Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

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 regarding 6 or 26-connectivity. Then the complex is thinned using the proposed method based on elementary collapses, which preserves significant geometric features. The final step reduces the number of cells using Discrete Morse Theory. The resulting skeleton is a reduction which preserves the homology of the original complex and the geometrical information of the output of the previous step. The result of this method, besides its skeletonization content, can be used for computing the homology of the original complex, which usually provides well shaped homology generators

Constructing Simplicial Complexes over Topological Spaces

The first step in topological data analysis is often the construction of a simplicial complex. This complex approximates the lost topology of a sampled point set. Current techniques often assume that the input is embedded in a metric -- often Euclidean -- space, and make significant use of the underlying geometry for efficient computation. Consequently, these techniques do not extend to non-Euclidean or non-metric spaces. In this thesis, we present an oracle-based framework for constructing simplicial complexes over arbitrary topological spaces. The framework consists of an oracle and an algorithm that builds the simplicial complex by making calls to the oracle. We compare different algorithmic approaches for the construction, as well as alternate ways of representing the simplicial complex in the computation. Finally, we demonstrate the utility of our framework as a tool for approaching problems of diverse nature by presenting three applications: to multiword search in Google, to the computational analysis of a language and to the study of protein structure

Exploring 3D Shapes through Real Functions

This thesis lays in the context of research on representation, modelling and coding knowledge related to digital shapes, where by shape it is meant any individual object having a visual appareance which exists in some two-, three- or higher dimensional space. Digital shapes are digital representations of either physically existing or virtual objects that can be processed by computer applications. While the technological advances in terms of hardware and software have made available plenty of tools for using and interacting with the geometry of shapes, to manipulate and retrieve huge amount of data it is necessary to define methods able to effectively code them. In this thesis a conceptual model is proposed which represents a given 3D object through the coding of its salient features and defines an abstraction of the object, discarding irrelevant details. The approach is based on the shape descriptors defined with respect to real functions, which provide a very useful shape abstraction method for the analysis and structuring of the information contained in the discrete shape model. A distinctive feature of these shape descriptors is their capability of combining topological and geometrical information properties of the shape, giving an abstraction of the main shape features. To fully develop this conceptual model, both theoretical and computational aspects have been considered, related to the definition and the extension of the different shape descriptors to the computational domain. Main emphasis is devoted to the application of these shape descriptors in computational settings; to this aim we display a number of application domains that span from shape retrieval, to shape classification and to best view selection.Questa tesi si colloca nell\u27ambito di ricerca riguardante la rappresentazione, la modellazione e la codifica della conoscenza connessa a forme digitali, dove per forma si intende l\u27aspetto visuale di ogni oggetto che esiste in due, tre o pi? dimensioni. Le forme digitali sono rappresentazioni di oggetti sia reali che virtuali, che possono essere manipolate da un calcolatore. Lo sviluppo tecnologico degli ultimi anni in materia di hardware e software ha messo a disposizione una grande quantit? di strumenti per acquisire, rappresentare e processare la geometria degli oggetti; tuttavia per gestire questa grande mole di dati ? necessario sviluppare metodi in grado di fornirne una codifica efficiente. In questa tesi si propone un modello concettuale che descrive un oggetto 3D attraverso la codifica delle caratteristiche salienti e ne definisce una bozza ad alto livello, tralasciando dettagli irrilevanti. Alla base di questo approccio ? l\u27utilizzo di descrittori basati su funzioni reali in quanto forniscono un\u27astrazione della forma molto utile per analizzare e strutturare l\u27informazione contenuta nel modello discreto della forma. Una peculiarit? di tali descrittori di forma ? la capacit? di combinare propriet? topologiche e geometriche consentendo di astrarne le principali caratteristiche. Per sviluppare questo modello concettuale, ? stato necessario considerare gli aspetti sia teorici che computazionali relativi alla definizione e all\u27estensione in ambito discreto di vari descrittori di forma. Particolare attenzione ? stata rivolta all\u27applicazione dei descrittori studiati in ambito computazionale; a questo scopo sono stati considerati numerosi contesti applicativi, che variano dal riconoscimento alla classificazione di forme, all\u27individuazione della posizione pi? significativa di un oggetto

