Scale Space and Variational Methods in Computer Vision: 9th International Conference, SSVM 2023, Santa Margherita di Pula, Italy, May 21–25, 2023, Proceedings (Lecture Notes in Computer Science)

Preface
Organization
Contents
Inverse Problems in Imaging
Explicit Diffusion of Gaussian Mixture Model Based Image Priors*-4pt
	1 Introduction
	2 Background
		2.1 Diffusion Eases Density Estimation and Sampling
		2.2 Diffusion, Empirical Bayes, and Denoising Score Matching
	3 Methods
		3.1 Patch Model
		3.2 Convolutional Model
	4 Numerical Results
		4.1 Numerical Optimization
		4.2 Sampling
		4.3 Image Denoising
		4.4 Noise Estimation and Blind Image Denoising
	5 Conclusion
	References
Efficient Neural Generation of 4K Masks for Homogeneous Diffusion Inpainting
	1 Introduction
	2 Homogeneous Diffusion Inpainting
		2.1 Model-Based Mask Optimisation
	3 Neural Mask Generation
	4 Coarse-to-Fine Approach for Mask Generation
	5 Experiments
		5.1 Experimental Setup
		5.2 Quality of Inpainting Approximations
		5.3 Justification of Mask Pixel Distribution
		5.4 High-Resolution Mask Generation
	6 Conclusions
	References
Theoretical Foundations for Pseudo-Inversion of Nonlinear Operators
	1 Introduction
	2 The Moore-Penrose Properties and Partial Notions of Inversion
	3 The {1,2}-Inverses of Nonlinear Operators
	4 A Pseudo-Inverse for Nonlinear Operators in Normed Spaces
	5 High-Level Properties of the Nonlinear Inverse
	6 Test Cases
	7 Conclusion
	References
A Frame Decomposition of the Funk-Radon Transform
	1 Introduction
	2 Background on Frames and Frame Decompositions
	3 Frame Decompositions of the Funk-Radon Transform
	4 Numerical Results
	5 Conclusion
	References
Prony-Based Super-Resolution Phase Retrieval of Sparse, Multidimensional Signals
	1 Introduction
	2 Preleminaries
		2.1 Fourier Transform of Measures
		2.2 Prony\'s Method
	3 The Phase Retrieval Problem
	4 Sparse Phase Retrieval on the Line
	5 Sparse Phase Retrieval on the Real Space
	6 Simulations
	7 Conclusion
	References
Limited Electrodes Models in Electrical Impedance Tomography Reconstruction
	1 Introduction
	2 Preliminaries on EIT Reconstructions
	3 EIT-Limited Electrodes Problem Setup
	4 A Compressed Sensing Approach to EIT-LE Problem
	5 A Learned Approach to EIT-LE Problem
		5.1 VNet Architecture
	6 Numerical Experiments
	7 Conclusion and Future Work
	7.1  Appendix: regularized Gauss-Newton method for the inverse EIT problem
	References
On Trainable Multiplicative Noise Removal Models
	1 Introduction
	2 Trainable Models for Multiplicative Noise Removal
		2.1 TNRD Model
		2.2 L-TNRD Model
		2.3 Feng et al Model
		2.4 Proposed Model
	3 Numerical Experiments
	4 Conclusions
	References
Surface Reconstruction from Noisy Point Cloud Using Directional G-norm
	1 Introduction
	2 Notation and Motivation
		2.1 Review on Computation of SDF
		2.2 Effect of Noise on SDF
	3 The Proposed Method: Directional G-norm Based Surface Reconstruction
		3.1 Minimisation Method
	4 Numerical Scheme
		4.1 Linear Systems
	5 Numerical Results
	6 Conclusion
	References
Regularized Material Decomposition for K-edge Separation in Hyperspectral Computed Tomography
	1 Introduction
	2 Hyperspectral Computed Tomography
	3 One-Stage Methods
	4 Experimental Setup
	5 Numerical Results
		5.1 One-stage Vs Two-Stage Method
		5.2 LS Vs WLS
		5.3 Regularization
	6 Conclusion
	References
Quaternary Image Decomposition with Cross-Correlation-Based Multi-parameter Selection
