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B-Spline Snakes

Investigator: Mathews Jacob

Summary: B-Spline snakes provide an attrative formalism for parametric curve detection. They can accomodate relatively general cost functions (including contour and region terms) and can be implemented quite efficiently.

Introduction

Snakes are a powerful framework for incorporating the description of the curve explicitly into the boundary detection problem. The optimal boundary is specified as the one that minimizes some cost function which includes external and internal forces. The external forces tend to lock the curve onto prominent image features (contours) while the internal ones constrain its rigidity (regularization).

Main Contributions

We are promoting the use of a special type of parametric active contour models: B-spline snakes. Their advantage over traditional snakes is twofold: (i) they have much fewer parameters, and (ii) there is, in principle, no need for internal forces. In addition, B-spline curves are easy to handle analytically. One can compute exact normals and calculate the moments of a closed B-spline curve using Green's theorem. Finally, one can also prove that the choice of a parametric cubic-spline model is optimal under suitable conditions (minimal-curvature curve).

To facilitate the use of B-spline snakes, we have introduced a unified formulation that enables the user to tune the image energy to the application at hand. The proposed cost function includes two terms: (i) a region-based criterion that tends to favor a homogeneous segmentation, and (ii) a shape-constraining term expressing our a priori knowledge of the class of objects to be detected. The main point is that these can be defined to be independent of the parametrization and that the cost function can be evaluated (and optimized) quite efficiently using contour integrals.

Collaborations: Prof. Michael Unser, Dr. Thierry Blu

Period: 1998-2003

Funding: Grant 2000-061420.00 from the Swiss Science Foundation

Major Publications

[1] 

M. Jacob, T. Blu, M. Unser, "Efficient Energies and Algorithms for Parametric Snakes," IEEE Transactions on Image Processing, vol. 13, no. 9, pp. 1231-1244, September 2004.

[2] 

M. Jacob, T. Blu, M. Unser, "An Exact Method for Computing the Area Moments of Wavelet and Spline Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 633-642, June 2001.

[3] 

P. Brigger, J. Hoeg, M. Unser, "B-Spline Snakes: A Flexible Tool for Parametric Contour Detection," IEEE Transactions on Image Processing, vol. 9, no. 9, pp. 1484-1496, September 2000.

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