Shape segmentation and retrieval based on the skeleton cut space

3D vormverzamelingen groeien snel in veel toepassingsgebieden. Om deze effectief te kunnen gebruiken bij modelleren, simuleren, of 3D contentontwikkeling moet men 3D vormen verwerken. Voorbeelden hiervan zijn het snijden van een vorm in zijn natuurlijke onderdelen (ook bekend als segmentatie), en het vinden van vormen die lijken op een gegeven model in een grote vormverzameling (ook bekend als opvraging). Dit proefschrift presenteert nieuwe methodes voor 3D vormsegmentatie en vormopvraging die gebaseerd zijn op het zogenaamde oppervlakskelet van een 3D vorm. Hoewel allang bekend, dergelijke skeletten kunnen alleen sinds kort snel, robuust, en bijna automatisch berekend worden. Deze ontwikkelingen stellen ons in staat om oppervlakskeletten te gebruiken om vormen te karakteriseren en analyseren zodat operaties zoals segmentatie en opvraging snel en automatisch gedaan kunnen worden. We vergelijken onze nieuwe methodes met moderne methodes voor dezelfde doeleinden en laten zien dat ons aanpak kwalitatief betere resultaten kan produceren. Ten slotte presenteren wij een nieuwe methode om oppervlakskeletten te extraheren die is veel simpeler dan, en heeft vergelijkbare snelheid met, de beste technieken in zijn klasse. Samenvattend, dit proefschrift laat zien hoe men een complete workflow kan implementeren voor het segmenteren en opvragen van 3D vormen gebruik makend van oppervlakskeletten alleen

Hierarchic Euclidean skeletons in cubical complexes

International audienceIn the 90s, several authors introduced the notion of a hierarchic family of 2D Euclidean skeletons, evolving smoothly under the control of a filtering parameter. We provide in this paper a discrete framework which formalizes and generalizes this notion, in particular to higher dimensions. This framework allows us to propose a new skeletonization scheme and to prove several important properties, such as topology preservation and stability w.r.t. parameter changes

Putting Chinese natural knowledge to work in an eighteenth-century Swiss canton: the case of Dr Laurent Garcin

Symposium: S048 - Putting Chinese natural knowledge to work in the long eighteenth centuryThis paper takes as a case study the experience of the eighteenth-century Swiss physician, Laurent Garcin (1683-1752), with Chinese medical and pharmacological knowledge. A Neuchâtel bourgeois of Huguenot origin, who studied in Leiden with Hermann Boerhaave, Garcin spent nine years (1720-1729) in South and Southeast Asia as a surgeon in the service of the Dutch East India Company. Upon his return to Neuchâtel in 1739 he became primus inter pares in the small local community of physician-botanists, introducing them to the artificial sexual system of classification. He practiced medicine, incorporating treatments acquired during his travels. taught botany, collected rare plants for major botanical gardens, and contributed to the Journal Helvetique on a range of topics; he was elected a Fellow of the Royal Society of London, where two of his papers were read in translation and published in the Philosophical Transactions; one of these concerned the mangosteen (Garcinia mangostana), leading Linnaeus to name the genus Garcinia after Garcin. He was likewise consulted as an expert on the East Indies, exotic flora, and medicines, and contributed to important publications on these topics. During his time with the Dutch East India Company Garcin encountered Chinese medical practitioners whose work he evaluated favourably as being on a par with that of the Brahmin physicians, whom he particularly esteemed. Yet Garcin never went to China, basing his entire experience of Chinese medical practice on what he witnessed in the Chinese diaspora in Southeast Asia (the ‘East Indies’). This case demonstrates that there were myriad routes to Europeans developing an understanding of Chinese natural knowledge; the Chinese diaspora also afforded a valuable opportunity for comparisons of its knowledge and practice with other non-European bodies of medical and natural (e.g. pharmacological) knowledge.postprin