New fast and stable Lagrangean method for image segmentation

In this paper we present new fast and stable Lagrangean approach to medical image segmentation. The Lagrangean approach consists in discretization of intrinsic partial differential equation for the evolving curve position vector. Since only a curve discretization by grid points is used it can be very fast provided that topological changes which may occur during the curve evolution from the initial guess to a final segmentation result are also resolved in a very fast way. The curve evolution model which we use for the Lagrangean segmentation includes expanding force in the normal direction, the advective term driving the curve from both sides to an edge and the curvature regularization. The numerical procedures are based on stable semi-implicit scheme in curvature part and on inflow-implicit/outflow explicit method in advective part which corresponds to tangential redistribution of grid points. The tangential velocity which is used to stabilize Lagrangean computations keeps the evolving curve uniformly discretized and this fact allows the fast O(n) solution of the topological changes. We present all deatails of our model, numerical procedures and we show their behaviour in medical image segmentation. In our model we do not need to take any special care of initial condition and the segmentation is done in less that 1 second.