
Scale Space and Variational Methods in Computer Vision
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions

Content
- Intro
- Preface
- Tribute to Mila Nikolova (1962-2018)
- Organization
- Contents
- 3D Vision and Feature Analysis
- The Fractional Harris-Laplace Feature Detector
- 1 Introduction
- 2 Fractional Differentiation
- 2.1 The CRONE Operator
- 3 The Harris-Laplace Detector
- 4 The Fractional Harris-Laplace Detector
- 5 Results
- 5.1 Boats1 Sequence
- 5.2 Boats2 Sequence
- 6 Discussion
- 7 Future Directions
- References
- Macrocanonical Models for Texture Synthesis
- 1 Introduction
- 2 Maximum Entropy Models
- 2.1 Microcanonical Models
- 2.2 Macrocanonical Models
- 2.3 Some Feature Examples
- 3 Minimization and Sampling Algorithm
- 3.1 Maximizing the Entropy
- 3.2 Sampling from Gibbs Measures
- 3.3 Combining Dynamics
- 4 Experiments
- 4.1 Empirical Convergence of the Sampling Algorithm
- 4.2 Neural Network Features
- 4.3 Comparison with State-of-the Art Methods
- 5 Perspectives
- References
- Finding Structure in Point Cloud Data with the Robust Isoperimetric Loss
- 1 Introduction
- 1.1 Previous Work and Challenges
- 2 Preliminaries and Main Assumptions
- 3 Proposed Approach
- 3.1 Outlier Estimation
- 3.2 Step 2: Adaptive Regularization Using the Isoperimetric Loss (IPL)
- 4 Experimental Results
- 4.1 Manifold Denoising
- 4.2 The RIPL Approach
- 4.3 Experiments with Real Data: Application to Motion Segmentation
- 4.4 Experiments with Real Data: Application with 3D Laser Scan Data
- 5 Discussion
- References
- Deep Eikonal Solvers
- 1 Introduction
- 2 Background
- 2.1 The Eikonal Equation
- 2.2 Numerical Approximation
- 2.3 Fast Eikonal Solvers
- 3 Deep Eikonal Solver
- 3.1 Training the Local Solver
- 3.2 Deep Eikonal Solver for Cartesian Grids
- 4 Deep Eikonal Solver for Triangulated Meshes
- 4.1 Experimental Results
- 5 Conclusion
- References
- A Splitting-Based Algorithm for Multi-view Stereopsis of Textureless Objects
- 1 Introduction
- 2 Preliminaries
- 3 A Generic Splitting Strategy for Multi-view Stereo
- 4 Regularizers for Textureless Multi-view Stereopsis
- 5 Experimental Results
- 6 Conclusion and Perspectives
- References
- Inpainting, Interpolation and Compression
- Pseudodifferential Inpainting: The Missing Link Between PDE- and RBF-Based Interpolation
- 1 Introduction
- 2 From Harmonic to Pseudodifferential Inpainting
- 3 Interpolation with Radial Basis Functions
- 4 Connecting both Worlds
- 5 One Numerical Algorithm for All Approaches
- 6 Experiments
- 7 Conclusions and Outlook
- References
- Towards PDE-Based Video Compression with Optimal Masks and Optic Flow
- 1 Introduction
- 2 Discussion of Considered Models and Methods
- 2.1 Image Inpainting with PDEs
- 2.2 Extension from Images to Videos
- 2.3 Optical Flow
- 3 Combining Optimal Masks with Flow Data
- 4 Experimental Evaluation
- 4.1 Methods Considered
- 4.2 Evaluation
- 4.3 Influence of the Optical Flow
- 4.4 Evaluation of the Reconstruction Error
- 5 Summary and Conclusion
- References
- Compressing Audio Signals with Inpainting-Based Sparsification
- 1 Introduction
- 2 A Framework for Inpainting-Based Audio Compression
- 3 Localised Sample Optimisation with 1-D Inpainting
- 4 Experiments
- 5 Conclusions and Outlook
- References
- Alternate Structural-Textural Video Inpainting for Spot Defects Correction in Movies
- 1 Introduction
