The goal of this project is to design an algorithm of low complexity describing the evolution of co-dimension one manifolds.
eg: A curve in xy-space evolving in time. We assume that the front gets propagated in the normal direction with a prescribed
speed function F which may depend on space as well as on time, and may vanish and change sign. To achieve our goal, we make
use of the level-set method, the fast marching method, and borrow some ideas from control theory, and the rich theory on
The resulting first-order algorithm is an augmented version of the traditional fast marching method: In regions where F is close to 0, a different formalism is used to accurately capture the evolution of the front. The predicted complexity of this method is comparable to that of the fast marching method.
Under the supervision of Prof.J.-C. Nave.