	1 Introduction
	2 Preliminaries and Notations
	3 Proposed Two-Stage Variational Decomposition Model
	4 On the Decomposition Stage I
		4.1 Insights on the Effect of Different Norms
		4.2 Analysis of the Model
	5 Multi-parameter Selection via Cross-Correlation
	6 An ADMM-Based Numerical Solution for Stage I
	7 Numerical Examples
	8 Conclusions
	References
Machine and Deep Learning in Imaging
EmNeF: Neural Fields for Embedded Variational Problems in Imaging
	1 Motivation
	2 Embedding
	3 EmNeF
	4 Network Architecture
		4.1 Implementation of the Constraints
	5 Numerical Results
		5.1 Denoising
		5.2 Stereo Matching
	6 Outlook
	References
GenHarris-ResNet: A Rotation Invariant Neural Network Based on Elementary Symmetric Polynomials
	1 Introduction
	2 Related Work
	3 Mathematical Preliminaries
		3.1 Gaussian Partial Derivatives
		3.2 Generalized Structure Tensor for Higher Derivatives
		3.3 Elementary Symmetric Polynomials
	4 GenHarris-ResNet
	5 Experiments
	6 Conclusion
	References
Compressive Learning of Deep Regularization for Denoising
	1 Introduction
	2 Background, Related Works
	3 Proposed Method
	4 Experiments
	5 Conclusions
	References
Graph Laplacian and Neural Networks for Inverse Problems in Imaging: GraphLaNet
	1 Introduction
	2 Building the Graph Laplacian
	3 Our Neural Network
	4 GraphLaNet
	5 Experimental Setup
		5.1 Few-View CT Reconstruction
		5.2 The Data Set
		5.3 Choice of Regularization Parameters
	6 Numerical Results
	7 Conclusion
	References
Learning Posterior Distributions in Underdetermined Inverse Problems
	1 Introduction
	2 Related Work
	3 Unequal Dimensionality Flow
		3.1 Unpaired Training with UnDimFlow
		3.2 Computing the Posterior p`3́9`42`\"̇613A``45`47`\"603Ax`3́9`42`\"̇613A``45`47`\"603Ay(x y)
		3.3 Recovering a Solution to the Inverse Problem During Inference
	4 Experimental Results
		4.1 Super-Resolution Under High Uncertainty
		4.2 Image Inpainting on Partitioned Training Dataset
	5 Conclusion
	A Appendix
		A.1 Additional Theoretical Results
		A.2 Further Results for Super-Resolution Under High Uncertainty
		A.3 Experimental Details
	References
Proximal Residual Flows for Bayesian Inverse Problems
	1 Introduction
	2 Proximal Residual Flows
		2.1 Residual Flows
		2.2 Proximal Neural Networks
		2.3 Proximal Residual Flows
	3 Conditional Proximal Residual Flows
	4 Numerical Examples
		4.1 Unconditional Examples
		4.2 Posterior Reconstruction
	5 Conclusions
	References
A Model is Worth Tens of Thousands of Examples
	1 Introduction
	2 One-Dimensional Signal Recovery
		2.1 Data Model and Optimal Solution
		2.2 Neural Models
	3 Two-Dimensional Geometric Estimation
		3.1 Data Model
		3.2 Expert Engineer\'s Solution
		3.3 Neural Models
		3.4 Results
	4 Conclusion
	A Pointflow Implementation Details
	References
Resolution-Invariant Image Classification Based on Fourier Neural Operators
	1 Introduction
	2 Construction of Neural Operators on Lebesgue Spaces
		2.1 Well-Definedness and Continuity
		2.2 Differentiability
	3 Connections to Convolutional Neural Networks
		3.1 Extension to Higher Input-Dimensions by Zero-Padding
		3.2 Convertibility and Complexity
		3.3 Adaptation to Even Dimensions
		3.4 Interpolation Equivariance
	4 Numerical Examples
		4.1 Expressivity for Varying Kernel Sizes
		4.2 Resolution Invariance
	5 Conclusion and Outlook
	References
Graph Laplacian for Semi-supervised Learning
