… In the following, we consider a nD digital image u as a function defined on a regular cubical
nD grid and having integral values (even if we can generalize our case to any totally ordered …

… tree of shapes; it works for nD … proof of our algorithm. This paper focuses on how the
proposed algorithm works and gives an insight into the reasons why it works; to give a formal proof …

… Before we proceed to a formal proof of this proposition we will have a closer look at the
condition on V as formulated in part (b). Let %’ be a set system closed under the formation of …

… proof that the shapes obtained with (c2n, c3n−1) form a tree … for a well-composed image,
this proof applies to our case. … to compute the morphological tree of shapes of nD images. In: …

… of variational problems, determining optimal shapes for tree roots and branches. Given a …
4, we briefly review the theory of optimal ramified transport, proving some estimates on the …

… We simply recall basic notions that will be necessary for the proofs of the present paper. We
… Géraud, “A first parallel algorithm to compute the morphological tree of shapes of nD images…

… This way, we will be able to compute a tree of shapes for filtering and segmentation … 4 recalls
how to compute the tree of shapes, Sect. 5 contains the proofs of properties stated in Sect. 3…

… A quasilinear algorithm to compute the tree of shapes of nD images. In Proceedings of
the International Symposium on Mathematical Morphology, pages 98–110. Springer Berlin …

… mathematical morphology as the Tree of Shapes which is of our … : Links between the
morphological tree of shapes and well-… A quasi-linear algorithm to compute the tree of shapes of …

… about trees in regions of other shape. In the case of Euclidean metric … Although there has
been no proof of a similar asymptotic … tree is only slightly more than the cost of the minimal tree. …