دانلود کتاب Scale Space Methods in Computer Vision: 4th International Conference, Scale-Space 2003, Isle of Skye, UK, June 10-12, 2003, Proceedings (Lecture Notes in Computer Science, 2695)

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Scale Space Methods in Computer Vision
Preface
Organization
Table of Contents
On Manifolds in Gaussian Scale Space
1 Introduction
2 The Deep Structure of Gaussian Scale Space
2.1 Gaussian Scale Space
2.2 Critical Points in Scale Space
2.3 Iso-intensity Manifolds
2.4 Scale Space Hierarchy
3 Classification of Manifolds
3.1 Zero Scale Space Saddles
3.2 One Scale Space Saddle
3.3 Two Scale Space Saddles
3.4 More Scale Space Saddles
4 Examples and Applications
4.1 Artificial Image
4.2 Zero Scale Space Saddles
4.3 Multiple Scale Space Saddles
4.4 MR Image
5 Conclusion and Discussion
References
Many-to-Many Matching of Scale-Space Feature Hierarchies Using Metric Embedding
1 Introduction
2 Related Work
3 Metric Embedding of Graphs
3.1 Low-Distortion Embedding
3.2 Tree Metric of a Distance Function
3.3 Path Partition of a Graph
3.4 Construction of the Embedding
4 Encoding Scale-Space Features
5 Distribution-Based Many-to-Many Matching
5.1 Embedding Point Distributions in the Same Normed Space
5.2 The Earth Mover\'s Distance
5.3 Choosing an Appropriate Transformation
5.4 The Final Algorithm
6 Experiments
7 Conclusions and Future Work
References
Content Based Image Retrieval Using Multiscale Top Points
1 Introduction
2 Image Representation Using Multiscale Top Points
2.1 Introduction
2.2 Critical Points, Critical Paths and Top Points
2.3 Minimal Variance Reconstructions from Multi Scale Points
3 Content Based Image Retrieval Using Multiscale Top Points
3.1 Introduction
3.2 Proportional Transportation Distance (PTD)
4 Experimental Results
4.1 Experiment 1
4.2 Experiment 2
4.3 Experiment 3
5 Conclusions and Discussion
References
Feature Coding with a Statistically Independent Cortical Representation
1 Introduction
2 Methods
2.1 Model of the Response of V1 Neurons
2.1.1 Linear Stage
2.1.2 Nonlinear Stage
2 Results
3 Conclusions
References
Scale-Space Image Analysis Based on Hermite Polynomials Theory
1 Introduction
1.1 Orthogonal Polynomials for Signal and Image Processing
1.2 Hermite Transform and Related Scale-Space Differential Structure
2 Basic Properties of Hermite Transform
2.1 Dimensional Separability and Its Computational Advantages
2.2 Dealing with Rotation in 2D
2.3 Mehler Formula and Its Applications to Scale-Space
2.4 New Hermite-Domain 1D Windowed Cross-Correlation
3 Dealing with any Number of Image Dimensions
3.1 Reducing and Extending the Number of Transform Dimensions
3.2 Generic Referential Change Readily Handled in Hermite Transform Domain Using our Results
3.3 Extending our $l_2$ Norm and Correlation Resultshfill penalty -@M to Several Dimensions
4 Numerical Simulations
5 Summary and Conclusions
References
A Complete System of Measurement Invariants for Abelian Lie Transformation Groups