	1 Introduction
	2 Setting and Notation
	3 Graph-Laplacian for SSL
		3.1 Motivation
		3.2 Semi-supervised Laplacian Definition
	4 Analysis of LSSL
	5 Experimental SSL Clustering Results
		5.1 2-Moons Clustering
		5.2 MNIST and F-MNIST
	6 Conclusions
	References
A Geometrically Aware Auto-Encoder for Multi-texture Synthesis
	1 Introduction
	2 Related Work
		2.1 Periodic Texture Synthesis
		2.2 Universality and Latent Representations of Textures
	3 Method
		3.1 Architecture Overview
		3.2 Texture Encoder
		3.3 Texture Generator
		3.4 Sine Waves
		3.5 Scale Independent Learnable Frequencies
		3.6 Image Specific Scale and Orientation Estimation
		3.7 Direct Sampling
		3.8 Losses
		3.9 Training
	4 Experiments
		4.1 Assessed Methods, Datasets and Evaluation Metrics
		4.2 Visual and Quantitative Results
		4.3 Geometric Completeness
		4.4 Spatial Interpolation
	5 Conclusion
	References
Fast Marching Energy CNN
	1 Introduction
	2 Computing Geodesic Distances and Their Gradient
	3 Model
	4 Experiments
	5 Conclusion
	References
Deep Accurate Solver for the Geodesic Problem
	1 Introduction
	2 Exact Distances on Polyhedral Approximations
	3 Geodesics: O(h3) Accuracy at O(N logN) Complexity
		3.1 Local Solver
		3.2 Training the Local Solver
		3.3 Learning to Augment
	4 Numerical Evaluation: Spheres and Beyond
		4.1 Generalization to Polynomial Surfaces
		4.2 Generalization to Arbitrary Surfaces
		4.3 Ablation Study
	5 Conclusions
	References
Deep Image Prior Regularized by Coupled Total Variation for Image Colorization
	1 Introduction
	2 Deep Image Prior and Image Colorization
		2.1 What Information Is Captured by Deep Image Prior?
		2.2 Deep Image Prior and Image Colorization
		2.3 From Probability Distributions over a Low-Resolution Grid to the Color Image
		2.4 Optimization Algorithm
	3 Numerical Experiments
		3.1 Parameters
		3.2 Experiments
	4 Conclusion
	References
Hybrid Training of Denoising Networks to Improve the Texture Acutance of Digital Cameras
	1 Introduction
	2 Related Works
	3 Texture Acutance: A Frequential Loss Assessing Texture Preservation
		3.1 Dead Leaves Images
		3.2 Texture Acutance
		3.3 Acutance Loss for Image Restoration CNNs
	4 Image Denoising Results with FFDNet
		4.1 Quantitative Evaluation
		4.2 Spectral Preservation
		4.3 RAW Image Denoising
	5 Conclusion
	References
Latent-Space Disentanglement with Untrained Generator Networks for the Isolation of Different Motion Types in Video Data
	1 Introduction
	2 Method
	3 Numerical Experiments
		3.1 Synthetic Data
		3.2 Cardiac MR Images
	References
Natural Numerical Networks on Directed Graphs in Satellite Image Classification
	1 Introduction
	2 Natural Numerical Network (NatNet)
		2.1 Mathematical Model
		2.2 Numerical Discretisation
		2.3 Construction of Relevancy Maps
	3 Natural Numerical Network in Nature Protection
		3.1 Training of the Network
		3.2 Application of the Trained Network
	References
Piece-wise Constant Image Segmentation with a Deep Image Prior Approach
	1 Introduction
	2 Proposed Approach
	3 Numerical Experiments
		3.1 Results
	4 Conclusions
	References
On the Inclusion of Topological Requirements in CNNs for Semantic Segmentation Applied to Radiotherapy
	1 Introduction
	2 Proposed Nested Framework Based on Deep Learning and Variational Approaches
		2.1 CNN Formalism
		2.2 Design of a Loss Function Blending Segmentation and Registration
