Variational B-spline level-set: a linear filtering approach for fast deformable model evolution

  • Authors:

  • Olivier Bernard;Denis Friboulet;Philippe Thévenaz;Michael Unser

  • Affiliations:

  • CNRS UMR 5220, Inserm U630, UCB, CREATIS, INSA, Villeurbanne Cedex, France;CNRS UMR 5220, Inserm U630, UCB, CREATIS, INSA, Villeurbanne Cedex, France;École polytechnique Fédérale de Lausanne, Lausanne, VD, Switzerland;École polytechnique Fédérale de Lausanne, Lausanne, VD, Switzerland

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 2009

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Abstract

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.