his paper presents how robust 1-pixel-wide and 8-connected skeletons can be obtained simultaneously with exact distance transform calculation. The proposed approach is based on the new concept of exact dilation. Two alternative algorithms for exact Euclidean distance transform calculation allowing exact dilation are described: a simpler approach based on the SEDR (sorted exact distance representation) data structure, which allows exact distance transform calculation; and a more effective strategy based on border propagation. In both techniques the distances are assigned strictly according to sequences of increasing exact distances in the orthogonal lattice. Because of the high accuracy allowed by such procedures, progressive dilations, high quality and accurate 1-pixel-wide and 8-connected skeletons can be obtained corresponding to the frontiers between previously labelled distinct connected objects. Although this method can be useful for determining generalized Dirichlet tessellations, which is also illustrated in this article, its full potential is harnessed by previously segmenting the contours of connected objects by removing their points corresponding to curvature peaks, which are obtained by using an effective multi-scale curvature estimation technique. In such a way, not only highquality 1-pixel-wide and 8-connected skeletons are obtained for any shape, but also the whole approach becomes considerably robust to small distortions in the object contours, thus avoiding one of the great shortcomings in traditional skeletonization methods. The application of such methods to an important problem in computational neuroscience and neuromorphometry, namely the automated extraction of tapered dendrograms, is described and illustrated. Considerations regarding distances in orthogonal lattices, typical problems in skeletonization, and the practical implementation of the proposed techniques are also included.