1 Introduction
2 Steerability and Equivariance
2.1 Lie Transformation Groups and Generators
2.2 Action on Measurements
3 Conjugate Generators
3.1 Deriving Conjugate Generators
3.2 Deriving Standard Bases
4 Measurements Invariants
4.1 Block Invariants
4.2 Cross Invariants
4.3 A Complete System of Invariants
5 Results
6 Conclusions
References
Equivalence Results for TV Diffusion and TV Regularisation
1 Introduction
2 Continuous TV Diffusion and TV Regularisation
2.1 TV Diffusion
2.2 TV Regularisation
3 Analytical Solution for Space-Discrete TV Diffusion
4 Analytical Solution for Discrete TV Regularisation
5 Conclusions
References
Correspondences between Wavelet Shrinkage and Nonlinear Diffusion*
1 Introduction
2 Nonlinear Diffusion
2.1 Basic Concept
2.2 Explicit Discretisation Scheme
3 Wavelet Shrinkage
3.1 Basic Concept
3.2 Discrete Translation-Invariant Scheme
4 Correspondence of Diffusivities and Shrinkage Functions
4.1 Basic Considerations
4.2 From Diffusivities to Shrinkage Functions
4.3 From Shrinkage Functions to Diffusivities
5 Denoising Experiment
6 Conclusions
References
Approximating Non-linear Diffusion
1 Introduction
2 Approximating Non-linear Diffusion
2.1 The Diffusion Echo
2.2 Maximum Entropy Approximation Filters
2.3 Illustrating Diffusion Approximations
3 Information Theoretical Evaluation
4 Application Evaluation
4.1 Multi-scale Watershed Segmentation
4.2 Non-linear Diffusion in MSWS
4.3 Approximating Non-linear Diffusion in MSWS
4.4 Multi-scale Scale Selection
5 Conclusion
References
A Generalized Discrete Scale-Space Formulation for 2-D and 3-D Signals
1 Introduction
2 Analysis of the Sampled Gaussian Kernel
3 DSS Formulation
3.1 Preliminaries
3.2 2-D DSS Formulation
3.3 3-D DSS Formulation
4 Properties of the DSS Kernels
4.1 Smoothing Kernel
4.2 Differencing Kernel
5 Validation of the DSS Kernels
5.1 Accuracy of Approximation
5.2 Fulfillment of the Non-enhancement Requirement
5.3 Accuracy of Edge Extraction
6 Conclusion
References
Real-Time Scale Selection in Hybrid Multi-scale Representations
1 Introduction
2 Related Work
3 Hybrid Pyramid Representation
3.1 Reduction Operators
3.2 Equivalent Convolution and Derivative Approximation Kernels
3.3 Measuring the Scale Parameter and the Subsampling Rate
4 Scale Selection in Hybrid Multi-scale Representation
4.1 Defining Normalized Derivatives with Spatial Subsampling
4.2 Detecting Scale-Space Maxima
4.3 Post-processing the Scale-Space Maxima from a Hybrid Pyramid
5 Trade-off: Computational Efficiency vs. Accuracy
6 Stability of the Scale Descriptors
7 Summary and Discussion
References
A Scale Space for Contour Registration Using Minimal Surfaces
1 Introduction
1.1 Proposed Work
1.2 Past Work in Registration
2 Method
2.1 Initialization
2.2 Evolution to Minimal Surface
2.3 Gradient Evolution for Rigid Registration
2.4 Motivation
3 Scale Space
3.1 Scale Space Parameter
3.2 Extreme Cases
3.3 Local Minima Decreasing
4 Implementation
4.1 Level Set Representation of Surface
4.2 Freezing of Top and Bottom Contours
4.3 PDE Implementation
5 Conclusion
6 Appendix
6.1 Existence of Catenoid
6.2 Existence of Minimal Surface for Arbitrary Closed Contours
References
The Extrema Edges
1 Introduction
2 Minimal Paths and Energy Partitions
3 The Path Variation
3.1 Definition
3.2 Path Variation and Image Distance
4 The Extrema Edges
4.1 The Extrema Partition
4.2 Definition of the Extrema Edges
4.3 Extrema Edges and Watersheds
5 Valuation of the Extrema Edges
6 Conclusion and Perspectives
References
The Maximum Principle for Beltrami Color Flow
1 Introduction
