B-spline snakes: a flexible tool for parametric contour detection

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. We start with a theoretical argument in favor of splines in the traditional formulation by showing that the optimal, curvature-constrained snake is a cubic spline, irrespective of the form of the external energy field. Unfortunately, such regularized snakes suffer from slow convergence speed because of a large number of control points, as well as from difficulties in determining the weight factors associated to the internal energies of the curve. We therefore propose an alternative formulation in which the intrinsic scale of the spline model is adjusted a priori; this leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies (i.e., the regularization term). In other words, we are now controlling the elasticity of the spline implicitly and rather intuitively by varying the spacing between the spline knots. The theory is embedded into a multiresolution formulation demonstrating improved stability in noisy image environments. Validation results are presented, comparing the traditional snake using internal energies and the proposed approach without internal energies, showing the similar performance of the latter. Several biomedical examples of applications are included to illustrate the versatility of the method