- 2 Related Work
- 3 Statement of the Problem
- 3.1 Structural Reconstruction Energy
- 3.2 Textural Reconstruction Energy
- 4 Optimization
- 4.1 Motion Estimation
- 4.2 Structural Reconstruction
- 4.3 Shift Maps Estimation and Textural Reconstruction
- 5 Experiments
- 5.1 Qualitative Results
- 5.2 Quantitative Results
- 6 Conclusion and Perspectives
- References
- Inverse Problems in Imaging
- Iterative Sampled Methods for Massive and Separable Nonlinear Inverse Problems
- 1 Introduction
- 2 Sampled Tikhonov Methods for Linear Inverse Problems
- 3 Iterative Sampled Methods for Separable Nonlinear Inverse Problems
- 4 Numerical Results
- 4.1 Experiment 1: Comparing sn-slimTik to Variable Projection
- 4.2 Experiment 2: sn-slimTik for a Massive Problem
- 5 Conclusions
- References
- Refitting Solutions Promoted by 12 Sparse Analysis Regularizations with Block Penalties
- 1 Introduction
- 1.1 Refitting
- 1.2 Outline and Contributions
- 2 Related Re-fitting Works
- 2.1 Properties of Bregman Divergence of ell12 Structured Regularizers
- 2.2 Bregman-Based Refitting
- 2.3 Flexible Quadratic Refitting Without Support Identification
- 3 Refitting with Block Penalties
- 3.1 Desired Properties of Refitting Block Penalties
- 3.2 A New Flexible Refitting Block Penalty
- 3.3 SD Block Penalty: The Best of Both Bregman Worlds
- 4 Refitting in Practice
- 4.1 Biased Problem and Posterior Refitting
- 4.2 Joint-Refitting Algorithm
- 5 Results
- 6 Conclusion
- References
- An Iteration Method for X-Ray CT Reconstruction from Variable-Truncation Projection Data
- 1 Introduction
- 2 Prior Knowledge of Background
- 3 CT Reconstruction Based on Sparse Representation
- 3.1 Determinations of r1t and r2t
- 3.2 Weight Matrix W
- 4 Numerical Experiments
- 5 Conclusions and Future Work
- References
- A New Iterative Method for CT Reconstruction with Uncertain View Angles
- 1 Introduction
- 1.1 Previous Work
- 1.2 Our Contribution
- 2 Our Method
- 2.1 An Iterative Algorithm
- 2.2 Approximation of L|x
- 3 Numerical Experiments
- 3.1 The Small Example
- 3.2 The Larger Example
- 4 Conclusion
- References
- Optimization Methods in Imaging
- Time Discrete Geodesics in Deep Feature Spaces for Image Morphing
- 1 Introduction
- 2 Review of the Metamorphosis Model
- 3 Time Discrete Metamorphosis Model in Feature Space
- 4 Fully Discrete Metamorphosis Model in Feature Space
- 5 Numerical Optimization Using the iPALM Algorithm
- 6 Numerical Results
- References
- Minimal Lipschitz Extensions for Vector-Valued Functions on Finite Graphs
- 1 Introduction
- 2 Minimal Lipschitz Extensions and Approximations
- 3 Midrange Filters and -Harmonic Extensions
- 4 -Laplacians on Scalar-Valued Functions
- 5 Conclusions
- References
- PDEs and Level-Set Methods
- The Convex-Hull-Stripping Median Approximates Affine Curvature Motion
- 1 Introduction
- 2 Theory of Convex-Hull-Stripping Median Filtering
- 2.1 The Convex-Hull-Stripping Median of Finite Sets
- 2.2 Continuous-Scale Limit
- 3 Experiments
- 4 Summary and Conclusions
- References
- Total Variation and Mean Curvature PDEs on the Space of Positions and Orientations
- 1 Introduction
- 2 Theory
- 2.1 The Homogeneous Space M of Positions and Orientations
- 2.2 Total-Roto Translation Variation, Mean Curvature Flows on M
- 2.3 Gradient-Flow Formulations and Convergence
- 2.4 Numerics
- 3 Experiments
