Approches De Topologie Algebrique Pour Lanalyse Dimages

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Approches de topologie algébrique pour l'analyse d'images

Author : Rabih Assaf
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Approches de topologie algébrique pour l'analyse d'images by : Rabih Assaf

Download or read book Approches de topologie algébrique pour l'analyse d'images written by Rabih Assaf and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: La topologie algébrique, bien que domaine abstrait des mathématiques, apporte de nouveaux concepts pour le traitement d'images. En effet, ces tâches sont complexes et restent limitées par différents facteurs tels que la nécessité d'utiliser un paramétrage, l'influence de l'arrière-plan ou la superposition d'objets. Nous proposons ici des méthodes dérivées de la topologie algébrique qui diffèrent des méthodes classiques de traitement d'images par l'intégration d'informations locales vers des échelles globales grâce à des invariants topologiques. Une première méthode de segmentation d'images a été développée en ajoutant aux caractéristiques statistiques classiques d'autres de nature topologique calculées par homologie persistante. Une autre méthode basée sur des complexes topologiques a été développée dans le but de segmenter les objets dans des images 2D et 3D. Cette méthode segmente des objets dans des images multidimensionnelles et fournit une réponse à certains problèmes habituels en restant robuste vis à vis du bruit et de la variabilité de l'arrière-plan. Son application aux images de grande taille peut se faire en utilisant des superpixels. Nous avons également montré que l'homologie relative détecte le mouvement d'objets dans une séquence d'images qui apparaissent et disparaissent du début à la fin. Enfin, nous posons les bases d'un ensemble de méthodes d'analyse d'images basé sur la théorie des faisceaux qui permet de fusionner des données locales en un ensemble cohérent. De plus, nous proposons une seconde approche qui permet de comprendre et d'interpréter la structure d'une image en utilisant les invariants fournis par la cohomologie des faisceaux.

Contribution à l'analyse topologique des images

Author : Christophe Lohou
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.:/5 (864 download)

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Book Synopsis Contribution à l'analyse topologique des images by : Christophe Lohou

Download or read book Contribution à l'analyse topologique des images written by Christophe Lohou and published by . This book was released on 2001 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cette thèse propose de nouveaux algorithmes de squelettisation d'images 2D et 3D selon deux approches : l'approche topologie digitale et l'approche topologie discrète. Dans la première partie, nous rappelons les notions fondamentales de topologie digitale et quelques algorithmes de squelettisation parmi les plus connus, basés sur la suppression de certains points simples. Puis, nous proposons une méthodologie permettant la production d'algorithmes de squelettisation fondés sur la suppression en parallèle de points P-simples. De tels algorithmes sont élaborés de façon à ce qu'ils suppriment au moins les points retirés par un autre algorithme donné. Nous appliquons cette méthodologie et produisons deux nouveaux algorithmes. Bien que les résultats semblent satisfaisants, la recherche et la mise en œuvre de tels algorithmes restent difficiles. Dans la deuxième partie, nous utilisons le cadre mathématique des ordres. De faç on plus directe qu'auparavant, nous proposons un algorithme de squelettisation consistant en la répétition de la suppression parallèle de points (n-simples, puis en la suppression parallèle de points (n-simples. Nous avons également proposé des définitions originales de points terminaux, nous permettant l'obtention de squelettes curvilignes ou surfaciques. Le schéma général de squelettisation est utilisé sur des images 2D, 3D binaires et 2D en niveaux de gris. Enfin, une étude de filtrage parallèle de squelettes est développée

Approche interpixel en analyse d'images : une topologie et des algorithmes de segmentation

Author : Christophe Fiorio
Publisher :
ISBN 13 :
Total Pages : 201 pages
Book Rating : 4.:/5 (494 download)

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Book Synopsis Approche interpixel en analyse d'images : une topologie et des algorithmes de segmentation by : Christophe Fiorio

