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Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution

O. Bernard, D. Friboulet, P. Thévenaz, M. Unser

IEEE Transactions on Image Processing, vol. 18, no. 6, pp. 1179-1191, June 2009.



In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.


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AUTHOR="Bernard, O. and Friboulet, D. and Th{\'{e}}venaz, P. and Unser,
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