Fast implementation of piecewise constant level set methods ∗

Level set methods have been proven to be efficient tools for tracing interface problems. Recently, some variants of the Osher-Sethian level set methods, which is called the Piecewise Constant Level Set Methods (PCLSM), have been proposed for some interface problems. The methods need to minimize a smooth cost functional under some special constraints. A fast algorithm for image segmentation is proposed and tested. The algorithm uses an operator splitting scheme to deal with the gradient descent equation. A special technique is used to tackle the constraint for the PCLSM. By choosing the time step and the penalization parameter properly, the cost functional is minimized and the constraint is fulfilled. Experiments for image segmentation is given. The efficiency of the algorithm and the quality of the obtained images are demonstrated.