Solving the PDE of the level set function requires numerical processing at each point of the image domain which is a time consuming process. Only we are interested in the change of the front. It is not important to get the solution at points far away from the front, so the solution is important at the points near the front. The points (highlighted in Fig. 9.23(b)) are called the narrow band points. The change of the level set function at these points only is considered. Other points (outside the narrow band) are called the far away points and they are given large positive or large negative values to be out of interest (not processed), and it speeds up the iterations. The use of the delta function defined by Eq. 9.64 is very important to give the narrow band points.
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