Fast Distance Field Interpolation for Reconstruction of Surfaces from Contours

One simple and robust way to get a reconstruction of surfaces from a given contour stack dealing well with branching and other problems which are generally difficult to solve is based on the well known MC-algorithm. To overcome the staircase artefacts produced by the MC-algorithm Jones et. al. 3 proposed to use a distance field interpolation between the slices and to run the MC-algorithm on this distance field. The main problem of this approach is the distance field computation as it is very time consuming especially if high resolution grids (e.g. 1024 1024 are used. Therefore, in the original algorithm the resolution of the chosen grid is much less than the resolution of the given contour sacrificing accuracy of the resulting surface. Especially in medical applications this is not accepted by the doctors. In this paper we introduce a new method for the computation of the discrete distance field, which is a breaktrough in terms of speed and accuracy. This new method allows us to reconstruct surfaces from contour stacks with guaranteed accuracy in reasonable time. Several examples show the power of this approach.