- 3.1 TVF and MCF on R3 S2 for Denoising FODFs in DW-MRI
- 3.2 TVF and MCF on R2 S1 for 2D Image Enhancement/Denoising
- 4 Conclusion
- References
- A Variational Convex Hull Algorithm
- 1 Introduction
- 2 Model Description
- 2.1 Preliminaries
- 2.2 Exact Convex Hull Model
- 2.3 The Algorithms for Proposed Models
- 3 Numerical Implementation
- 3.1 Discretization Scheme
- 3.2 Initialization and Determination of Landmarks
- 4 Numerical Experiment
- 4.1 Exact Convex Hull Model
- 4.2 Convex Hull Model for Outliers
- 5 Conclusion
- References
- PDE Evolutions for M-Smoothers: From Common Myths to Robust Numerics
- 1 Introduction
- 2 M-Smoothers, Mode and Partial Differential Equations
- 3 An L-stable Numerical Scheme for the PDE Limit
- 4 Experiments
- 5 Summary and Conclusions
- References
- Registration and Reconstruction
- Variational Registration of Multiple Images with the SVD Based SqN Distance Measure
- 1 Introduction
- 2 Registration Approaches for Multiple Images
- 2.1 Variational Registration Approach for Two Images
- 2.2 Sequential Registration Approach for Multiple Images
- 2.3 Global Registration Approach for Multiple Images
- 2.4 Schatten q-norm Based Image Similarity Measure DS,q
- 2.5 Volume Minimization of the Feature Parallelotope
- 2.6 Correlation Maximization of Normalized Features
- 2.7 Correlation Maximization and Schatten q-norms
- 3 Numerical Methods
- 4 Results
- 5 Discussion and Conclusions
- References
- Multi-tasking to Correct: Motion-Compensated MRI via Joint Reconstruction and Registration
- 1 Introduction
- 2 Joint Model for Motion Correction in MRI
- 2.1 Mathematical Model and Notation
- 2.2 Joint Variational Model
- 2.3 Numerical Method: Optimisation Scheme
- 3 Numerical Experiments
- 4 Conclusion
- References
- Variational Image Registration for Inhomogeneous-Resolution Pairs
- 1 Introduction
- 2 Mathematical Preliminaries
- 3 Numerical Method for Variational Image Registration
- 3.1 Rational-Order Pyramid Transform
- 3.2 Discretisation of Variational Method
- 4 Resolution Interpolation
- 5 Numerical Examples
- 5.1 Registration of Inhomogeneous-Resolution Pair
- 5.2 Resolution Interpolation
- 6 Conclusions
- References
- Scale-Space Methods
- Computing Nonlinear Eigenfunctions via Gradient Flow Extinction
- 1 Introduction
- 2 Gradient Flows and Eigenfunctions
- 3 An Iterative Scheme to Compute Nonlinear Spectral Decompositions
- 3.1 The Spectral Case
- 3.2 The General Case
- 4 Applications
- 4.1 Numerical Computation of Extinction Profiles
- 4.2 1D Total Variation Example
- 4.3 Spectral Clustering with Extinction Profiles
- 4.4 Outlook: Advanced Clustering with Higher-Order Eigenfunctions
- References
- Sparsification Scale-Spaces
- 1 Introduction
- 2 Theoretical Results
- 2.1 Formalisation of Discrete Sparsification Scale-Spaces
- 2.2 Scale-Space Properties
- 3 Specific Aspects and Experiments
- 4 Conclusions and Future Work
- References
- Stable Explicit p-Laplacian Flows Based on Nonlinear Eigenvalue Analysis
- 1 Introduction
- 2 Preliminary
- 2.1 Eigenfunctions of the p-Laplacian
- 3 Analysis of Explicit Schemes for Shape Preserving Flows
- 3.1 Convergence Criterion for Adaptive Step Size
- 3.2 Stability Criterion for Fixed Step Size
- 4 Arbitrary Initial Conditions
- 5 Results and Conclusion
- References
- Provably Scale-Covariant Networks from Oriented Quasi Quadrature Measures in Cascade
