Scale Space and Variational Methods in Computer Vision

Name: Scale Space and Variational Methods in Computer Vision | Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 -- June 2, 2011, Revised Selected Papers
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Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29 -- June 2, 2011, Revised Selected Papers

Alfred M. Bruckstein Bart M. ter Haar Romeny Alexander M. Bronstein Michael M. Bronstein(Editor)

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Published on 3. January 2012

XIV, 798 pages

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Content

Title Page
Preface
Organization
Table of Contents
Part I: Denoising and Enhancement (O1 and O5)
Fiber Enhancement in Diffusion-Weighted MRI
Introduction
Motivation for Morphological Scale Spaces on R3S2
A Moving Frame of Reference for Scale Spaces on R3S2
The Evolution Equations for Scale Spaces on DW-MRI
Solving the Evolutions by Convolution on R3 S2
Conclusion
References
Numerical Schemes for Linear and Non-linear Enhancement of DW-MRI
Introduction
The Euclidean Motion Group SE(3)
Left-Invariant Derivatives
Convection-Diffusion Processes
Finite Difference Schemes for R3 S2 Diffusion
Efficient Computation of Left-invariant Derivatives
Numerical Contour Enhancement
Perona-Malik Diffusion on R3 S2
Enhancement of DTI of the Human Brain
Conclusion
References
Optimising Spatial and Tonal Datafor Homogeneous Diffusion Inpainting
Introduction
Image Inpainting with Homogeneous Diffusion
Optimising Spatial Data
Probabilistic Sparsification
Nonlocal Pixel Exchange
Results
Optimising Tonal Data
Grey Value Optimisation
Results
Conclusion
References
Nonlocal Surface Fairing
Introduction
Nonlocal Means Image Denoising
The Nonlocal Variational Fairing
Non Local Surface Diffusion Flow (NL-SDF)
Numerical Results
Conclusions
References
Nonlocal Filters for Removing Multiplicative Noise
Introduction
Nonlocal Filters for Multiplicative Noise
The Similarity Measure of Deledalle et al.
Properties in the Presence of Additive Noise
Properties in the Presence of Multiplicative Noise
A New Similarity Measure for Multiplicative Noise
Weight Definition of Our Nonlocal Filters
Numerical Results
References
Volumetric Nonlinear Anisotropic Diffusion on GPUs
Introduction and Motivation
Contribution
Prerequisites
Inhomogeneous Diffusion
Nonlinear Anisotropic Diffusion
Surface Structure and the Hessian
Tangent Space Projection of the Hessian
Algorithm: Retrieving the Diffusion Tensor
Implementation
Discretization
Results
Conclusions
References
A Statistical Multiresolution Strategy for Image Reconstruction
Introduction
Statistical Multiresolution Estimation
Existence of SMRE
An a Priori Parameter Selection Method
On the Choice of S
Algorithmic Methodology
Inexact Uzawa Algorithm
Subproblems
Numerical Results
Denoising
Deconvolution and Inpainting
Conclusion
References
A Variational Approach for Exact Histogram Specification
Introduction
Variational Approach for Exact Histogram Specification
Sorting Algorithms
A Variational Approach
Experimental Results
Contrast Compression
Histogram Equalization Inversion
Conclusions
References
Joint ToF Image Denoising and Registration with a CT Surface in Radiation Therapy
Introduction
A Joint Registration and Denoising Approach
Numerical Minimization Algorithm
Validation and Application of the Model
Discussion and Conclusion
References
Either Fit to Data Entries or Locally to Prior: The Minimizers of Objectives with Nonsmooth Nonconvex Data Fidelity and Regularization
Introduction
Motivation
Notations
Outline of the Paper
Preliminaries
The Objective F Is Not Too Bad
(Local) Minimizers Are Strict
Either Fidelity or Prior
Strict Minimizers Solve Exactly Linear Systems
Local Stability of Strict Minimizers
A Special Case
Numerical Examples
Concluding Notes
References
A Study on Convex Optimization Approaches to Image Fusion
Introduction
Convex Optimization Models
Equivalent Convex Formulations
Variational Image Decompositions
Global and Exact Optimization
Duality Based Algorithms
Experiments
Fusing Binary Images
Applications to Medical Imaging and Remote Sensing
Conclusion and Acknowledgements
References
Efficient Beltrami Flow in Patch-Space
Introduction
The Beltrami Framework
Operating in Patch-Space
Implementation and Results
Parameter Optimization
Reducing Time Complexity
Residual Noise
Non-gaussian Denoising
Conclusions
Future Work
References
A Fast Augmented Lagrangian Method for Euler's Elastica Model
Introduction
Augmented Lagrangian Method for Euler's Elastica Model
The Existing Algorithm
The Proposed Algorithm
Numerical Solutions for Subproblems
Notations
Sub-problems
u-sub Problem.