Download or read book Approche interpixel en analyse d'images : une topologie et des algorithmes de segmentation written by Christophe Fiorio and published by . This book was released on 1995 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: LE BUT DE TOUT PROCESSUS DE SEGMENTATION D'IMAGES EST LA CARACTERISATION DES ENTITES REPRESENTEES DANS L'IMAGE. LA PLUPART DES METHODES EXISTANTES S'APPUIENT SUR LES SEULS ELEMENTS MATERIALISES FORMANT L'ENSEMBLE IMAGE: LES PIXELS OU LES VOXELS. NOUS PROPOSONS DE PRENDRE EN COMPTE LES ELEMENTS DE BORD DES PIXELS OU DES VOXELS AFIN D'ETUDIER LES LIAISONS ET CONNEXIONS ENTRE CES DERNIERS. CECI NOUS PERMET DE DEFINIR UNE TOPOLOGIE ADAPTEE A L'ANALYSE D'IMAGES: LA TOPOLOGIE-ETOILE. UN RESULTAT IMPORTANT DE CETTE TOPOLOGIE EST QU'ELLE PERMET DE RECUPERER SANS PEINE LES THEOREMES DE LA GEOMETRIE CLASSIQUE SUR IR#N. NOUS ASSOCIONS A CETTE ETUDE TOPOLOGIQUE UN DETECTEUR DE CONTOURS EN INTERPIXEL ET DES ALGORITHMES DE SEGMENTATION EXHIBANT UNE COOPERATION PARFAITE REGION-CONTOUR. EN OUTRE LE GRAPHE DES FRONTIERES, EXTENSION PROPOSEE DU GRAPHE D'ADJACENCE, S'INSCRIT LUI-AUSSI DANS LE CADRE D'UNE APPROCHE GLOBALE COMBINATOIRE EN ANALYSE D'IMAGES

CARI '96

Author : Pierre Moukeli
Publisher : Orstom Editions
ISBN 13 :
Total Pages : 902 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis CARI '96 by : Pierre Moukeli

Download or read book CARI '96 written by Pierre Moukeli and published by Orstom Editions. This book was released on 1996 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Operads

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3642303625
Total Pages : 649 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Algebraic Operads by : Jean-Louis Loday

Download or read book Algebraic Operads written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2012-08-08 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

(Mostly) Commutative Algebra

Author : Antoine Chambert-Loir
Publisher : Springer Nature
ISBN 13 : 3030615952
Total Pages : 466 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis (Mostly) Commutative Algebra by : Antoine Chambert-Loir

Download or read book (Mostly) Commutative Algebra written by Antoine Chambert-Loir and published by Springer Nature. This book was released on 2021-04-08 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.

Discrete Geometry for Computer Imagery

Author : Gilles Bertrand
Publisher : Springer
ISBN 13 : 9783662170458
Total Pages : 462 pages
Book Rating : 4.1/5 (74 download)

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Book Synopsis Discrete Geometry for Computer Imagery by : Gilles Bertrand

Download or read book Discrete Geometry for Computer Imagery written by Gilles Bertrand and published by Springer. This book was released on 2014-03-12 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain papers presented at the 8th Discrete Geometry for Computer Imagery conference, held 17-19, March 1999 at ESIEE, Marne-la- Vall ee. The domains of discrete geometry and computer imagery are closely related. Discrete geometry provides both theoretical and algorithmic models for the p- cessing, analysis and synthesis of images; in return computer imagery, in its variety of applications, constitutes a remarkable experimentational eld and is a source of challenging problems. The number of returning participants, the arrival each year of contributions from new laboratories and new researchers, as well as the quality and originality of the results have contributed to the success of the conference and are an - dication of the dynamism of this eld. The DGCI has become one of the major conferences related to this topic, including participating researchers and la- ratories from all over the world. Of the 41 papers received this year, 24 have been selected for presentation and 7 for poster sessions. In addition to these, four invited speakers have contributed to the conference. The site of Marne-la-Vall ee, just 20 min away from Paris, is particularly we- suited to hold the conference. Indeed, as a newly built city, it showcases a great amount of modern creative architecture, whose pure lines and original shapes o er a favorable context for the topic of Geometry.

Combinatorial Enumeration

Author : Ian P. Goulden
Publisher : Courier Corporation
ISBN 13 : 0486435970
Total Pages : 609 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Combinatorial Enumeration by : Ian P. Goulden

Download or read book Combinatorial Enumeration written by Ian P. Goulden and published by Courier Corporation. This book was released on 2004-06-23 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.

Arakelov Geometry and Diophantine Applications

Author : Emmanuel Peyre
Publisher : Springer Nature
ISBN 13 : 3030575594
Total Pages : 469 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Arakelov Geometry and Diophantine Applications by : Emmanuel Peyre

Download or read book Arakelov Geometry and Diophantine Applications written by Emmanuel Peyre and published by Springer Nature. This book was released on 2021-03-10 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

Random Polynomials

Author : A. T. Bharucha-Reid
Publisher : Academic Press
ISBN 13 : 148319146X
Total Pages : 223 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Random Polynomials by : A. T. Bharucha-Reid