2 The Beltrami Framework
2.1 Polyakov Action: A Measure on the Space of Embedding Maps
3 Extremum Principle for Functional Solutions
4 Extremum Principle for Distributional Solutions
5 The Discrete Maximum Principle and Stability
6 Details of the Implementation and Results
7 Concluding Remarks
References
The Monogenic Scale Space on a Bounded Domain and Its Applications
1 Introduction
1.1 Scale Spaces beyond the Gaussian Case
1.2 Why Using a Vector Valued Scale Space?
2 The Monogenic Scale Space
2.1 Extending the Poisson Scale Space
2.2 The Features of the Monogenic Scale Space
3 Implementation on a Bounded Domain
3.1 Eigenfunction Implementation for the Poisson Scale Space
3.2 Eigenfunction Implementation for the Monogenic Scale Space
4 Examples and Applications
4.1 Visualization and Reconstruction from Local Features
4.2 Phase Congruency in Scale Space
5 Conclusion
References
Using the Complex Ginzburg–Landau Equation for Digital Inpainting in 2D and 3D
1 Introduction
2 The Ginzburg--Landau Equation
2.1 Motivation
2.2 Physical Foundations of the Ginzburg--Landau Equation
2.3 Algorithm
2.4 Three Dimensional Inpainting
3 Results and Conclusion
References
Least Squares and Robust Estimation of Local Image Structure
1 Introduction
2 Least Squares Estimation of Local Image Structure
3 Robust Estimation of Local Image Structure
3.1 Zero-Order Image Structure
3.2 Higher-Order Image Structure
3.3 Color Image Structure
4 Robust Estimation of Orientation
5 Conclusion
References
Regularity Classes for Locally Orderless Images
1 Introduction
2 Theory
2.1 Ansatz
2.2 Raw Image Scale
2.3 Distortions Induced by Spatial Deformations
3 Conclusion
A Hermite Polynomials and Parabolic Cylinder Functions
References
Mode Estimation Using Pessimistic Scale Space Tracking
1 Introduction
1.1 Previous Methods for Mode Estimation
2 Mode Estimation Using the Fréchet Definition
3 Mode Estimation Using Scale Space Tracking (SST)
4 Mode Estimation Using Pessimistic Scale Space Tracking (PSST)
5 Results on Handwriting Data
6 Results on Image Profiles
7 Conclusions
References
Properties of Brownian Image Models in Scale-Space
1 Introduction
2 The Gaussian Model
3 The Brownian Model
4 Covariance Structure of Natural Images in Jet Space
5 Summary and Conclusion
A Analytical Expression for Jet Covariance Matrix
References
Image Decomposition Application to SAR Images
1 Introduction
1.1 Preliminaries
1.2 Related Works
2 Our Approach
2.1 Presentation
2.2 Discretization
2.3 Total Variation Minimization as a Project
2.4 Application to Problem (20)
2.5 Algorithm
3 Mathematical Results
3.1 Existence and Uniqueness of a Solution for (20)
3.2 Convergence of the Algorithm
3.3 Link with Meyer\'s Model
3.4 Role of $\\lambda$
4 SAR Images Restoration
4.1 Introduction
4.2 Results on Sythetic Images
4.3 Results on Real Images
5 Conclusion
References
Basic Morphological Operations, Band-Limited Images and Sampling
1 Introduction
1.1 Band-Limited Signals and Uniform Sampling
1.2 Sampling Morphological Operations
2 Sampling-Free Dilations
2.1 Representing a 1D Signal as a Piece-Wise Polynomial
2.2 Converting the Sequence of Sampleshfill penalty -@M into a Piece-Wise Polynomial
2.3 Dilations
2.4 Implementation
2.5 Erosions, Closings and Openings
3 Results
3.1 A First Examination of the Algorithm
3.2 Granulometry
4 Extension to Multi-dimensional Images
5 Conclusion
References
An Explanation for the Logarithmic Connection between Linear and Morphological Systems
1 Introduction
2 The (max,+)- and the (min,+)-Algebra
3 Convolution Induced by an Algebra
