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Mathematical Image Processing : University of Orléans, France, March 29th - April 1st, 2010 / edited by Maïtine Bergounioux
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Proceedings in Mathematics ; 5 | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011Description: Online-Ressource (X, 197p. 30 illus., 14 illus. in color, digital)ISBN:- 9783642196041
- 006.601/51
- 519.6
- QA402.5-402.6
- TA1637
Contents:
Summary: Function spaces vs. Scaling Functions: Tools for Image Classification. Stéphane Jaffard, Patrice Abry and Stéphane Roux -- A Second Order Model for 3D-texture Extraction. Maïtine Bergounioux and Minh Phuong Tran -- Analysis of Texture Anisotropy Through Extended Fractional Brownian Fields. Hermine Biermé and Frédéric J.P. Richard -- Image Reconstruction via Hypoelliptic Diffusion on the Bundle of Directions of the Plane. Ugo Boscain, Jean Duplaix, Jean-Paul Gauthier, Francesco Rossi -- Projective Invariant Features Detection and the Registration group. Françoise Dibos -- Morphological Component Analysis for Decomposing Dynamic Textures. Sloven Dubois, Renaud Péteri and Michel Ménard -- Texture Enhancing Based on Variational Image Decomposition. F. Frühauf, C. Pontow, O. Scherzer -- A Locally Anisotropic Model for Image Texture Extraction. Loïc Piffet -- A Neural Field Model for Motion Estimation. Émilien Tlapale, Pierre Kornprobst, Guillaume Masson and Olivier Faugeras -- Non-Local Regularization and Registration of Multi-Valued Images by PDE’s and VariationalMethods on Higher Dimensional Spaces. David Tschumperlé and Luc Brun.Summary: The contributions appearing in this volume are a snapshot of the different topics that were discussed during the conference. They mainly concern, image reconstruction, texture extraction and image classification and involve a variety of different methods and applications. Therefore it was impossible to split the papers into generic groups which is why they are presented in alphabetic order. However they mainly concern : texture analysis (5 papers) with different techniques (variational analysis, wavelet and morphological component analysis, fractional Brownian fields), geometrical methods (2 papers ) for restoration and invariant feature detection, classification (with multifractal analysis), neurosciences imaging and analysis of Multi-Valued Images.PPN: PPN: 1650945221Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Mathematical Image Processing; Preface; Contents; List of Contributors; Function Spaces Vs. Scaling Functions: Tools for Image Classification; 1 Introduction; 2 Scaling Functions and Function Spaces; 2.1 Orthonormal and Biorthogonal Wavelet Bases; 2.2 The Wavelet Scaling Function; 2.3 The Uniform Hölder Exponent; 2.4 Scaling Functions for Image Model Validation; 2.5 Multifractal Formalism; 2.6 Wavelet Leaders; 2.7 Scaling Function for Measures; 3 Extensions of the Scaling Function: q-Leaders and Fractional Integration; 3.1 q-Leaders; 3.2 Fractional Integration
3.3 The q-Fractional Scaling Function4 An Introduction to the Grand Canonical Formalism; 4.1 Oscillation Exponents: Discussion of Possible Definitions; 4.2 Properties and Wavelet Estimationof the Oscillation Exponent; 4.3 Derivation of β-Leaders; 4.4 Derivation of Grand Canonical Formalisms; 4.5 Concavity of the Scaling Function; 5 Concluding Remarks; References; A Second Order Model for 3D-Texture Extraction; 1 Introduction; 1.1 Bounded Variation Spaces of First and Second Order; 1.2 The Abstract Second-Order Model; 1.3 Discretization of the 3D: Problem
1.4 Numerical Computation of the Solution of (3)2 Introducing Anisotropy; 3 Numerical Examples; References; Analysis of Texture Anisotropy Based on Some Gaussian Fields with Spectral Density; 1 Introduction; 2 Main Properties; 2.1 Random Fields; 2.2 Line and Projection Processes; 2.3 Process Regularity; 3 Parameter Estimation; 3.1 Generalized Quadratic Variations; 3.2 Convergence Results; 4 Numerical Study; 5 Applications; References; Image Reconstruction Via Hypoelliptic Diffusion on the Bundle of Directions of the Plane; 1 Introduction; 2 The Mathematical Model and the Algorithm
2.1 Reconstruction of a Curve2.2 Left-Invariant Sub-Riemannian Manifolds; 2.3 Lift of a Curve on PTR2 and the Sub-Riemannian Problem; 2.4 The Sub-Riemannian Problem on SE(2); 2.5 The Hypoelliptic Heat Kernel; 2.6 The Mathematical Algorithm; 3 Numerical Implementation; 3.1 STEPS 2-3: Lift of an Image; 3.2 STEP 4: Hypoelliptic Evolution; 4 Results of Image Reconstruction; References; Projective Invariant Features Detection and the Registration Group; 1 Introduction; 2 The Registration Group; 2.1 Definition and Properties
2.2 3D Homogeneous Image Associated to a Planar Image f and Deformations of f2.3 Projective Group or Registration Group?; 3 Projective Invariant Analysis; 3.1 The 2D Projective Analysis of f and the Registration Group; 4 From ASIFT to PSIFT, a First Approach; 4.1 The Matrix Decomposition Theorem of Morel and Yu; 4.2 Towards a PSIFT Algorithm; 5 Conclusion; References; Morphological Component Analysis for Decomposing Dynamic Textures; 1 Introduction; 2 Decomposing a Dynamic Texture Using Morphological Component Analysis; 2.1 Morphological Component Analysis Approach
2.2 Choice of the Dictionary
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