I am happy to announce that the following paper has been accepted
for publication in the Journal of Mathematical Imaging and Vision (JMIV):
A Tutorial on Well-Composedness
Nicolas Boutry (1), Thierry Géraud (1) and Laurent Najman (2)
(1) LRDE, EPITA,
Le Kremlin-Bicêtre, France
(2) Université Paris-Est, LIGM, Équipe A3SI, ESIEE,
Marne-la-Vallée, France
Abstract:
Due to digitization, usual discrete signals generally present
topological paradoxes, such as the connectivity paradoxes of
Rosenfeld. To get rid of those paradoxes, and to restore some
topological properties to the objects contained in the image,
like manifoldness, Latecki proposed a new class of images, called
well-composed images, with no topological issues. Furthermore,
well-composed images have some other interesting properties: for
example, the Euler number is locally computable, boundaries of
objects separate background from foreground, the tree of shapes
is well defined, and so on. Last, but not the least, some recent
works in mathematical morphology have shown that very nice
practical results can be obtained thanks to well-composed
images. Believing in its prime importance in digital topology, we
then propose this state-of-the-art of well-composedness,
summarizing its different flavours, the different methods
existing to produce well-composed signals, and the various topics
that are related to well-composedness.
URL:
http://publications.lrde.epita.fr/boutry.17.jmiv
Nicolas Boutry