p-sub Problem.
n-sub Problem.
h-sub Problem.
Numerical Examples
Conclusion and Future Work
References
Deblurring Space-Variant Blur by Adding Noisy Image
Introduction
Regularization
Translation Based Operator Space
Summary of the Trajectory Methods
Noise Contributors in Image Restoration
The Relative Immunity to Noise of the Auxiliary System
Numerical Examples
Summary and Conclusions
References
Fast Algorithms for p-elastica Energy with the Application to Image Inpainting and Curve Reconstruction
Introduction
Review of ALM for Euler's Elastica Model
Proposed Algorithms
Method 1
Method 2
Numerical Results
Image Inpainting
Curve Reconstruction
Conclusion
References
The Beltrami-Mumford-Shah Functional
Introduction
Inhomogeneous Diffusion
Isotropic Diffusion
Inhomogeneous Diffusion
TV and MAP
The Mumford-Shah Functional
The Ambrosio-Tortorelli Functional
The Beltrami Framework
The Beltrami-Mumford-Shah Functional
Results
Numerical Implementation
Results
Summary and Conclusions
References
An Adaptive Norm Algorithm for Image Restoration
Introduction
Description of the HQ-Algorithm for L1-TV Regularization
The Adaptive Norm Algorithm (ANA)
The Coherence Matrix Construction
Experiments and Results
Conclusions
References
Variational Image Denoising with Adaptive Constraint Sets
Introduction
Problem
Approach
A Quasi-Variational Inequality
Existence of Solutions
Algorithm
Adaptive Anisotropic TV Minimization for Image Denoising
Anisotropic TV with a Single Direction
Anisotropic TV with Double Directions
Anisotropic Spatio-temporal TV Minimization
Experiments
Anisotropic TV Minimization with Double Directions
Adaptive Motion-Based TV Minimization for Image Sequences
Conclusion
References
Simultaneous Denoising and Illumination Correction via Local Data-Fidelity and Nonlocal Regularization
Introduction
The Proposed Model
Some Model Assumptions
The Local Fidelity Term
Nonlocal TV
The Proposed Cost Functional
Algorithm: Augmented Lagrangian Method and EM
Numerical Experiments
Parameters and Initial Values Selection
Experimental Results
Conclusion
References
Anisotropic Non-Local Means with Spatially Adaptive Patch Shapes
Introduction
An Overview of the NLM
From Patches to Shapes: Beyond the Rare Patch Effect
Aggregation of Shape-Based Estimates
Classical Methods
Uniformly weighted aggregation (UWA).
Variance-based decision, Weighted Average (WAV).
SURE-Based Methods
Minimizer of the risk estimates (MRE).
Exponentially Weighted Aggregation (EWA).
