Variational B-Spline Level-Set Method for Fast Image Segmentation

In the field of image segmentation, most of level-set-based active contour approaches are based on a discrete representation of the associated implicit function. We present in this paper a different formulation where the level-set is modelled as a continuous parametric function expressed on a B-spline basis. Starting from the Mumford-Shah energy functional, we show that this formulation allows computing 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-splines parameters. 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 1D convolutions, which yields a very efficient algorithm. The behaviour of this approach is illustrated on biomedical images from various fields.