- 1 Introduction
- 2 The Quasi Quadrature Measure over a 1-D Signal
- 3 Oriented Quasi Quadrature Modelling of Complex Cells
- 4 Hierarchies of Oriented Quasi Quadrature Measures
- 5 Application to Texture Analysis
- 6 Summary and Discussion
- References
- A Fast Multi-layer Approximation to Semi-discrete Optimal Transport
- 1 Introduction
- 2 Semi-discrete Optimal Transport
- 3 Multi-layer Approximation of the Transport Map
- 3.1 Multi-scale Semi-discrete Optimal Transport
- 3.2 Multi-layer Transport Map
- 4 Numerical Experiments
- 4.1 One-Dimensional Example
- 4.2 Texture Synthesis
- 5 Discussion and Conclusion
- References
- Segmentation and Labeling
- Global Similarity with Additive Smoothness for Spectral Segmentation
- 1 Introduction
- 2 Method
- 2.1 Conventional Affinity Matrix
- 2.2 Full-Range Affinity Matrix
- 3 Results
- 4 Conclusion
- References
- Segmentation of 2D and 3D Objects with Intrinsically Similarity Invariant Shape Regularisers
- 1 Introduction
- 2 Derivation of the Model
- 3 First Variations and Optimisation
- 4 Experimental Validation
- 5 Conclusion
- References
- Lattice Metric Space Application to Grain Defect Detection
- 1 Introduction
- 2 Lattice Metric Space: Review and New Properties
- 2.1 Review on Lattice Metric Space
- 2.2 Properties in Relation to Grain Defect Detection
- 3 Lattice Clustering Algorithm
- 4 Numerical Experiments and Discussion
- 5 Conclusion
- References
- Learning Adaptive Regularization for Image Labeling Using Geometric Assignment
- 1 Introduction
- 2 Preliminaries
- 2.1 Assignment Flow
- 2.2 Linear Assignment Flow
- 3 Learning Adaptive Regularization Parameters
- 3.1 Parameter Estimation by Trajectory Optimization
- 3.2 Parameter Estimation: Continuous Approach
- 3.3 Parameter Estimation: Discrete Approach
- 3.4 Differentiate or Discretize First?
- 3.5 Parameter Estimation Algorithm
- 3.6 Parameter Prediction
- 4 Experiments
- 5 Conclusion
- References
- Direct MRI Segmentation from k-Space Data by Iterative Potts Minimization
- 1 Introduction
- 2 Proposed Method
- 3 Experiments
- 4 Conclusion
- References
- A Balanced Phase Field Model for Active Contours
- 1 Introduction
- 2 The Phase Field Model
- 2.1 Minimizing the Contour Energy Using Phase Field
- 3 Higher Order Smoothness Terms for Phase Field Model
- 3.1 Approximate System Energy
- 3.2 Cubic Ansatz
- 3.3 The Motion of the Level Sets
- 3.4 Motion of the Level Sets of the Original Model
- 4 Phase Field Model for Reinitialization Purpose
- 4.1 Determining Weights
- 5 Experimental Evaluation
- 5.1 Stability Tests: Comparing to the Ginzburg-Landau Model
- 5.2 Comparing to the Reaction-Diffusion Model
- 6 Discussion
- References
- Unsupervised Labeling by Geometric and Spatially Regularized Self-assignment
- 1 Introduction
- 2 Assignment Flow: Supervised Labeling
- 3 Approach: Label Learning Through Self-assignment
- 3.1 Rationale
- 3.2 Computational Approach
- 3.3 Spatially Regularized Optimal Transport
- 4 Related Work
- 4.1 Nonnegative Matrix Factorization (NMF)
- 4.2 Discrete Optimal Mass Transport (DOMT)
- 5 Experiments
- 6 Conclusion
- References
- Variational Methods
- Aorta Centerline Smoothing and Registration Using Variational Models
- 1 Introduction
- 2 Related Work
- 3 Variational Methods for Aorta Centerline Smoothing
- 4 Variational Methods for Aorta Centerline Registration
- 5 Experimental Setup
