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 …

The Tree of Shapes (ToS) is a morphological, tree-based representation of an image,
translating the inclusion of its level lines. It features many invariants to image changes …

In previous work we proposed a combinatorial algorithm to “locally repair” the cubical
complex Q (I) that is canonically associated with a given 3D picture I. The algorithm …

In discrete topology, discrete surfaces are well-known for their strong topological and
regularity properties. Their definition is recursive, and checking if a poset is a discrete …

Abstract A 3D binary image I can be naturally represented by a combinatorial-algebraic
structure called cubical complex and denoted by Q (I), whose basic building blocks are …

Many text segmentation methods are elaborate and thus are not suitable to real-time
implementation on mobile devices. Having an efficient and effective method, robust to noise …

The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in
an image along a path between two points, where the image is considered as a vertex …

In digital topology, it is well-known that, in 2D and in 3D, a digital set X ⊆ Z^ n is digitally
well-composed (DWC), ie, does not contain any critical configuration, if its immersion in the …

We build upon the work developed in 4 in which we presented a method to “locally repair”
the cubical complex Q (I) associated to a 3D binary image I, to obtain a “well-composed” …

In 2013, Najman and Géraud proved that by working on a well-composed discrete
representation of a gray-level image, we can compute what is called its tree of shapes, a …