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In binary images, the Distance Transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for d-dimensional images. We also present a d-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape.
Shape representation, distance transformation, reverse Euclidean distance transformation, medial axis extraction, d--dimensional shapes.

A. Montanvert and D. Coeurjolly, "Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 29, no. , pp. 437-448, 2007.
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