Method

This section will give an algorithmic summary of the level set method for shape modeling.

1. Calculate the image gradient at each point in the image.
2. Initialize $\psi$. This is done by first making $\psi = 0$ at the points specified by the user in the initial boundary. The value of $\psi$ at all the other points is $\pm d_{xy}$, where $d_{xy}$ is the distance of point $(x,y)$ from the closest point on the level set $\psi = 0$. The value is positive or negative depending on whether the point is outside or inside the boundary.
3. Calculate the velocity at the points on the level set $\psi = 0$ using the equations given in the previous section. The velocity of other points is equal to the velocity of the closest point on the level set $\psi = 0$. This step is knows as extending the velocity. This is done because, the curvature term is defined only on the front, so it does not make sense to calculate velocities at every point but it should only be calculated at the front.
4. Use the velocities to update the function $\psi$ using equation 4.
5. Repeat steps 2 through 4 till the solution converges or for a fixed (large) number of iterations.
6. The function $\psi$ is reinitialized every fixed number of iterations to the signed distance function.