The mastoid of human temporal bone contains numerous air cells connected to each others. In order to gain further knowledge about these air cells, a more compact representation is needed to obtain an estimate of the size distribution of these cells. Already existing skeletonization methods often fail in producing a faithful skeleton mostly due to noise hampering the binary representation of the data. This paper proposes a different approach by extracting geometrical information embedded in the Euclidean distance transform of a volume via a structure tensor analysis based on quadrature filters, from which a secondary structure tensor allows the extraction of surface skeleton along with a curve skeleton from its eigenvalues. Preliminary results obtained on a X-ray micro-CT scans of a human temporal bone show very promising results.