Regularizing the Risk Maps with Anisotropic Diffusion
Numerical and Visual Results
Conclusion
References
Part II: Segmentation (O2)
Entropy-Scale Profiles for Texture Segmentation
Introduction
Methodology
Image Model
Image Decomposition
Entropy Profile
Texture Segmentation
Experimental Results
Conclusion
References
Non-local Active Contours
Introduction
Non-local Active Contours
Pairwise Patch Interaction
Pairwise Interaction Energy
Non-local Active Contour Energy
Experimental Results and Comparisons
Hybrid Region/Edge Based Active Contours
Gray-Level and Color Features
Gabor Features
Conclusion
References
From a Modified Ambrosio-Tortorelli to a Randomized Part Hierarchy Tree
Introduction
A Modified Energy and Its Minimizer
Randomized Hierarchy Tree
Experimental Results and Discussion
References
A Continuous Max-Flow Approach to Minimal Partitions with Label Cost Prior
Introduction
Previous Works
Convex Relaxation Approaches
Convex Relaxed MDL Approach
Continuous Max-Flow Approach
Continuous Max-Flow Formulation
Equivalent Primal-Dual Model
Equivalent Dual Model
Fast Continuous Max-Flow Algorithm
Numerical Experiments
Conclusions
References
Robust Edge Detection Using Mumford-Shah Model and Binary Level Set Method
Introduction
Formulation of the Model
Description of the Algorithm
Numerical Experiments
Concluding Remarks
References
Bifurcation of Segment Edge Curves in Scale Space
Introduction
Gaussian Scale Space
Segmentation Using Second-Order Derivatives
Scale Space Hierarchy
Segment Edge Curve Bifurcation
Conclusions
References
Efficient Minimization of the Non-local Potts Model
Efficient Minimization of the Non-Local Potts Model.
Introduction
Non-local Potts Model
Minimization
Applications
Multi-label Segmentation
Stereo
Conclusion
References
Sulci Detection in Photos of the Human Cortex Based on Learned Discriminative Dictionaries
Introduction
Learning Discriminative Dictionaries
Minimization Algorithm
Segmentation with Discriminative Dictionaries
Results
Conclusion
References
An Efficient and Effective Toolfor Image Segmentation, Total Variations and Regularization
Introduction
Relationship to Continuous Models
The Methodology
Experimental Results
Denoising by Modifying the Ratio between the Separation and Deviation Penalties
Increasing Deviation for a Selected Color
Comparison of Image Segmentation with Separation-deviation to the Normalized Cut Approach
Conclusions
References
Supervised Scale-Invariant Segmentation (and Detection)
Introduction
Work's Novelty and Related Methods
Remark and Outline
Scale Space Theory and Pixel-Based Segmentation
Scale Space and Gaussian Derivatives
Supervised Pixel Classification
Supervised Scale-Invariant Segmentation
Additional Remarks
Illustrative Experiments
Classifiers and Features
Shapes
Textures
Discussion and Conclusion
References
A Geodesic Voting Shape Prior to Constrain the Level Set Evolution for the Segmentation of Tubular Trees
Introduction
Background
Minimal Paths
Geodesic Voting for Segmentation of Tree Structures
Active Contours without Edges
From the Voting Tree to the Tubular Tree
Results and Discussion
Conclusion
References
Amoeba Active Contours
Introduction
Amoeba Active Contour Filtering
Space-Continuous Analysis
Experiments
Conclusion
References
A Hybrid Scheme for Contour Detectionand Completion Based on Topological Gradient and Fast Marching Algorithms -Application to Inpainting and Segmentation
Introduction
A 2D Algorithm Based on the Minimal Paths and Fast Marching Methods
Minimal Paths
Multiple Minimal Paths
Main Algorithm
Numerical Experiments
Numerical Results for 2D Segmentation
Numerical Results for a New Way of 2D Inpainting
Conclusions and Perspectives
References
A Segmentation Quality Measure Based on Rich Descriptors and Classification Methods
Introduction
Segment Score
Feature Generation
Feature Generation Using a Discriminative Online Classifier.
Junctions-based features.