4 Elements of Convex Analysis
5 A Link between Laplace Transform and Conjugation
6 The Cramer Transform
7 Conclusions
References
Temporal Scale Spaces
1 Introduction
2 Temporal Measurement
2.1 Linearity
2.2 Causality
2.3 Covariance
2.4 Cascade Property
2.5 Extended Point
3 Characterization of Causal Scale Space Kernels
4 Stable Density Functions
4.1 Scaling Properties
5 Recursive Formulation
5.1 Fractional Derivatives
5.2 Infinitesimal Generator
5.3 Evolution Equation
6 Discretization of Causal Scale Spaces
6.1 Discrete Second Derivative on Log Spaced Grid
7 Numerical Scheme for the Signaling Equation
8 Discussion
References
Temporal Structure Tree in Digital Linear Scale Space
1 Introduction
2 Stationary-Curves and Tree in Linear Scale Space
2.1 Linear Scale Space Analysis
2.2 Structure Tree and View-Field
3 Digital Scale-Space Analysis
3.1 Digital Linear Scale Space
3.2 Stationary Points on Digital Topographical Maps
3.3 Digital Stationary-Curves
3.4 Combinatorial Property of Structure Tree
4 Temporal Structure Tree
5 Scale Space Analysis for 3D Objects
6 Conclusions
References
Appendix: Discritization of Convolution
Interest Point Detection and Scale Selection in Space-Time*
1 Introduction
2 Interest Point Detection
2.1 Interest Points in Spatial Domain
2.2 Interest Points in the Spatio-Temporal Domain
2.3 Experimental Results on Synthetic Data
3 Scale Selection in Space-Time
4 Scale-Adapted Space-Time Interest Points
5 Experiments
6 Summary and Discussion
References
Towards Recognition-Based Variational Segmentation Using Shape Priors and Dynamic Labeling
1 Introduction
2 Region-Based Segmentation with Level Sets
2.1 A Level Set Framework for the Mumford-Shah Functional
2.2 Redistancing
2.3 Numerical Results
3 Global Shape Prior in the Level Set Segmentation
4 Selective Shape Prior by Static Labeling
5 Selective Shape Prior by Dynamic Labeling
6 Evolution of Labeling Function and Level Set Function
7 Limitations and Future Work
8 Conclusion
References
PDE Based Shape from Specularities
1 Introduction
1.1 Previous Work
1.2 Contribution of Paper
2 Background
2.1 Camera Model
2.2 Structure and Motion Estimation
2.3 Level Set Methods
2.4 Specular Reflection
3 Surface Constraints from Specularites
3.1 Specular Constrains
3.2 Regularization
3.3 Induced Objective Function
4 Level Set Implementation
4.1 Force Field Method
4.2 Normal Constraints
4.3 Point Constraints
4.4 Range Adaptation
5 Experiments
6 Summary and Conclusions
References
A Markov Random Field Approach to Multi-scale Shape Analysis
1 Introduction
2 Multi-scale Shape Representation by M-reps
3 Probabilistic M-reps Models
3.1 Markov Random Fields
3.2 Markov Random Field M-reps Models
4 MRF Models for Boundary Displacement
4.1 Model Description
4.2 Parameter Estimation
5 Markov Random Field Models for Object Sections
5.1 The MRF Model
5.2 Discussion
6 Residue Statistics of Hippocampi
7 Conclusions
References
Variational Dense Motion Estimation Using the Helmholtz Decomposition
1 Introduction
2 Description of the Approach
2.1 Helmholtz Decomposition and BCCE
2.2 Structure-Preserving Regularization
2.3 Extensions to Multiple Resolutions
2.4 Minimization and Discretization
3 Experimental Results
3.1 Parameter Studies
3.2 Comparison with the Approaches of Corpetti et al. and Horn and Schunck
3.3 Reconstructing the Vortexes of a Landing Air Plane
4 Conclusion
References
Regularizing a Set of Unstructured 3D Points from a Sequence of Stereo Images
1 Introduction
2 Notation
3 The 3D Regularizing Model
4 Finite Elements Method
4.1 Solving the System
