
Combinatorial Image Analysis
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Content
- Title Page
- Preface
- Organization
- Table of Contents
- Invited Papers
- Recognition of Human Activities
- References
- Complexity and Approximability Issues in Combinatorial Image Analysis
- Combinatorial Image Analysis and Discrete Geometry
- Theoretical vs. Practical Performance: An Example
- Guarding a Set of Segments, Set Cover, and Vertex Cover
- GSS: Complexity, Polynomial Classes, Approximate Algorithms and Their Theoretical and Experimental Performance
- Still Open: What Is GSS Approximability?
- References
- Intelligent Image Analysis of Diffusion Weighted Data Sets: A New Tool for Functional Imaging
- Introduction
- Materials and Methods
- Results and Discussion
- Conclusion
- References
- Computational Methods for the Prediction of Protein-Protein Interactions
- Recognition of Proteins Binding Sites
- Protein-Protein Interaction Networks: Analysis and Comparison
- References
- Digital Geometry and Topology, Combinatorics in Digital Spaces
- A Family of Topology-Preserving 3D Parallel 6-Subiteration Thinning Algorithms
- Introduction
- Basic Notions and Results
- New Sufficient Conditions for Topology Preserving Parallel Reductions
- The New 6-Subiteration Thinning Algorithms
- Examples of the New 6-Subiteration Thinning Algorithms
- Conclusions
- References
- On Topology Preservation for Hexagonal Parallel Thinning Algorithms
- Introduction
- Basic Notions
- Sufficient Conditions for Topology Preserving Parallel Reductions
- A New Topology Preserving Thinning Algorithm
- Conclusions
- References
- Accurate Curvature Estimation along Digital Contours with Maximal Digital Circular Arcs
- Introduction
- Curvature Estimation Based on the Set of Maximal Digital Circular Arcs
- On the Multigrid Convergence of the MDCA Estimator
- Multigrid Convergence Definition for a Curvature Estimator
- Relation with Growth of MDCAs
- Experimental Evaluation
- Comparisons
- Implementation Issues
- Accuracy and Running Time
- Conclusion and Perspectives
- References
- Combining Topological Maps, Multi-Label Simple Points, and Minimum-Length Polygons for Efficient Digital Partition Model
- Introduction
- Preliminaries Notions
- Pixels, Image and Regions
- Interpixel Topology and Cubical Complexes
- Multi-label Simple Points
- Minimum Length Polygon
- Topological Map
- Deformable Model Process
- Energies
- Operations
- Update Energies for Flip
- Energy Minimization Algorithm
- Experiments
- Conclusion
- References
- Construction of 3D Orthogonal Cover of a Digital Object
- Introduction
- Definitions and Preliminaries
- Proposed Algorithm
- DCEL Construction
- Face Merging
- Time Complexity
- Results and Conclusion
- References
- Skeleton Path Based Approach for Nonrigid 3D Shape Analysis and Retrieval
- Introduction
- Proposed Approach
- Skeleton Path
- Endpoints Matching
- Experimental Results
- Symmetric Components Discovery
- Matching Skeletons with Different Graph Structures
- Retrieval on McGill 3D Articulated Shape Database
- Conclusions
- References
- The Number of Khalimsky-Continuous Functions between Two Points
- Introduction
- The Khalimsky Topology and Khalimsky-Continuous Functions
- Khalimsky-Continuous Functions with Two Fixed Endpoints
- Conclusion
- References
- Cup Products on Polyhedral Approximations of 3D Digital Images
- Introduction
- 3D Digital Pictures and Cellular Complexes
- Computing the Cohomology Ring of P(I)
- Conclusions and Plans for Future Work
- References
- Digital Geometry of Curves and Surfaces
- A Jordan Curve Theorem in the Digital Plane
- Introduction
- Preliminaries
- Topology $w$
- Conclusion
- References
- Maximal Planes and Multiscale Tangential Cover of 3D Digital Objects
- Introduction
- Definition of Maximal Hyperplanes
- Digital Surface and Tightiest Hyperplane
- Neighborhood, -Thick Disk and Extension
- Maximal Disks and Hierarchy of Active Vertices
- Computation and Time Complexity
- Algorithm Design
- Time Complexity Analysis
- Application
- Conclusion and Perspectives
- References
- Recognition of Digital Hyperplanes and Level Layers with Forbidden Points
- Problem Statement
- Why a New Problem of Recognition?
