no. 8, pp. 1079-1090, Aug. 2007.
[17] N. Kharma, H. Moghnieh, J. Yao, Y. Guo, A. Abu-Baker, J. Laganiere, G. Rouleau, and M. Cheriet, "Automatic Segmentation of Cells from Microscopic Imagery Using Ellipse Detection," IET Image Processing, vol. 1, no. 1, pp. 39-47, Mar. 2007.
[18] C. Yap and H. Lee, "Identification of Cell Nucleus Using a Mumford-Shah Ellipse Detector," Proc. Fourth Int'l Symp. Visual Computing, pp. 582-593, Dec. 2008.
[19] E. Dura, J. Bell, and D. Lane, "Superellipse Fitting for the Recovery and Classification of Mine-Like Shapes in Sidescan Sonar Images," IEEE J. Oceanic Eng., vol. 33, no. 4, pp. 434-444, Oct. 2008.
[20] H. Li, D. Chen, and Q. Yang, "Image Processing Technique for Characteristic Test of Cell Based on Electrorotation Chip," Proc. Second Int'l Conf. Bioinformatics and Biomedical Eng., vol. 2, pp. 2526-2529, May 2008.
[21] D. Pedoe, "Thinking Geometrically," The Am. Math. Monthly, vol. 77, no. 7, pp. 711-721, Aug.-Sept. 1970.
[22] L. Shepp and B. Logan, "The Fourier Reconstruction of a Head Section," IEEE Trans. Nuclear Science, vol. 21, no. 3, pp. 21-43, June 1974.
[23] J. Wuest, E. Denarié, E. Brühwiler, L. Tamarit, M. Kocher, and E. Gallucci, "Tomography Analysis of Fiber Distribution and Orientation in Ultra High-Performance Fiber-Reinforced Composites with High-Fiber Dosages," Experimental Techniques, Sept./Oct. 2008.