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  • Research Article
  • Open Access

Locally Regularized Smoothing B-Snake

EURASIP Journal on Advances in Signal Processing20072007:076241

  • Received: 22 July 2005
  • Accepted: 17 December 2006
  • Published:


We propose a locally regularized snake based on smoothing-spline filtering. The proposed algorithm associates a regularization process with a force equilibrium scheme leading the snake's deformation. In this algorithm, the regularization is implemented with a smoothing of the deformation forces. The regularization level is controlled through a unique parameter that can vary along the contour. It provides a locally regularized smoothing B-snake that offers a powerful framework to introduce prior knowledge. We illustrate the snake behavior on synthetic and real images, with global and local regularization.


  • Information Technology
  • Prior Knowledge
  • Quantum Information
  • Real Image
  • Equilibrium Scheme

Authors’ Affiliations

CREATIS, CNRS UMR 5220, Inserm U 630, INSA, Bâtiment Blaise Pascal, Villeurbanne, 69621, France


  1. Kass M, Witkin A, Terzopoulos D: Snakes: active contour models. Proceedings of the 1st International Conference on Computer Vision, June 1987, London, UK 259–268.Google Scholar
  2. Menet S, Saint-Marc P, Medioni G: B-snakes: implementation and application to stereo. Proceedings of Image Understanding Workshop, September 1990, Pittsburgh, Pa, USA 720–726.Google Scholar
  3. Cohen LD, Cohen I: Finite-element methods for active contour models and balloons for 2-D and 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1993,15(11):1131-1147. 10.1109/34.244675View ArticleGoogle Scholar
  4. Xu C, Prince JL: Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing 1998,7(3):359-369. 10.1109/83.661186MathSciNetView ArticleGoogle Scholar
  5. Wang M, Evans J, Hassebrook L, Knapp C: A multistage, optimal active contour model. IEEE Transactions on Image Processing 1996,5(11):1586-1591. 10.1109/83.541430View ArticleGoogle Scholar
  6. Brigger P, Hoeg J, Unser M: B-spline snakes: a flexible tool for parametric contour detection. IEEE Transactions on Image Processing 2000,9(9):1484-1496. 10.1109/83.862624MathSciNetView ArticleGoogle Scholar
  7. Brigger P, Unser M: Multi-scale B-spline snakes for general contour detection. Wavelet Applications in Signal and Image Processing VI, July 1998, San Diego, Calif, USA, Proceedings of SPIE 3458: 92–102.View ArticleGoogle Scholar
  8. Precioso F, Barlaud M, Blu T, Unser M: Robust real-time segmentation of images and videos using a smooth-spline snake-based algorithm. IEEE Transactions on Image Processing 2005,14(7):910-924.View ArticleGoogle Scholar
  9. Reinsch CH: Smoothing by spline functions. Numerische Mathematik 1967,10(3):177-183. 10.1007/BF02162161MathSciNetView ArticleGoogle Scholar
  10. Unser M, Aldroubi A, Eden M: B-spline signal processing—part I. Theory. IEEE Transactions on Signal Processing 1993,41(2):821-833. 10.1109/78.193220View ArticleGoogle Scholar
  11. Jacob M, Blu T, Unser M: Efficient energies and algorithms for parametric snakes. IEEE Transactions on Image Processing 2004,13(9):1231-1244. 10.1109/TIP.2004.832919View ArticleGoogle Scholar
  12. Flickner M, Sawhney H, Pryor D, Lotspiech J: Intelligent interactive image outlining using spline snakes. Proceedings of the 28th Asilomar Conference on Signals, Systems and Computers, October-November 1994, Pacific Grove, Calif, USA 1: 731–735.Google Scholar
  13. Unser M, Aldroubi A, Eden M: B-spline signal processing—part II. Efficient design and applications. IEEE Transactions on Signal Processing 1993,41(2):834-848. 10.1109/78.193221View ArticleGoogle Scholar
  14. Weruaga L, Verdú R, Morales J: Frequency domain formulation of active parametric deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence 2004,26(12):1568-1578. 10.1109/TPAMI.2004.124View ArticleGoogle Scholar


© Jérôme Velut et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.