- 6 Conclusions
- References
- A Connection Between Image Processing and Artificial Neural Networks Layers Through a Geometric Model of Visual Perception
- 1 Introduction
- 2 From Wilson-Cowan Equations to Image Processing
- 2.1 Wilson-Cowan Equations Encoding the Edges and Textures
- 2.2 Properties of the Equations
- 2.3 Connection to Image Processing Models
- 3 Wilson-Cowan Equations and Color Perception Models
- 3.1 A Geometric Model of Color Perception
- 3.2 Connection to Image Processing Models
- 4 Connection to Artificial Neural Networks
- 4.1 A New Operator and Its Connections to Existing Layers
- 4.2 Learning the Parameters of the Operator
- 4.3 Experiments
- 5 Conclusion
- References
- A Cortical-Inspired Model for Orientation-Dependent Contrast Perception: A Link with Wilson-Cowan Equations
- 1 Introduction
- 2 Orientation-Independent Variational Models
- 3 A Cortical-Inspired Model
- 3.1 Functional Lifting
- 3.2 WC-Type Mean Field Modelling
- 3.3 Discretisation via Gradient Descent
- 4 Numerical Results
- 4.1 Grating Induction with Oriented Relative Background
- 4.2 Poggendorff Illusion
- 5 Conclusions
- References
- A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions
- 1 Introduction
- 2 Primal and Dual Formulations
- 3 Basic Properties and Relationship with Other `3´9`42`"?613A``45`47`"603ATV-type Regularizers
- 4 Numerical Experiments
- 4.1 1D Experiments
- 4.2 2D Experiments
- 5 Conclusions
- References
- A Non-convex Nonseparable Approach to Single-Molecule Localization Microscopy
- 1 Introduction
- 2 Image Formation Modelling
- 3 Penalty Function
- 4 Optimization Model NCNS for SMLM Problem
- 4.1 Solving the Minimization Step
- 5 Numerical Experiments
- 5.1 Performance Evaluation
- 6 Conclusion and Future Work
- References
- Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy
- 1 Introduction
- 2 Mathematical Preliminaries
- 2.1 PCR Functions
- 2.2 The 1-Anisotropic ROF Model
- 3 The Averaging Operator AG
- 3.1 Preservation of Piecewise Constancy
- 4 Conclusion
- References
- Total Directional Variation for Video Denoising
- 1 Introduction
- 2 Total Directional Variation for Video Denoising
- 2.1 The Directional Information
- 2.2 The Regulariser
- 2.3 Connections to Optical Flow
- 2.4 The Minimisation Problem
- 3 The Discrete Model
- 3.1 Discretisation of Derivative Operators and Vector Fields
- 3.2 TDV for Video Denoising
- 4 Results
- 4.1 Selection of Parameters
- 4.2 Numerical Results
- 4.3 Discussion of Results
- 5 Conclusions
- References
- Joint CNN and Variational Model for Fully-Automatic Image Colorization
- 1 Introduction
- 2 A CNN to Compute a Statistical Distribution of Color
- 3 A Variational Model for Image Colorization with Channels Coupling
- 4 Joining Total Variation Model with CNN
- 5 Numerical Results
- 6 Conclusion
- References
- A Variational Perspective on the Assignment Flow
- 1 Introduction
- 2 Preliminaries
- 3 Model
- 4 Optimization Approach
- 5 Experiments
- 6 Conclusion
- References
- Functional Liftings of Vectorial Variational Problems with Laplacian Regularization
- 1 Introduction
- 2 A Calibration Method with Vectorial Second-Order Terms
- 2.1 Continuous Formulation
- 2.2 Connection to the Discretization-First Approach [15]
- 2.3 Numerical Aspects
- 3 Numerical Results
- 4 Conclusion
- References
- Author Index
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.