Directly Estimated Segment Score
Enhanced, Indirect Estimation of the Segment Score
Segment Search
Selecting a Base Hypothesis
Generating New Hypotheses
Experiments
Data and Implementation Details
Score Validity
Segmentation Results
Discussion
References
Framelet-Based Algorithm for Segmentation of Tubular Structures
Introduction
Framelet-Based Algorithm
Framelet-Based Algorithm for Segmentation
Initializing and Refining the Range
Numerical Examples
Conclusions and Future Work
References
Weakly Convex Coupling Continuous Cuts and Shape Priors
Introduction
Overview, Related Work
Contribution, Organization
Variational Models
Segmentation by Continuous Cuts
MRF Based Shape Priors
Variational Shape Priors
Ising Shape Prior
Hierarchical Part Based Shape Prior
Coupling Convex Models
Variational Approach
Shape Constrained Cuts
Experiments and Discussion
Setup
Results
Conclusions and Further Work
References
Part III: Image Representation and Invariants (O3)
Wasserstein Barycenter and Its Application to Texture Mixing
Introduction
Previous Work on Texture Synthesis and Mixing
Contributions
Wasserstein Distance and Its Approximation
Wasserstein Distance
Sliced Wasserstein Distance
Barycenter in Wasserstein Space
Wasserstein Barycenter
Gradient Descent Algorithm
Computing the Projection on a Distribution
Texture Synthesis and Mixing
Multiscale Oriented Decompositions
First Order Statistical Mixing
Higher Order Statistical Mixing
Conclusion
References
Theoretical Foundations of Gaussian Convolution by Extended Box Filtering
Introduction
Conventional Box Filtering
Extended Box Filter
Experiments
Qualitative Gain
Runtime
Summary
References
From High Definition Image to Low Space Optimization
Introduction
Coresets for Dictionaries
k-Dictionary Queries
Coreset for a Single k-Dictionary Query
Coreset for all k-Dictionary Queries
Example Application: Approximating the Optimal Dictionary
The k-Dictionary Problem
Coreset for the k-Dictionary Problem
Experimental Results
Synthetic Data
Coresets for High-Definition Images
Conclusions and Further Work
References
Measuring Ge odesic Distancesvia the Uniformization Theorem
Introduction
Introduction to Conformal Mapping
Construction of a Discrete Harmonic Map
Fast Marching on the Conformal Map
Controlling the Conformal Factor
Bounding the Conformal Factor
Conclusions
References
Polyakov Action on (?,G)-Equivariant Functions Application to Color Image Regularization
Introduction
Color Images as (,G)-Equivariant Functions on Principal Bundles
The General Construction
Interpretation of the (,G)-Equivariance for Color Images
The Group (I-R+,).
The Group DC(3).
The Group SO(3).
Minimization of the Polyakov Action Related to the Graph of (,G)-Equivariant Functions: A Case Study
The Case (,G) Is the Natural Representation of (I-R+,) on I-R3
Riemannian Geometry of (I-R+,).
The Induced Metric h.
Minimization with Respect to the Embedding .
The Case (,G) Is the Trivial Representation of (I-R+,) on I-R3
The Induced Metric h.
Minimization with Respect to the Embedding .
The Case (,G) Is the Natural Representation of DC(3) on I-R3
Riemannian Geometry of DC(3).
The Induced Metric h.
Minimization with Respect to the Embedding .
The Case (,G) Is the Natural Representation of SO(3) on I-R3
Riemannian Geometry of SO(3).
The Induced Metric h.
Minimization with Respect to the Embedding .
Experiments
Conclusion
References
Curvature Minimization for Surface Reconstruction with Features
Introduction
An Overview of the Proposed Method
Global Minimization for Surface Reconstruction via Graph Cuts
Feature Sensitive Local Minimization
Numerical Experiments
Acknowledgement.
References
Should We Search for a Global Minimizerof Least Squares Regularized with an $\ell$0 Penalty to Get the Exact Solution of an under Determined Linear System?
Introduction
Notations and Definitions
Content of the Paper
Local Minimizers
Minimizers of Fd Solve Linear Programming Problems
Strict Minimizers
Necessary and Sufficient Conditions
Stability of Strict (local) Minimizers
Global Minimizers
Exact Recovery
Originals with an M-Length Support
An Assumption on A That Holds for a.e. A
Necessary and Sufficient Conditions
Numerical Toy-Example
Concluding Remarks
References
Weak Statistical Constraints for Variational Stereo Imaging of Oceanic Waves
Introduction
The Variational Framework
Multi-Image Setup and Graph Surface Representation
Proposed Energy Functional
Energy Minimization. Optimality Condition
Numerical Solution.
