Abstract: Medial representations are powerful tools for describing and parameterizing the volumetric shape of anatomical structures. Accurate computation of one pixel wide medial surfaces is mandatory. Those surfaces must represent faithfully the geometry of the volume. Although morphological methods produce excellent results in 2D, their complexity and quality drops across dimensions, due to a more complex description of pixel neighborhoods. This paper introduces a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. Our experiments show its higher performance for medical imaging applications in terms of simplicity of medial structures and capability for reconstructing the anatomical volume