An approach for the skeletonization of two-dimensional (2-D) or 3-D objects is presented.Two local measures, φ and d, are introduced to characterize skeleton points in n-D, whose good localization is ensured by Euclidean distance mapping techniques. These measures allow the level of detail in the resulting skeleton to be controlled.Thresholding these measures does not generally yield a well-defined skeleton: a low threshold preserves the original object's topology but produces a noise sensitive skeleton, while a larger threshold produces a more robust skeleton but it is generally not homotopic with the original object.To overcome these drawbacks, functions of these measures can be introduced. Although they generally yield convincing experimental results, they are still sensitive to noise. Instead, a novel global step for 2-D and 3-D images called topological reconstruction is introduced, that will provide the skeleton with robustness with respect to noise and ensure homotopy with the original object. Moreover, this method is not iterative (like thinning approaches) and hence has reasonable computational time for 3-D objects. Results on synthetic 2-D patterns and on real 3-D medical objects are presented.