4.2 Numerical Scheme
5 Experimental Results
5.1 Single Stereo Pair
5.2 Stereo Sequence
6 Conclusions
References
Image Reconstruction from Multiscale Critical Points
1 Introduction
2 Minimal Variance Reconstruction
2.1 Definitions
2.2 Theory
2.3 Mixed Correlation Matrix
3 Experimental Results
3.1 Random Points
3.2 Critical Points
4 Influence of Limited Calculation Precision on Reconstructions
5 Conclusions and Discussion
References
Texture Classification through Multiscale Orientation Histogram Analysis
1 Introduction
2 Edge Orientation Estimation
3 Orientation-Based Texture Classification
4 Texture Classification through Multiscale Analysis
4.1 Gaussian Multiscale Analysis
4.2 Scale Estimation
4.3 Multiscale Texture Orientation Histogram Comparison
5 Robustness of Texture Classification under Darkening, Lightening and Inversion
6 Conclusion
References
α Scale Spaces on a Bounded Domain
1 Introduction
2 $\\alpha$ Scale Spaces on the Unbounded Domain
2.1 Poisson Scale Space on the Unbounded Domain
2.2 Clifford Analytic Extension of the Poisson Scale Space on the Unbounded Domain
3 $\\alpha$ Scale Spaces on the Bounded Domain with Neumann Boundary Conditions
3.1 The Rectangle Case
3.2 The Disc Case
4 Truncation of the Fourier Series Expansions
5 Conclusion
References
Efficient Beltrami Flow Using a Short Time Kernel
1 Introduction
2 The Beltrami Flow
3 A Short Time Kernel for the Beltrami Flow
4 Solving the Eikonal Equation on Image Manifolds
5 Simulations and Results
6 Conclusions
References
Evolution of the Critical Points in the Curvature and Affine Morphological Scale Spaces
1 Introduction
2 Preliminaries and Notation
3 The Behaviour of the CSS Near Critical Points
3.1 Circularization of an Extremum by the CSS
3.2 Formation of a Plateau Near a Saddle Point
3.3 Numerical Method for Implementing CSS
4 Elliptization of an Extremum by the AMSS
4.1 Some Important Estimates
4.2 Elliptization of the Extrema
5 Conclusion and Future Work
References
Appendix: Proof of some Estimates of Section 5
MAPS: Multiscale Attention-Based PreSegmentation of Color Images
1 Introduction
2 Visual Attention Model
2.1 Feature Maps
2.2 Conspicuity Maps
2.3 Saliency Map
2.4 Selection of Salient Locations
3 Multiscale Attention-Based PreSegmentation (MAPS)
3.1 Segmentation-Relevant Scene Data
3.2 Presegmentation of the Multiscale Map $M_{j^*,k^*}$
4 Refined Segmentation
4.1 The Method
4.2 Segmentation Examples
5 Conclusion
References
Convex Colour Sieves
1 Background
2 Colour Sieves
3 Colour Sieve Algorithm
4 Discussion
References
Scale-Space on Image Profiles about an Object Boundary
1 Introduction
2 Related Work
2.1 Geometry-Driven Diffusion
2.2 Profile Model
2.3 Active Appearance Models
3 Method: Profile Scale-Space Model
3.1 Toy Example
3.2 Scale-Space in Object-Intrinsic Coordinates
3.3 Local Statistical Model
4 Application to the Corpus Callosum
5 Discussion / Conclusion
5.1 Application to Analysis and Discrimination
5.2 Application to Segmentation
5.3 Extension to 3D/nD Images
5.4 Conclusion
References
Iris Feature Extraction and Matching Based on Multiscale and Directional Image Representation
1 Introduction
2 Directional Filter Bank (DFB)
3 Feature Extraction
3.1 Iris Localization
3.2 Generation of Feature Vector
4 Matching
5 Experimental Results
6 Conclusion
References
Fast Computation of Scale Normalised Gaussian Receptive Fields
1 Introduction
2 Fast Computation of Chromatic Receptive Fields
3 A Scale Invariant Half Octave Pyramid
3.1 The O(N) Scale-Invariant Pyramid
4 Experimental Comparison of Fast Gaussian Filters