		2.3 A First Theoretical Result
	3 Towards a Tractable Numerical Algorithm
		3.1 Optimisation Strategy for the Nested Model
		3.2 Splitting Strategy for Problem (P)
	4 Experiments and Results
		4.1 Dataset
		4.2 Implementation
		4.3 Protocol and Evaluation Metrics
		4.4 Results
	5 Conclusion
	References
Optimization for Imaging: Theory and Methods
A Relaxed Proximal Gradient Descent Algorithm for Convergent Plug-and-Play with Proximal Denoiser
	1 Introduction
		1.1 Proximal Algorithms
		1.2 Plug-and-Play Algorithms
		1.3 Contributions and Outline
	2 Relaxed Proximal Denoiser
		2.1 Gradient Step Denoiser
		2.2 Proximal Denoiser
		2.3 Relaxed Denoiser
	3 Plug-and-Play Proximal Gradient Descent (PnP-PGD)
		3.1 Useful Inequalities
		3.2 Proximal Gradient Descent with a Weakly Convex Function
		3.3 Prox-PnP Proximal Gradient Descent (Prox-PnP-PGD)
	4 PnP Relaxed Proximal Gradient Descent (PnP-PGD)
		4.1 PGD Algorithm
		4.2 Prox-PnP-PGD Algorithm
	5 Experiments
	6 Conclusion
	References
Off-the-Grid Charge Algorithm for Curve Reconstruction in Inverse Problems
	1 Introduction
		1.1 Notations
		1.2 Related Works
	2 Optimisation in the Space of Divergence Vector Fields
		2.1 The Space of Charges
		2.2 The CROC Functional and Its Minimiser Structure
	3 The Charge (Sliding) Frank-Wolfe for Off-the-Grid Curve Reconstruction
	4 A Numerical Illustration for Super-Resolution
	5 Conclusion
	References
Convergence Guarantees of Overparametrized Wide Deep Inverse Prior
	1 Introduction
		1.1 Problem Statement
		1.2 Contributions
		1.3 Relation to Prior Work
	2 DIP Guarantees
		2.1 Notations
		2.2 Main Result
	3 Proof
	4 Numerical Experiments
	5 Conclusion and Future Work
	References
On the Remarkable Efficiency of SMART
	1 Introduction
	2 Preliminaries
	3 SMART and Convex Acceleration
	4 SMART: A Geometric Perspective
	5 Experiments
	6 Conclusion
	References
Wasserstein Gradient Flows of the Discrepancy with Distance Kernel on the Line
	1 Introduction
	2 Wasserstein Gradient Flows
	3 Wasserstein Gradient Flows on the Line
	4 Discrepancies
	5 MMD Flows on the Line
	6 Intuitive Examples
		6.1 Flow Between Dirac Measures
		6.2 Flow on Restricted Sets
	7 Conclusions
	References
A Quasi-Newton Primal-Dual Algorithm with Line Search
	1 Introduction
		1.1 Related Work
	2 Problem Setup: A Class of Saddle Point Problems
	3 Our Quasi-Newton Primal-Dual Algorithm with Line Search
	4 Convergence Analysis of Algorithm 1
	5 Computing and Representing the Quasi-Newton Metric
	6 Proximal Calculus and Efficient Implementation
	7 Numerical Experiment
	8 Conclusion
	References
Stochastic Gradient Descent for Linear Inverse Problems in Variable Exponent Lebesgue Spaces
	1 Introduction
	2 Optimisation in Banach Spaces
		2.1 Variable Exponent Lebesgue Spaces (pn)(R)
	3 Modular-Based Gradient Descent in (pn)(R)
	4 Stochastic Modular-Based Gradient-Descent in (pn)(R)
	5 Numerical Results
	6 Conclusions
	References
An Efficient Line Search for Sparse Reconstruction
	1 Introduction
	2 Related Work
	3 Efficient Step Sizes for Convex Nonsmooth Optimization
		3.1 Convergence Analysis
		3.2 Numerical Experiments
	4 Conclusion and Future Work
	References
Learned Discretization Schemes for the Second-Order Total Generalized Variation
	1 Introduction
	2 Problem Setting
		2.1 Notation
		2.2 Finite Difference Operators
		2.3 Second-Order TGV Discretization
		2.4 Interpolation Operators
	3 -Convergence of the Discretization
