n-dimensional skeletonization: a unified mathematical framework [also Erratum 11(4) (Oct 2002)]

Antoine Manzanera; Thierry M. Bernard; Francoise J. Preteux; Bernard Longuet

doi:10.1117/1.1426080

1 January 2002 n-dimensional skeletonization: a unified mathematical framework [also Erratum 11(4) (Oct 2002)]

Antoine Manzanera, Thierry M. Bernard, Francoise J. Preteux, Bernard Longuet

Journal of Electronic Imaging, Vol. 11, Issue 1, (January 2002). https://doi.org/10.1117/1.1426080

We present a skeletonization algorithm defined by explicit Boolean conditions which are dimension independent. The proposed procedure leads to new thinning algorithms in two dimensions (2D) and three dimensions (3D). We establish the mathematical properties of the resulting skeleton referred to as the MB skeleton. From a topological point of view, we prove that the algorithm preserves connectivity in 2D and 3D. From a metric point of view, we show that the MB skeleton is located on a median hypersurface (MHS) that we define. This MHS does not correspond to the standard notion of median axis/surface in 2D/3D, as it combines the various distances associated with the hypercubic grid. The MHS specificities prove to make the skeleton robust with respect to noise and rotation. Then we present the algorithmic properties of the MB skeleton: First, the algorithm is fully parallel, which means that no spatial subiterations are needed. This property, together with the symmetry of the Boolean n-dimensional patterns, leads to a perfectly isotropic skeleton. Second, we emphasize the extreme conciseness of the Boolean expression, and derive the computational efficiency of the procedure.

©(2002) Society of Photo-Optical Instrumentation Engineers (SPIE)

Citation Download Citation

Antoine Manzanera, Thierry M. Bernard, Francoise J. Preteux, and Bernard Longuet "n-dimensional skeletonization: a unified mathematical framework [also Erratum 11(4) (Oct 2002)]," Journal of Electronic Imaging 11(1), (1 January 2002). https://doi.org/10.1117/1.1426080

Published: 1 January 2002

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available