Geometric Steerable Medial Maps

To provide more intuitive and easily interpretable representations of complex shapes/organs, medial manifolds should reach a compromise between simplicity in geometry and capability of restoring the anatomy/shape of the organ/volume. Existing morphological methods show excellent results when applied to 2D objects, but their quality drops across dimensions. This paper contributes to the computation of medial manifolds from a theoretical and a practical point of view. First, we introduce a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. Second, we present a validation protocol for assessing the suitability of medial surfaces for anatomical representation in medical applications. We evaluate quantitatively the performance of our method with respect to existing approaches and show its higher performance for medical imaging applications in terms of medial simplicity and capability of reconstructing the anatomical volume.