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Article Dans Une Revue IEEE Transactions on Image Processing Année : 2009

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

Olivier Bernard
Denis Friboulet
Michael Unser
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Résumé

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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Dates et versions

hal-00819449 , version 1 (01-05-2013)

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  • HAL Id : hal-00819449 , version 1

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Olivier Bernard, Denis Friboulet, Philippe Thevenaz, Michael Unser. Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution. IEEE Transactions on Image Processing, 2009, 18 (6), pp.1179-1191. ⟨hal-00819449⟩
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