	4 Numerical Methods
		4.1 Image Reconstruction
		4.2 Learning Interpolation Filters
		4.3 Filter Settings
	5 Numerical Results
		5.1 Data Sets
		5.2 Results
	6 Conclusion
	References
Fluctuation-Based Deconvolution in Fluorescence Microscopy Using Plug-and-Play Denoisers
	1 Introduction
	2 Plug-and-Play Approaches for Inverse Problems
	3 Deconvolution via Sparse Auto-Covariance Analysis
		3.1 Plug-and-Play Extension
	4 Numerical Results
		4.1 Simulated Data
		4.2 Real Data
	5 Conclusions
	References
Segmenting MR Images Through Texture Extraction and Multiplicative Components Optimization
	1 Introduction
	2 A CT Evolution Algorithm for MR Image Denoising and Bias Correction
		2.1 Implementation Details
	3 Results on Brain MRI Segmentation
	4 Conclusions
	References
Scale Space, PDEs, Flow, Motion and Registration
Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)
	1 Introduction
	2 Lifted Space of Positions and Orientations M2
	3 Existing Reeds-Shepp Car Models
	4 Illumination Enhancement
	5 TV-Flow Enhancement
	6 A Finsler Metric on M2 that Includes the Enhancements
	7 Experimental Results
	References
Geometric Adaptations of PDE-G-CNNs
	1 Introduction
	2 Preliminaries
	3 Analysis of Erosion and Dilation on SE(2)
	4 Left-Invariant Convection on a Lie Group
	5 No Need to Train the Lifting Layer in a PDE-G-CNN
	6 Nondiagonal Metric for Erosion and Dilation
	7 Conclusion
	References
The Variational Approach to the Flow of Sobolev-Diffeomorphisms Model
	1 Introduction
	2 The Flow of Diffeomorphisms Model
	3 The Weak Form of the Geodesic Equation
	4 A First Variational Time Discretization
	5 Relaxed Time Discretization
	6 Numerical Experiments
	7 Conclusions
	References
Image Comparison and Scaling via Nonlinear Elasticity
	1 Introduction
	2 Nonlinear Elasticity Model
		2.1 Comparing Images
		2.2 Properties of
		2.3 Existence of Minimizers
	3 Linear Scaling
	4 Discussion
	References
Learning Differential Invariants of Planar Curves
	1 Introduction
	2 Related Work
	3 Mathematical Framework
	4 Method
		4.1 Learning Differential Invariants
		4.2 Training Scheme
	5 Experiments and Results
		5.1 Datasets and Training
		5.2 Qualitative Evaluation
		5.3 Quantitative Evaluation
	6 Conclusions and Future Research
	References
Diffusion–Shock Inpainting
	1 Introduction
	2 Review of Coherence-Enhancing Shock Filtering
		2.1 PDE-Based Morphology
		2.2 Coherence-Enhancing Shock Filtering
	3 Diffusion–Shock Inpainting
	4 Numerical Algorithm
	5 Experiments
	6 Conclusions and Future Work
	References
Generalised Scale-Space Properties for Probabilistic Diffusion Models
	1 Introduction
	2 Probabilistic Diffusion
	3 Generalised Probabilistic Diffusion Scale-Space
		3.1 Generalised Scale-Space Properties
		3.2 PDE Formulation and Reverse Process
	4 Probabilistic Diffusion Models and Osmosis
		4.1 Continuous Osmosis Filtering
		4.2 Visual Comparison
		4.3 Common Structural Properties
		4.4 Differences
	5 Conclusions and Outlook
	References
Gromov–Wasserstein Transfer Operators
	1 Introduction
	2 Optimal Transport and Transfer Operators
	3 Transfer Operators from GW Transport Plans
	4 Numerical Examples
	5 Conclusions
	References
Optimal Transport Between GMM for Multiscale Texture Synthesis
	1 Introduction
	2 Reminders on Optimal Transport Between Gaussian Mixture Models
		2.1 Definition of MW2
		2.2 Using MW2 in Practice
