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.
@ARTICLE(http://bigwww.epfl.ch/publications/bernard0901.html,
AUTHOR="Bernard, O. and Friboulet, D. and Th{\'{e}}venaz, P. and Unser,
M.",
TITLE="Variational \mbox{{B}-Spline} Level-Set: {A} Linear Filtering
Approach for Fast Deformable Model Evolution",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2009",
volume="18",
number="6",
pages="1179--1191",
month="June",
note="")