Fast and Accurate Redistancing for Level Set Methods

Although the Level Set Method [4] has only recently been introduced as an image processing tool, it has already proved useful in delineating contours and in segmenting objects. However, since this method represents contours with images, processing time may increase considerably. To offset this problem, it is common to create a narrow band of the image points lying within a given distance to the contour, and then process the contour evolution inside this narrow band. The use of the narrow band and numerical considerations require computing the distance to the evolving contour every few iterations. Several techniques have been proposed for computing this distance [2, 5]. In [1], the authors identify the problem of preserving the exact position of the interface and propose to solve a new Partial Differential Equation for this purpose. In [5], a nlog(n) algorithm is proposed to compute the distance by propagation until a given distance to the contour is reached. In this paper, we present two improvements: 1) We estimate the Euclidean distance to the interpolated surface for all voxels that are neighbors to the surface; and 2) We apply a fast approximation of the Distance Transform only in the narrow band, which, in turn, reduces the complexity of nlog(n) to n, where n is the size of the narrow band.