Euclidean Homotopic Skeleton Based On Critical Kernels

Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. It allows to easily design parallel thinning algorithms which produce new types of skeletons, with specific geometrical properties, while guaranteeing their topological soundness. In this paper, we demonstrate that it is possible to define a skeleton based on the Euclidean distance, rather than on the common discrete distances, in the context of critical kernels. We provide the necessary definitions as well as an efficient algorithm to compute this skeleton. © 2006 IEEE.307314Bertrand, G., Skeletons in derived grids (1984) In procs. Int. Conf. Patt. Recogn, pp. 326-329Bertrand, G., On critical kernels (2005), Technical Report IGM2005-5, Institut Gaspard-Monge, Université de Marne-la-Vallée, FranceBertrand, G., Couprie, M., New 2d parallel thinning algorithms based on critical kernels (2006) LNCS, 4040, pp. 45-59. , Combinatorial Image Analysis, of, SpringerBlum, H., An associative machine for dealing with the visual field and some of its biological implications (1961) Biological prototypes and synthetic systems, 1, pp. 244-260Blum, H., A transformation for extracting new descriptors of shape (1967) Models for the Perception of Speech and Visual Form, pp. 362-380. , W. Wathendunn, editor, MIT PressCouprie, M., Coeurjolly, D., Zrour, R., Discrete bisector function and Euclidean skeleton in 2d and 3d (2006) Image and Vision Computing, , acceptedDavies, E., Plummer, A., Thinning algorithms: A critique and a new methodology (1981) Pattern Recognition, 14, pp. 53-63de Souza, A.F., (2005) Expansão por dilatação e por erosão visando a extração de esqueletos e contornos em imagens digitais, , PhD thesis, INPE, BrazilHirata, T., A unified linear-time algorithm for computing distance maps (1996) Information Processing Letters, 58 (3), pp. 129-133Rémy, E., Thiel, E., Exact medial axis with Euclidean distance (2005) Image and Vision Computing, 23 (2), pp. 167-175Saúde, A.V., Couprie, M., Lotufo, R., Exact Euclidean medial axis in higher resolution (2006) LNCS, , A. Kuba, K. Palágyi, and L. Nyúl, editors, Discrete Geometry for Computer Imagery, Springer, OctH. Talbot and L. Vincent. Euclidean skeletons and conditional bisectors. In Procs. VCIP'92, SPIE, ume 1818, pages 862-876, 1992Vincent, L., Efficient computation of various types of skeletons (1991) Procs. Medical Imaging V, SPIE, 1445, pp. 297-31