4.1 Fast Gaussian Filters
4.1.1 The FIR Implementation of a Gaussian
4.2 Binomial Filters
4.2.1 Recursive Filters
4.3 Laplacian as a Difference of Gaussians
5 Comparison of Scale Invariance
6 Determining Intrinsic Scale
6.1 Computing Characteristic Scale
6.2 Estimating Size from Intrinsic Scale
7 Invariance to Rotation
8 Synthesis of Normalized Receptive Fields
9 Summary and Conclusion
References
A Multiphase Level Set Framework for Motion Segmentation
1 Introduction
2 Motion Estimation as Bayesian Inference
3 A Variational Framework for Motion Segmentation
4 A Multiphase Level Set Implementation
4.1 The Two Phase Model
4.2 The General Multiphase Model
4.3 Redistancing
5 Ground Truth Experiments
5.1 Segmenting Multiply Connected Moving Objects
5.2 Segmenting Several Differently Moving Regions
5.3 Multiple Moving Objects and Moving Background
6 Real-World Application: Segmentation of Moving Cars
7 Conclusion
References
Segmentation of Coarse and Fine Scale Features Using Multi-scale Diffusion and Mumford-Shah
1 Introduction
2 The Mumford Shah Model
3 Multi-scale Diffusion with Mumford-Shah
4 Topology Preservation with Mumford Shah
5 Conclusion
References
On the Number of Modes of a Gaussian Mixture
1 Introduction
2 The Conjecture
3 Approaches to Proving the Conjecture
3.1 System of Equations for the Stationary Points of the Density
3.2 Scale-Space Theory
3.3 Kernel Density Estimation in 1D
4 Algorithms for Finding All the Modes
4.1 The Fixed-Point Iteration Algorithm as an EM Algorithm
4.2 Particular Cases
4.3 Brute-Force Search for Counterexamples
5 Applications
5.1 Multivalued Regression and Data Reconstruction
5.2 Clustering
6 Conclusion
References
Fully Automatic Segmentation of MRI Brain Images Using Probabilistic Anisotropic Diffusion and Multi-scale Watersheds
1 Introduction
2 Approaches to Brain Segmentation
3 Proposed Method
3.1 Intensity Normalization
3.2 Spatial Normalization by Affine Warping
3.3 Capturing the Intensity Distributions of Different Tissues
3.4 Multi-scale Watershed Segmentation
3.5 Probabilistic Diffusion Using Prior Knowledge
3.6 Combining Probabilistic Diffusion with Watershed Segmentation
3.7 Post-processing
4 Experimental Results
4.1 Qualitative Evaluation
4.2 Quantitative Performance Measures
5 Summary and Discussion
References
Error-Bounds on Curvature Estimation
1 Introduction
2 Analytic Derivation of a Simple Case
3 Using $N$ Edgels
4 Numeric Examples
5 Discussion
6 Conclusion
References
Multiresolution Approach to Biomedical Image Segmentation with Statistical Models of Appearance
1 Introduction
2 Related Work
3 Image Segmentation with Statistical Models of Appearance
3.1 Statistical Model -- General Description
3.2 Training the Statistical Model
3.3 Image Segmentation with the Statistical Model
4 Multiresolution Approach
4.1 First Multiresolution Approach - Gaussian Pyramid of Statistical Models
4.2 Second Multiresolution Approach - Gaussian Pyramid within the Statistical Model
5 Experimental Results
6 Summary and Discussion
References
A Common Viewpoint on Broad Kernel Filtering and Nonlinear Diffusion
1 Introduction
2 Importance of Extended Neighborhood
2.1 Smoothing on 1D 3-Neighborhood
2.2 Smoothing on 1D 5-Neighborhood
2.3 Adaptive Smoothing on 1D 5-Neighborhood
3 Generalized Adaptive Smoothing and Nonlinear Diffusion on Extended Neighborhood
4 Bilateral Filtering
5 Mean Shift-Based Filtering
6 Experiments
7 Conclusion
8 Appendix: Scales in RNAs and Digital TV Filtering
References
Efficient and Consistent Recursive Filtering of Images with Reflective Extension
1 Introduction