- Exact Formulation
- From Arbitrary Functions to Affine Separation
- Computation by Linear Programming
- Rewriting the Problem in Terms of Computational Geometry
- The GJK Algorithm and Our Variant
- The Classical GJK Algorithm
- Our GJK Variant
- Experimental Results and Potential Applications
- Experimental Results
- Potential Applications
- Conclusion
- References
- A Simple and Flexible Mesh Parameterization Method
- Minimizing Angle Distortion
- Main Problem
- A Differentiable Measure of Angle Distortion
- Minimization Algorithm
- The Algorithm
- Necessity of Additional Constraints
- Stabilizing the Boundary
- Main Idea
- Preserving Metric Boundary
- Preserving Boundary Angles
- Finding a Natural Boundary
- Introduction of New Constraints
- Adding Energies: Areas, Lengths Preservation
- Constrained Texture Mapping
- Conclusion
- References
- Ellipse Constraints for Improved Wide-Baseline Feature Matching and Reconstruction
- Introduction
- Previous Work
- Background
- Parametrization
- Application to Feature Matching
- Descriptors
- Matching
- Non-linear Optimization
- Reconstruction
- Results and Experiments
- Outdoor Data Set
- Conclusion and Outlook
- References
- Reconstruction of Concurrent Lines from Leaning Points
- Introduction
- Domains and Leaning Points
- Geometric Figure Recognition
- Constructions with Leaning Points and Leaning Lines
- Concluding Remarks
- References
- Isoperimetrically Optimal Polygons in the Triangular Grid
- Introduction
- Preliminary Results: The Square Grid
- Square Grid with 4-Neighborhood
- Square Grid with 8-Neighborhood
- Definitions and Notions for the Triangular Grid
- Digital Circles
- The Shape of Optimal Circles
- The Side-Lengths of Optimal Polygons
- Conclusions and Future Work
- References
- Dynamic Minimum Length Polygon
- Introduction
- Preliminaries
- Minimum Length Polygon
- Algebra on Reversible Polygonal Representations
- Grid-Vector, Grid-Curve
- Christoffel Words, Interpixel Path, RPR
- Simplification Rules
- Grid-Vectors Fusion Rules
- Merging Grid-Vectors
- Split and Merge Formulae
- Simplification Rules for Operators
- Concluding Remarks
- References
- Grammars and Models for Image Analysis. Tilings and Patterns
- On Some Classes of 2D Languages and Their Relations
- Introduction
- Preliminaries
- Closure Properties and Hierarchy
- Comparisons
- Conclusions
- References
- Petri Net Generating Hexagonal Arrays
- Introduction
- Hexagonal Arrays and Arrowheads
- Hexagonal Array Token Petri Net Structure
- Firing Rules
- Arrowhead Catenation Rules as Labels
- Comparison Results
- Adjunct Hexagonal Array Token Petri Net Structure
- Adjunction Rules as Labels
- Conclusion
- References
- Binary Images, $M$-Vectors, and Ambiguity
- Introduction
- Preliminaries
- $M$-Vector of a Binary Array
- Ambiguity of a Binary Array
- Conclusion
- References
- Shuffle on Trajectories over Finite Array Languages
- Introduction
- Preliminaries
- Shuffle on Trajectories
- Conclusion
- References
- Planar Configurations Induced by Exact Polyominoes
- Introduction
- Definitions and Results
- Probing the Plane with Diamond Polyominoes
- Experimental Results Obtained with Sage
- Conclusions
- References
- Discrete Tomography
- Convex-Set Perimeter Estimation from Its Two Projections
- Introduction
- State of the Art
- Convex Inclusion and Perimetric Inequality
- Projection Inclusion and Convex-Set Inclusion
- Estimation of Convex-Set Perimeter
- Unique Reconstruction
- Multiple Reconstruction
- Conclusion
- References
- Solving the Two Color Problem: An Heuristic Algorithm
- Introduction and Definitions
- The Heuristic Algorithm
- Type 1 Switching Components
- Type 2 Switching Components
- Type 3 Switching Components
- Generating Instances of 2-Color
- Results
- Conclusions
- References
- Approximating Bicolored Images from Discrete Projections
- Introduction
- Definitions and Notations
- Flow Models to MB(H, V )
- Max-flow Associated Problem
- Min-cost Max-flow Associated Problem
- Polynomial Case
- Heuristics
- Results
- Random Images
- Squares Shaped Images
- Conclusion
- References
- Discrete Q-Convex Sets Reconstruction from Discrete Point X-Rays
- Introduction
- Definition and Notations
- Classical Definitions and Notations
- Q-Convexity