Weak Enforcement of Wave Height Distributions
Applications
Conclusion
References
Novel Schemes for Hyperbolic PDEs Using Osmosis Filters from Visual Computing
Introduction
Diffusion Filters and Osmosis
Osmosis Schemes for HDEs
Numerical Experiments
Conclusion
References
Fast PDE-Based Image Analysis in Your Pocket
Introduction
Models and Solvers
Diffusion Filtering
Variational Optic Flow
Implementation on an Android Phone
Android Basics
Image Processing with Android
Retrieval of Camera Data.
YUV Conversion.
Software Design
Optimisations
Experiments
Our Interactive Camera Applications
Performance Analysis
Linear Diffusion.
Nonlinear Isotropic Diffusion.
Conclusions and Outlook
References
A Sampling Theorem for a 2D Surface
Introduction
Geometric Recovery of Surface Coordinates
Geometrical Representation
Mathematical Model
Sampling Rate Determination
Experimental Results
Conclusion and Future Works
References
Quadrature Nodes Meet Stippling Dots
Introduction
Quadrature Errors in RKHSs
Discrepancies
Least Squares Functionals for Bandlimited Functions
Efficient Minimization Algorithm on S2
Numerical Results on S2
Conclusions
References
Part IV: Shape Analysis (O4)
Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching
Introduction
Problem Formulation
Invariance
Choice of the Metric
Choice of the Descriptor
Correspondence as a Graph Labeling Problem
Hierarchical Matching
Probabilistic Matching and Shape Prototypes
Results
Conclusions
References
A Correspondence-Less Approach to Matching of Deformable Shapes
Introduction
Background
Partial Matching
Discretization and Numerical Aspects
Results
Conclusions
References
Hierarchical Matching of Non-rigid Shapes
Introduction
Non-Rigid Correspondence in a Brief
Problem Formulation
Mathematical Background
Choice of Metric
Choice of Descriptors
Integer Quadratic Programming
Hierarchical Formulation
Results
Conclusions
References
Photometric Heat Kernel Signatures
Introduction
Background
Photometric Heat Kernel Signatures
Numerical Implementation
Results
Conclusions
References
Human Activity Modeling as Brownian Motion on Shape Manifold
Introduction
Background
A Infinite Dimensional Shape Manifold
Connection on Manifold
Dynamics of Human Activity on a Shape Manifold
Flat Connection on a Shape Manifold
Stochastic Analysis in a Euclidean Space
Human Activity as a Brownian Motion on Manifold
Human Activity as a Piecewise Brownian Motion on Manifold
Conclusion
References
3D Curve Evolution Algorithm with Tangential Redistribution for a Fully Automatic Findingof an Ideal Camera Path in Virtual Colonoscopy
Introduction
The Colon Segmentation and the Initial Trajectory Guess
Finding the Optimal Camera Trajectory
References
Distance Images and Intermediate-Level Vision
Introduction
Global Distance Information Signaled Locally
Mathematical Formulation
Edge Producing Model
Density Scale Space
Diffusion Map Embedding
Summary and a Psychophysical View
Acknowledgments.
References
Shape Palindromes: Analysis of Intrinsic Symmetries in 2D Articulated Shapes
Introduction
Model
Symmetry Analysis
Extrinsic Symmetry Characterization
Intrinsic Symmetry Characterization
Numerical Implementation
Fourier Analysis
Dynamic Programming
Computational Complexity
Results
Conclusions
References
Kernel Bundle EPDiff: Evolution Equations for Multi-scale Diffeomorphic Image Registratio n
Introduction
Content and Outline
The LDDMM Framework
Kernel, Momentum and LDDKBM
Kernel and Momentum
The Kernel Bundle and LDDKBM
EPDiff and KB-EPDiff
Euler-Lagrange Equations
Scale Conservation and KB-EPDiff
KB-EPDiff for Landmarks: An Example
Experiments
Hand Outlines
KB-EPDiff across Scales
Conclusion
References
Deformable Shape Retrieval by Learning Diffusion Kernels
Introduction
Background
Diffusion Geometry
Heat Diffusion
Diffusion Distances
Invariance
Distance Distributions
Optimal Diffusion Kernels
Discretization
Interpolation Operators
Results
Conclusions
References
Part V: Optical Flow (O6)
Stochastic Models for Local Optical Flow Estimation
Introduction
Stochastic Luminance Function and Conservation Constraints
Notations - Conventions
Stochastic Luminance Function
Isotropic Uncertainties.
