Incorporating prior knowledge into a segmentation task, whether it be under the form of
geometrical constraints (area/volume penalisation, convexity enforcement, etc.) or of …

Rigid motions (ie transformations based on translations and rotations) are simple, yet
important, transformations in image processing. In R^ n R n, they are both topology and …

Abstract A 3D image I is well-composed if it does not contain critical edges or vertices
(where the boundary of I is non-manifold). The process of transforming an image into a well …

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 …

As opposed to the 3D cubic grid, the body-centered cubic (BCC) grid has some favorable
topological properties: each set of voxels in the grid is a 3-manifold, with 2-manifold …

For well-composed (manifold) objects in the 3D cubical grid, the Euler characteristic is equal
to half of the Euler characteristic of the object boundary, which in turn is equal to the number …

Rigid motions on 2D digital images were recently investigated with the purpose of
preserving geometric and topological properties. From the application point of view, such …

The tree of shapes (ToS) is a famous self-dual hierarchical structure in mathematical
morphology, which represents the inclusion relationship of the shapes (ie the interior of the …

In this article, we present the $ n $-dimensional version of the waterpixels, namely the
watervoxels. Waterpixels constitute a simple, yet efficient alternative to standard superpixel …