- Reconstruction Algorithm for Two Source Points
- Problem Presentation
- Filling Operations
- Example
- Conclusion
- References
- Discrete Tomography Reconstruction Based on the Multi-well Potential
- Introduction
- Reconstruction Problem
- Proposed Method
- Experimental Results
- Concluding Remarks
- References
- Image Segmentation, Representation, Reconstruction, and Compression. Fuzzy and Stochastic Image Analysis
- An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals
- Introduction
- Definition of Singularity Analysis
- MSC and Its Connection with Reconstruction
- General Conditions to Define UPM-Measures
- Calculus on Reduced Neighborhoods: Cross Fourier Transform
- Local Correlation Singularity Measure
- Conclusions
- References
- Community Detection for Hierarchical Image Segmentation
- Introduction
- Related Work
- Optimizing the Modularity
- The Louvain Method
- A Modified Louvain Method
- The Weighted Modularity
- Experimental Results
- Conclusion
- References
- BCIF: Another Algorithm for Lossless True Color Image Compression
- Introduction
- The Algorithm
- Filtering
- Color Filtering
- The Filter Selection Model
- Compression
- Huffman Tree Coding
- Benchmarks
- Conclusions
- References
- Distance Measures between Digital Fuzzy Objects and Their Applicability in Image Processing
- Introduction
- Background
- Basic Notions
- Related Work on Distances between Crisp Sets
- Related Work on Distances between Fuzzy Sets
- The Sum of Minimal Distances and Complement Weighted Sum of Minimal Distances for Fuzzy Sets
- Evaluation
- Evaluation of Monotonicity in Noise Free and Noisy Conditions
- Comparative Evaluation on Matching Crisp and Fuzzy Objects
- Summary and Conclusions
- References
- Unsupervised Polygonal Reconstruction of Noisy Contours by a Discrete Irregular Approach
- Introduction
- Preamble and Previous Work
- Definitions
- Previous Algorithm for Irregular Object Vectorization
- Unsupervised Polygonalization of Noisy Digital Contours
- A Novel Approach to Vectorize Irregular Isothetic Objects
- Polygonalization of Noisy Contours by an Irregular Discrete Approach
- Experimental Results
- Conclusion and Future Works
- References
- Applications to Medical Imaging and Biometrics
- Boar Spermatozoa Classification Using Longitudinal and Transversal Profiles (LTP) Descriptor in Digital Images
- Introduction
- Dataset
- Image Acquisition
- Segmentation and Preprocessing
- Image Descriptors
- Previous Work
- Our Approach: Longitudinal and Transversal Profiles (LTP) Descriptor
- Classification
- Results
- Conclusions
- References
- Topology-Preserving Registration: A Solution via Graph Cuts
- Introduction
- Background
- Registration Method
- Design of the Field
- Optimization Procedure
- Results
- Conclusion
- References
- Support Vector Machine Approach to Cardiac SPECT Diagnosis
- Introduction
- Support Vector Classification
- Analyzed Data
- Completed Experiments and Selected Research Results
- Conclusion
- References
- An Entropy-Based Technique for Nonrigid Medical Image Alignment
- Introduction
- Proposed Method
- Jensen-Tsallis (JT) Similarity
- Problem Statement
- Transformation Model
- Optimization of the JT Similarity
- Derivative of the JT Similarity
- Summary of the Proposed Algorithm
- Experimental Results
- Multimodality Test
- Conclusions
- References
- Precipitates Segmentation from Scanning Electron Microscope Images through Machine Learning Techniques
- Introduction
- Pattern Recognition by Optimum-Path Forest
- Training
- Classification
- Pruning Irrelevant Patterns
- Methodology
- Experimental Results
- Robustness of Classifiers
- Automatic Labeling Images
- Conclusions
- References
- Nonlinear Dynamical Analysis of Magnetic Resonance Spectroscopy Data
- Introduction
- Problems Associated with NMR Data
- Complexity Measures and Information Theory
- Nonlinear Dynamical Analysis
- Conclusions
- References
- A Shared Parameter Model for Gesture and Sub-gesture Analysis
- Introduction
- Related Work
- Feature Extraction
- Model Description and Parameter Learning
- Inference
- Parameter Estimation
- Inference with Multiple Hand Locations
- Experiments and Results
- Conclusion and Future Work
- References
- Author Index
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