Scale Space and Variational Methods in Computer Vision

Name: Scale Space and Variational Methods in Computer Vision | 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings
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7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings

Jan Lellmann Martin Burger Jan Modersitzki(Editor)

Springer (Publisher)

Published on 21. June 2019

XVII, 574 pages

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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
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Scale Space and Variational Methods in Computer Vision

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