	3 TextoGMM, a Multiscale Texture Synthesis Approach with Optimal Transport Between Patches
		3.1 Monoscale Model
		3.2 Multiscale Model
		3.3 Adaptation to Style Transfer and Texture Mixing
	4 Experiments
	5 Conclusion
	References
Asymptotic Result for a Decoupled Nonlinear Elasticity-Based Multiscale Registration Model
	1 Introduction
		1.1 Original Mathematical Model
		1.2 Towards a Decoupled Problem
	2 Main Result
	3 Conclusion
	References
Image Blending with Osmosis
	1 Introduction
		1.1 Our Contributions
		1.2 Related Work
		1.3 Organisation of the Paper
	2 Osmosis
		2.1 Continuous Model
		2.2 Theoretical Properties
		2.3 Incompatible Drift Vector Fields and Gradient Domain Methods
		2.4 Discrete Osmosis
	3 Blending with Osmosis
		3.1 Drift Vector Blending
		3.2 Seam Removal
		3.3 Alpha Blending with Osmosis
	4 Experiments
		4.1 Invariances of Osmosis Blending in Practice
		4.2 Comparing Variants of Osmosis Blending
		4.3 Plausibility Check: Low Brightness Differences
		4.4 High Brightness Differences
	5 Conclusions
	References
-Pixels for Hierarchical Analysis of Digital Objects
	1 Introduction
	2 Pixels and Discrete Object
	3 Reconstruction of Line
	4 Polygonalisation of -String
	5 Numerical Examples
	6 Conclusions
	References
Hypergraph p-Laplacians, Scale Spaces, and Information Flow in Networks
	1 Introduction
		1.1 Motivation
		1.2 Related Work
		1.3 Main Contributions
	2 Introduction of Oriented Hypergraphs
	3 Functions on Oriented Hypergraphs
	4 First-Order Differential Operators on Hypergraphs
	5 p-Laplacian Operators on Hypergraphs
	6 Scale Spaces Based on Hypergraph p-Laplacians
	7 Numerical Experiments
	8 Conclusion
	References
On Photometric Stereo in the Presence of a Refractive Interface
	1 Introduction
	2 Background
	3 Geometry of Refractive PS
	4 Image Formation Model Under Directional Lighting
	5 Solving Refractive PS
	6 Conclusion and Future Work
	References
Multi-view Normal Estimation – Application to Slanted Plane-Sweeping
	1 Introduction
	2 Related Work
	3 Slanted Plane-Sweeping
		3.1 Photo-Consistency-Based MVS
		3.2 Plane-Sweeping
		3.3 Surface Normal Estimation
	4 Experiments
		4.1 Implementation Details
		4.2 Synthetic Data
		4.3 Real Data
	5 Conclusion and Perspectives
	References
Partial Shape Similarity by Multi-metric Hamiltonian Spectra Matching
	1 Introduction
	2 Background
		2.1 The Laplace-Beltrami Operator
		2.2 The Hamiltonian Operator in Shape Analysis
	3 A Single Surface Treated as Two Manifolds
		3.1 Scale Invariance as a Measure of Choice
	4 Dual Spectra Alignment for Region Localization
	5 Experiments
		5.1 Datasets
		5.2 Competing Methods
		5.3 Results
		5.4 Ablation Study
	6 Future Research Directions
	References
Modeling Large-Scale Joint Distributions and Inference by Randomized Assignment
	1 Introduction
	2 (S-)Assignment Flows
		2.1 Definition
		2.2 Embedding
	3 Randomized Assignment Flow
	4 Approximation of Energy-Based Models
	5 Experiments
	6 Discussion and Conclusion
	References
Quantum State Assignment Flows
	1 Introduction
	2 Information Geometry
		2.1 Categorial Distributions
		2.2 Density Matrices
	3 Quantum State Assignment Flows
		3.1 Basic Relations
		3.2 Single-Vertex Quantum State Assignment Flow
		3.3 Quantum State Assignment Flow
		3.4 Riemannian Gradient Flow Parametrization
		3.5 Recovering the Assignment Flow for Categorial Distributions
	4 Experiments and Discussion
	5 Conclusion
	References
Author Index