Download or read book Random Polynomials written by A. T. Bharucha-Reid and published by Academic Press. This book was released on 2014-05-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Random Polynomials focuses on a comprehensive treatment of random algebraic, orthogonal, and trigonometric polynomials. The publication first offers information on the basic definitions and properties of random algebraic polynomials and random matrices. Discussions focus on Newton's formula for random algebraic polynomials, random characteristic polynomials, measurability of the zeros of a random algebraic polynomial, and random power series and random algebraic polynomials. The text then elaborates on the number and expected number of real zeros of random algebraic polynomials; number and expected number of real zeros of other random polynomials; and variance of the number of real zeros of random algebraic polynomials. Topics include the expected number of real zeros of random orthogonal polynomials and the number and expected number of real zeros of trigonometric polynomials. The book takes a look at convergence and limit theorems for random polynomials and distribution of the zeros of random algebraic polynomials, including limit theorems for random algebraic polynomials and random companion matrices and distribution of the zeros of random algebraic polynomials. The publication is a dependable reference for probabilists, statisticians, physicists, engineers, and economists.

General Orthogonal Polynomials

Author : Herbert Stahl
Publisher : Cambridge University Press
ISBN 13 : 9780521415347
Total Pages : 272 pages
Book Rating : 4.4/5 (153 download)

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Book Synopsis General Orthogonal Polynomials by : Herbert Stahl

Download or read book General Orthogonal Polynomials written by Herbert Stahl and published by Cambridge University Press. This book was released on 1992-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.

Déformation, quantification, théorie de Lie

Author : Alberto S. Cattaneo
Publisher : Societe Mathematique de France
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Déformation, quantification, théorie de Lie by : Alberto S. Cattaneo

Download or read book Déformation, quantification, théorie de Lie written by Alberto S. Cattaneo and published by Societe Mathematique de France. This book was released on 2005 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.

Researching the History of Mathematics Education

Author : Fulvia Furinghetti
Publisher : Springer
ISBN 13 : 3319682946
Total Pages : 323 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Researching the History of Mathematics Education by : Fulvia Furinghetti

Download or read book Researching the History of Mathematics Education written by Fulvia Furinghetti and published by Springer. This book was released on 2017-12-04 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers insights into the history of mathematics education, covering both the current state of the art of research and the methodology of the field. History of mathematics education is treated in the book as a part of social history. This book grew out of the presentations delivered at the International Congress on Mathematics Education in Hamburg. Modern development and growing internationalization of mathematics education made it clear that many urgent questions benefit from a historical approach. The chapters present viewpoints from the following countries: Belgium, Brazil, Cambodia, China, Cyprus, Germany, Iceland, Italy, the Netherlands, Russia,Spain and Sweden. Each chapter represents significant directions of historical studies. The book is a valuable source for every historian of mathematics education and those interested in mathematics education and its development.

From Riemann to Differential Geometry and Relativity

Author : Lizhen Ji
Publisher : Springer
ISBN 13 : 3319600397
Total Pages : 664 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis From Riemann to Differential Geometry and Relativity by : Lizhen Ji

Download or read book From Riemann to Differential Geometry and Relativity written by Lizhen Ji and published by Springer. This book was released on 2017-10-03 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Amongst Mathematicians

Author : Elena Nardi
Publisher : Springer Science & Business Media
ISBN 13 : 0387371419
Total Pages : 349 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Amongst Mathematicians by : Elena Nardi

Download or read book Amongst Mathematicians written by Elena Nardi and published by Springer Science & Business Media. This book was released on 2008 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

Representation Theorems in Hardy Spaces

Author : Javad Mashreghi
Publisher : Cambridge University Press
ISBN 13 : 0521517680
Total Pages : 385 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Representation Theorems in Hardy Spaces by : Javad Mashreghi

Download or read book Representation Theorems in Hardy Spaces written by Javad Mashreghi and published by Cambridge University Press. This book was released on 2009-03-19 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane.

Directed Algebraic Topology

Author : Marco Grandis
Publisher : Cambridge University Press
ISBN 13 : 1139482580
Total Pages : 445 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Directed Algebraic Topology by : Marco Grandis

Download or read book Directed Algebraic Topology written by Marco Grandis and published by Cambridge University Press. This book was released on 2009-09-17 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from that of classical algebraic topology by the principle that directed spaces have privileged directions and directed paths therein need not be reversible. Its homotopical tools (corresponding in the classical case to ordinary homotopies, fundamental group and fundamental groupoid) should be similarly 'non-reversible': directed homotopies, fundamental monoid and fundamental category. Homotopy constructions occur here in a directed version, which gives rise to new 'shapes', like directed cones and directed spheres. Applications will deal with domains where privileged directions appear, including rewrite systems, traffic networks and biological systems. The most developed examples can be found in the area of concurrency.