Homological Spanning Forests for Discrete Objects

Computing and representing topological information form an important part in many applications such as image representation and compression, classification, pattern recognition, geometric modelling, etc. The homology of digital objects is an algebraic notion that provides a concise description of their topology in terms of connected components, tunnels and cavities. The purpose of this work is to develop a theoretical and practical frame- work for efficiently extracting and exploiting useful homological information in the context of nD digital images. To achieve this goal, we intend to combine known techniques in algebraic topology, and image processing. The main notion created for this purpose consists of a combinatorial representation called Homological Spanning Forest (or HSF, for short) of a digital object or a digital image. This new model is composed of a set of directed forests, which can be constructed under an underlying cell complex format of the image. HSF’s are based on the algebraic concept of chain homotopies and they can be considered as a suitable generalization to higher dimensional cell complexes of the topological meaning of a spanning tree of a geometric graph. Based on the HSF representation, we present here a 2D homology-based framework for sequential and parallel digital image processing.Premio Extraordinario de Doctorado U

De hydrophytis notulae praecipue chorologicae. IV

Notes mainly chorological, concerning hydrophytes and helophytes, IVPalabras clave. Elemento atlántico, fitogeografía, MarruecosKey words. Atlantic element, phytogeography, Morocc

Computing the Component-Labeling and the Adjacency Tree of a Binary Digital Image in Near Logarithmic-Time

Connected component labeling (CCL) of binary images is one of the fundamental operations in real time applications. The adjacency tree (AdjT) of the connected components offers a region-based representation where each node represents a region which is surrounded by another region of the opposite color. In this paper, a fully parallel algorithm for computing the CCL and AdjT of a binary digital image is described and implemented, without the need of using any geometric information. The time complexity order for an image of m × n pixels under the assumption that a processing element exists for each pixel is near O(log(m+ n)). Results for a multicore processor show a very good scalability until the so-called memory bandwidth bottleneck is reached. The inherent parallelism of our approach points to the direction that even better results will be obtained in other less classical computing architectures.Ministerio de Economía y Competitividad MTM2016-81030-PMinisterio de Economía y Competitividad TEC2012-37868-C04-0

Una introducción a la literatura científica

We discuss the convenience of an early introduction of undergraduate students to the reading of scientific papers, mostly divulgative or historical. This can encourage them to deeper readings and to search and discover in the scientific writings new sources of learning and pleasure. The aim of this activity is twofold: mainly, to approach the students to bibliographical sources different from the traditional textbooks and, collaterally, to habituate them to get acquainted with scientific information in foreign languages (mostly English). In this manner, the students can get further knowlegde and they can also learn new points of view or different topics from those commonly discussed during a typical academic course

Homological spanning forest framework for 2D image analysis

A 2D topology-based digital image processing framework is presented here. This framework consists of the computation of a flexible geometric graph-based structure, starting from a raster representation of a digital image I. This structure is called Homological Spanning Forest (HSF for short), and it is built on a cell complex associated to I. The HSF framework allows an efficient and accurate topological analysis of regions of interest (ROIs) by using a four-level architecture. By topological analysis, we mean not only the computation of Euler characteristic, genus or Betti numbers, but also advanced computational algebraic topological information derived from homological classification of cycles. An initial HSF representation can be modified to obtain a different one, in which ROIs are almost isolated and ready to be topologically analyzed. The HSF framework is susceptible of being parallelized and generalized to higher dimensions

Cell AT-models for digital volumes

In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional holes: connected components, ”tunnels” and cavities) is extracted from a linear map (called homology gradient vector field) acting on a polyhedral cell complex P(V) homologically equivalent to V. We develop here an alternative way for constructing P(V) based on homological algebra arguments as well as a new more efficient algorithm for computing a homology gradient vector field based on the contractibility of the maximal cells of P(V)

Influenza di esposizione ed altitudine sulla distribuzione della vegetazione seriale nelle Alpi Orobie (Lombardia, Italia)

Influenza di esposizione ed altitudine sulla distribuzione della vegetazione seriale nelle Alpi Orobie (Lombardia, Italia). Il presente lavoro si occupa di indagare gli effetti che l’esposizione e l’altitudine esercitano sulle formazioni erbacee ed arbustive della Val Varrone, valle prealpina orientale del bacino imbrifero del lago di Como. Tramite cluster analysis sono stati caratterizzati 6 aggruppamenti vegetali attribuibili a 6 associazioni fitosociologiche. Gli aggruppamenti sono stati poi caratterizzati dal punto di vista ecologico, d’accordo con i parametri di Landolt. Dall’analisi dell’assolazione, tramite la formula di Bartorelli, le comunità vegetali vengono distribuite spazialmente nel territorio. L’associazione Centaureo –Arrhenatheretum è diffusa a basse quote principalmente su versanti con esposizione meridionale. L’associazione Festucetum variae, invece, è stata rilevata ad altitudini piú elevate, sempre con esposizione sud. In corrispondenza della fascia intermedia, l’associazione Homogyno alpinae-Nardetum presenta la maggior ampiezza altitudinale, le associazioni Rumicetum alpinii e Alnetum viridis prediligono fasce altitudinali meno ampie, mentre l’associazione Vaccinio-Rhododendretum ferrugineum cresce su pendii ripidi. La vegetazione seriale delle Alpi Orobie (lato orientale del lago di Como) risulta essere simile a quella dell’Alto Lario Occidentale (lato occidentale)

Towards optimality in discrete Morse Theory through chain homotopies

Once a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced from its critical elements. The main objective of this paper is to define optimal discrete gradient vector fields on general finite cell complexes, where optimality entails having the least number of critical elements. Our approach is to consider this problem as a homology computation question for chain complexes endowed with extra algebraic nilpotent operator