Anisotropic Uncertainties.
Uncertainty Models for Luminance Conservation
Uncertainty Estimation
Estimation of
Estimation of
Application of the Proposed Luminance Models
Experimental Results
Conclusion
Expectation of a Function of a Stochastic Process
References
Optic Flow Scale Space
Introduction
Variational Optic Flow as Whittaker-Tikhonov Regularisation
Towards Regularisation in a Spatially Varying Norm
Analysing the Matrix-Weighted Norm
Generalisation of the Matrix-Weighted Norm
Optic Flow Scale Space
Numerical Realisation
Scale Selection
Experiments
Conclusion
References
Group-Valued Regularization Framework for Motion Segmentation of Dynamic Non-rigid Shapes
Introduction
Problem Formulation
Diffusion-Based Regularization
Numerical Considerations
Initial Correspondence Estimation
Diffusion of Lie Group Elements
A Patch-Based Data Term
Visualizing Lie Group Clustering on Surfaces
Results
Conclusion
References
Wavelet-Based Fluid Motion Estimation
Introduction
Optical Flow Background
Non-linear Data Model
Classical Multi-resolution Strategy
The Aperture Problem and Usual Regularization Schemes
Wavelet Formulation
Wavelet Decomposition
Wavelet Data Term
Multiscale Estimation
Regularizations
Wavelet Properties
Polynomial Approximation on a Truncated Basis
High-Order Regularization
Results
Synthetic PIV Sequence
Real PIV Sequence
Conclusion
References
Multiscale Weighted Ensemble Kalman Filter for Fluid Flow Estimation
Introduction
Stochastic Lucas-Kanade Estimator
Luminance Variation with Uncertainties
Data Model with Uncertainties and Local Estimation
Multiresolution Analysis and Uncertainty Estimation
Monte Carlo Implementation of Stochastic Filtering with the Weighted-Ensemble Kalman Filter
Stochastic Filtering, Filtering Distribution
Linear Gaussian Models and the Kalman Filter
Particle Implementation of the Nonlinear Filtering
Ensemble Kalman Filtering
Weighted EnKF
WEnKF Assimilation of SLK Observations
Multiscale SLK-WEnKF Filtering
Experimental Results and Comparisons
Conclusion
References
Over-Parameterized Optical Flow Using a Stereoscopic Constraint
Introduction
Background
The Variational Framework
Epipolar Geometry
Estimation of the Fundamental Matrix
A Flow Model Based on Local Homographies
Euler-Lagrange Equations
Minimization with respect to ai.
Minimization with respect to vAT.
Implementation
Experimental Results
Conclusions
References
Robust Optic-Flow Estimation with Bayesian Inference of Model and Hyper-parameters
Introduction
Short Overview of Optic-Flow Estimation
Data and Prior Models
Standard Optic-Flow Estimation
A Bayesian Framework for Model and Hyper-parameter Selection
Bayesian Formulation of the Optic-Flow Estimation Problem
Bayesian Inference for Robust Optic-Flow Estimation
Experiments
Fluid Motion Image Sequence
Computer Vision Scenes
Conclusion
References
Regularization of Positive Definite Matrix Fields Based on Multiplicative Calculus
Introduction
Theory
Multiplicative Differentiation
Multiplicative Integration
Linear Functions and Linear Mappings
Taylor Expansions
Critical Points
Differential Equations
The Non-commutative Case
Multiscale Representation of Positive Definite Matrix Fields
Conclusion and Discussion
References
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Scale Space and Variational Methods in Computer Vision

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