Contribution à l'analyse topologique des images : étude d'algorithmes de squelettisation pour images 2D et 3D, selon une approche topologie digitale ou topologie discrète.
Christophe Lohou · HAL (Le Centre pour la Communication Scientifique Directe) · 2001
This thesis proposes new thinning algorithms for 2D or 3D images according to two approaches using either the digital topology or the discrete topology. In the first part, we recall some fundamental notions of digital topology and several thinning algorithms among the well-known ones, which delete simple points. Then, we propose a methodology to produce new thinning algorithms based on the parallel deletion of P-simple points. Such algorithms are conceived in order to they delete at least the points removed by another one given existent thinning algorithm. By applying this methodology, we produce two new algorithms. Although results seem to be satisfying, the proposal and encoding of new proposed algorithms are not easy. In the second part, we use the concept of partially order set (or poset). We propose more straightforwardly than before, a thinning algorithm consisting in the repetition of parallel deletion of alpha_n-simple points, followed by the parallel deletion of beta_n-simple points. We also have proposed new definitions of end points which permits us to obtain either curve skeletons or surface skeletons. The thinning scheme is used on 2D, 3D binary images, or on 2D grayscale images. At last, a study of a parallel filtering of skeletons is developped.