SHAPE RECOGNITION AND REPRESENTATION

n-dimensional skeletonization: a unified mathematical framework

[+] Author Affiliations
Antoine Manzanera, Thierry M. Bernard

Ecole Nat. Sup. de Techniques Avance´es, Lab. d’Electronique et d’Informatique, 32 Blvd. Victor, F-75015 Paris, France E-mail: manzaner@ensta.fr

Franc¸oise Pre⁁teux

Institut National des Te´le´communications, Unite´ de Projet ARTEMIS, Evry, France

Bernard Longuet

EADS/Ae´rospatiale-Matra-Missiles, Chatillon, France

J. Electron. Imaging. 11(1), 25-37 (Jan 01, 2002). doi:10.1117/1.1426080
History: Received Mar. 21, 2000; Revised Sep. 14, 2001; Accepted Sep. 14, 2001
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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 SPIE and IS&T.

© 2002 SPIE and IS&T

Citation

Antoine Manzanera ; Thierry M. Bernard ; Franc¸oise Pre⁁teux and Bernard Longuet
"n-dimensional skeletonization: a unified mathematical framework", J. Electron. Imaging. 11(1), 25-37 (Jan 01, 2002). ; http://dx.doi.org/10.1117/1.1426080


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