Variational B-spline level-set: a linear filtering approach for fast deformable model evolution.
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.
Bernard
Olivier
O
CREATIS, INSA, UCB, CNRS UMR 5220, Inserm U630, 69621 Villeurbanne Cedex, France. bernard@creatis.insa-lyon.fr
Friboulet
Denis
D
Thévenaz
Philippe
P
Unser
Michael
M
D000465:Algorithms; D003198:Computer Simulation; D005453:Fluorescence; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical; D012815:Signal Processing, Computer-Assisted; D014057:Tomography, X-Ray Computed