2 Discrete Filtering
2.1 Filtering on Infinite Domains
2.2 Filtering on Finite Domains
3 Reflective Domains
3.1 Indexing
3.2 Convolution
3.3 Equivalence to Symmetric Filtering
4 Recursive Filtering in a Reflective Domain
4.1 Existence
4.2 Stability
4.3 $LDL^T$ Decomposition and Solution
4.4 A Recursive Filtering Algorithm for Reflective Domains
5 Application to Deriche\'s Recursive Gaussian Approximations
6 Results
6.1 Accuracy
6.2 Timing
7 Conclusion
References
Shape Description Using Gradient Vector Field Histograms
1 Introduction
2 The Multiresolution Pyramidal Framework
2.1 The Gradient Vector Field Pyramid
2.2 The Vector Field Disparity Map
2.3 Shape Axes Extraction
3 Shape Description
3.1 Description by Parts
3.2 Shape Description Using the Gradient Vector Field
3.3 Part Axes
3.4 Gradient Vector Field Histograms
3.5 Saliency of Part
4 Matching Parts and Shapes
4.1 Part and Shape Distances
5 Experimental Results
5.1 Geometric Invariance
5.2 Robustness to Boundary Distortions
5.3 Silhouettes Classification
6 Conclusions
References
Comparing Objective and Subjective Quality Results for Compression Pre-processing with Non-linear Diffusion
1 Introduction
2 Non-linear Diffusion and Adaptive Filtering
3 Artefact Reduction
4 Results
5 Conclusion
References
Computation of Generic Features for Object Classification
1 Introduction
2 Composition of Generic Features (Classtons)
3 Clustering Approaches
3.1 K-Means Clustering
3.2 K-Means with Pruning
3.3 DBScan Clustering
3.4 Evaluation
4 Feature Prototype Generation
4.1 Feature Description
4.2 Cluster Representation
4.3 Quality of Clustering Results
5 Experiments and Observations
5.1 The Test Database
5.2 Experiments
6 Conclusion
References
Gaussian Scale Space from Insufficient Image Information
1 Introduction
2 Scale Space from Insufficient Image Information
2.1 Bayesian Formulation
2.2 Image Priors and Inference
3 Reconstruction Examples and Induced Scale Spaces: Some Experiments
3.1 The Observed Images
3.2 The Apertures
3.3 Inferred Images and Their Induced Scale Space
4 Discussion, Provisional Conclusions and Remarks
References
Families of Generalised Morphological Scale Spaces
1 Introduction
2 Generalised Morphological Scale Spaces
2.1 A Family of Algebraic Operations
2.2 Definition of Generalised Dilation and Erosion Scale Spaces
2.3 Limit Statements
2.4 Properties of the $(q,p)$-Dilations
2.5 Comparison to the Construction of Florack et al.
3 Experiment
4 Conclusion
References
Detection and Localization of Random Signals*
1 Introduction
2 Bayesian Detection and Localization of Random Signals
2.1 Detection as Binary Decision
2.2 Random Object Variability and Image Formation
2.3 Detection under Random Position and Size
2.4 Detection and Localization under Random Shape
2.5 Bayesian Localization of Random Signals
2.6 Pseudo-Linear Scale-Space on Energies and Probabilities
3 Experiments
4 Conclusion
References
Continuous Curve Matching with Scale-Space Curvature and Extrema-Based Scale Selection
1 Introduction
2 Curve Matching Theory and Algorithm
2.1 Curves and Reparameterization
2.2 Curve Matching Formulation
2.3 Diffeomorphic Reparameterization
2.4 Reparameterization Matching Energy Functions
2.5 Matching Algorithm Implementation
2.6 Continuous Approximation from Discrete Solution
3 Matching Smoothed Curves
3.1 Motivation for Linear Diffusion
3.2 Intra-Curve Inter-Scale Matching
3.3 Curvature Conservative Scale-Space Image and Variational Energy
3.4 Cross-Product Space of Extrema Topology for Choosing Matching Scales
4 Conclusion
References
Author Index