Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper, we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the n-dimensional object from a group of (n - 1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for three-dimensional tooth reconstruction.