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Free discontinuity problems in image and signal segmentation / A. Vitti (2008) 

Public Titre : Free discontinuity problems in image and signal segmentation Type de document : Thèse/HDR Auteurs : A. Vitti, Auteur Editeur : Trente : Universita degli studi di Trento Année de publication : 2008 Importance : 134 p. Format : 21 x 30 cm Note générale : Bibliographie Doctoral thesis in environmental engineering Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Traitement du signal [Termes IGN] calcul variationnel [Termes IGN] discontinuité [Termes IGN] discrétisation [Termes IGN] méthode des éléments finis [Termes IGN] segmentation d'image [Termes IGN] signal monodimensionnel [Termes IGN] traitement du signal Index. décimale : THESE Thèses et HDR Résumé : (Auteur) [introduction] This thesis aims to inspect and to understand, from an engineering point of view, the mathematical framework of variational problems and in particular of ”Free Discontinuity Problems” where the concept of image and signal segmentation can be rigorously formulated. The second objective is to develop end-user software libraries and programs implementing two variational segmentation models to perform practically images and one dimensional signals segmentation. In the thesis there are no original mathematical contributions, that would be outside the competences of the author. The mathematical problems have been approached and studied with the aim of making a bridge between the theory and the applications. Part 1 of the thesis is the outcome of this study. The main thesis results are the development of original software libraries and programs to perform segmentation of images and of one dimensional signals and the application of such programs to real data sets. The developed numerical programs allowed also to study and to reproduce in practice the well known features of the theoretical formulations of segmentation approached as a ”Free Discontinuity Problem”. This work deals with the Mumford and Shah functional and with the Blake and Zisserman functional. The Mumford and Shah functional in dimension two is introduced, studied, implemented numerically and applied to the segmentation of images. An extension of the Mumford and Shah is treated analogously. The Blake and Zisserman functional is introduced and studied in dimension two and then in dimension one, while the numerical implementation and the applications are performed in dimension one, i.e to the segmentation of one dimensional signals. Specifically, the thesis faces the problem of segmenting environmental images, such as aerophotogrammetry images and one dimensional signal time series arising from Geodesy, such as GNSS (Global Navigation Satellite System) permanent stations coordinates. [...] Note de contenu : Introduction Part 1 A Review of the Mathematical Theory of Variational Segmentation 1 Mathematical Framework 1.1 Variational Problems 1.1.1 Classical and Direct Methods in the Calculus of Variations 1.2 Free Discontinuity Problems 1.2.1 A General Introduction 1.2.2 The Space of Special Functions of Bounded Variation 1.2.3 Some Essential Features About ¡-convergence 1.3 Variational Segmentation: The Mumford and Shah Model 2 The Mumford and Shah Model 2.1 The Mumford and Shah Model for Image Segmentation 2.1.1 The Mumford and Shah Functional 2.1.2 Weak Formulation in SBV 2.1.3 Approximations of the Weak Formulation 2.1.4 Drawbacks of the Mumford and Shah Model 2.2 Controlling the Curvature in the Mumford and Shah Model 2.3 Euler Equation and Gradient Flow 2.3.1 The Euler Equation Associated to the Elliptic Approximation of the Mumford and Shah Model without and with the Curvature Term 2.4 Finite Differences Discretisation 2.5 The Gradient Effect in Dimension One 3 The Blake and Zisserman Model 3.1 The Blake and Zisserman Model for One Dimensional Signal Segmentation 3.2 The Ambrosio and Tortorelli Approximation 3.3 Finite Elements Discretisation Part 2 Numerical Applications 4 Software Implementations 4.1 The seglib Library for Images Segmentation 4.1.1 The GRASS GIS module r.seg 4.2 The seglib1d Library for One Dimensional Signals Segmentation 4.2.1 The sigseg Program 5 Segmentation of Images 5.1 Segmentation of Synthetic Images 5.1.1 Test Image A 5.1.2 Test Image B 5.1.3 Test Image C 5.1.4 Test Image D 5.2 Segmentation of Real Images 5.2.1 Lenna 5.2.2 Aeroplane 5.3 Segmentation of Real ”Environmental” Images 5.3.1 Pebbles 5.3.2 Braided River-bed 5.3.3 High Resolution Ortho-Photo 6 Segmentation of One Dimensional Signals 6.1 Segmentation of Synthetic One Dimensional Signals 6.1.1 Occurrence and overcoming of the Gradient Effect 6.1.2 A Complex Signal and a Complex Noisy Signal 6.2 Segmentation of GNSS Coordinates Time Series 6.2.1 Detection of a Singular Jump 6.2.2 Different Segmentations of the Same Time Series Numéro de notice : 13785 Affiliation des auteurs : non IGN Thématique : IMAGERIE/POSITIONNEMENT Nature : Thèse française Note de thèse : Thèse de doctorat : ingénierie de l'environnement : Italie, université de Trente : 2008 nature-HAL : Thèse DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=45233

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