GONZÁLEZ LORENZO , Aldo

La théorie de l'homologie formalise la notion de trou dans un espace. Pour un sous-ensemble de l'espace Euclidien, on définit une séquence de groupes d'homologie, dont leurs rangs sont interprétés comme le nombre de trous de chaque dimension. Ainsi, β0, le rang du groupe d'homologie de dimension zéro, est le nombre de composantes connexes, β1...

Tout objet discret n-dimensionnel peut être transformé en complexe cubique, dont on peut étudier les groupes d'homologie pour mieux comprendre l'objet original. Une approche classique consiste à calculer la Forme Normale de Smith de matrices encodant le complexe cubique. Un certain nombre de travaux développent des méthodes permettant de...

n-dimensional discrete objects can be interpreted as cubical complexes which are suitable for the study of their homology groups in order to understand the original discrete object. The classic approach consists in computing the Normal Smith Form of some matrices associated to the cubical complex. Further approaches deal mainly with a...

Given a binary object (2D or 3D), its Betti numbers characterize the number of holes in each dimension. They are obtained algebraically, and even though they are perfectly defined, there is no unique way to display these holes. We propose two geometric measures for the holes, which are uniquely defined and try to compensate the loss of...

This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset of voxels of a volume nor a subcomplex of a cubical complex: it is a chain complex together with a reduction from the original complex. Starting from the binary volume we build a cubical complex which represents it...

Discrete gradient vector fields are combinatorial structures that can be used for accelerating the homology computation of CW complexes, such as simplicial or cubical complexes, by reducing their number of cells. Consequently, they provide a bound for the Betti numbers (the most basic homological information). A discrete gradient vector field...

Betti numbers are topological invariants that count the number of holes of each dimension in a space. Cubical complexes are a class of CW complex whose cells are cubes of different dimensions such as points, segments, squares, cubes, etc. They are particularly useful for modeling structured data such as binary volumes. We introduce a fast and...

This paper analyses the topological information of a digital object O under a combined combinatorial-algebraic point of view. Working with a topology-preserving cellularization K(O) of the object, algebraic and combinatorial tools are jointly used. The combinatorial entities used here are vector fields, V-paths and directed graphs. In the...

To prevent the release of large quantities of CO2 into the atmosphere, carbon capture and storage (CCS) represents a potential means of mitigating the contribution of fossil fuel emissions to global warming and ocean acidification. Fluvial saline aquifers are favourite targeted reservoirs for CO2 storage. These reservoirs are very...