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[null,"1.","Record Nr.",null,"UNINA9910639897103321"]
[null,null,"Autore",null,"Bloch Isabelle"]
[null,null,"Titolo",null,"Fuzzy sets methods in image processing and understanding : medical imaging applications / / Isabelle Bloch, Anca Ralescu"]
[null,null,"Pubbl/distr/stampa",null,"Cham, Switzerland : , : Springer, , [2023]"]
[{"$nulls":4},"©2023"]
[null,null,"ISBN",null,"3-031-19425-X"]
[null,null,"Descrizione fisica",null,"1 online resource (311 pages)"]
[null,null,"Disciplina",null,"910.5"]
[null,null,"Soggetti",null,"Fuzzy sets"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Intro -- Acknowledgments -- Contents -- 1 Introduction -- 1.1 Fuzzy Sets and Image Understanding Under Imprecision -- 1.1.1 Sources of Imprecision -- 1.1.2 Advantages and Usefulness of Fuzzy Sets -- 1.1.3 Semantic Gap -- 1.1.4 A Short Review of Existing Books -- 1.2 Representations -- 1.3 Low Level-Clustering, Enhancement, Filtering, Edge Detection -- 1.4 Intermediate Level -- 1.5 Higher Level -- 1.5.1 Representations of Structural Information -- 1.5.2 Fusion -- 1.5.3 Scene Understanding -- 1.6 Emerging Topics -- 1.6.1 Mining and Retrieval -- 1.6.2 Towards Bipolarity -- 1.6.3 Towards More Interactions Between Knowledge and Image Information -- 1.6.4 Deep Neuro-Fuzzy Systems -- References -- 2 Preliminaries -- 2.1 Imprecision in Images and Related Knowledge -- 2.2 Basic Definitions of Fuzzy Sets Theory -- 2.2.1 Fuzzy Sets -- 2.2.2 Set Theoretical Operations: Original Definitions of L. Zadeh -- 2.2.3 Structure and Types of Fuzzy Sets -- 2.2.4 α-Cuts -- 2.2.5 Cardinality -- 2.2.6 Convexity -- 2.2.7 Fuzzy Number -- 2.3 Main Operators on Fuzzy Sets -- 2.3.1 Fuzzy Complementation -- 2.3.2 Triangular Norms and Conorms -- 2.3.3 Mean Operators -- 2.3.4 Symmetric Sums -- 2.3.5 Adaptive Operators -- 2.3.6 Logical Connectives -- 2.4 Linguistic Variable -- 2.4.1 Definition -- 2.4.2 Example of Linguistic Variable -- 2.4.3 Modifiers -- 2.5 Translating a Crisp Operation into a Fuzzy Operation -- 2.5.1 Extension Principle -- Definition -- Application to the Compatibility of Two Fuzzy Sets -- Application to Fuzzy Numbers -- 2.5.2 Combination of Results on α-Cuts -- Reconstruction from α-Cuts -- Extension Principle Based on α-Cuts -- 2.5.3 Translating Binary Terms into Functional Ones -- 2.5.4 Comparison -- 2.6 "]
[{"$nulls":4},"Summary of the Main Notations -- References -- 3 Fuzzy Spatial Objects -- 3.1 Fuzzy Sets in the Spatial Domain -- 3.2 Set Theoretical Operations."]
[{"$nulls":4},"3.2.1 Degree of Intersection -- Crisp Case -- Direct Extension -- Introducing the Volume of the Overlapping Domain -- Properties -- Application to the Non-contradiction Principle -- 3.2.2 Degree of Union and Covering -- 3.2.3 Degree of Inclusion -- Inclusion from Other Set Operations -- Inclusion from Fuzzy Implication -- Other Axiomatic Definitions for the Fuzzy Inclusion -- Inclusion and Fuzzy Entropy -- 3.2.4 Degree of Equality -- 3.3 Topology: Neighborhood, Boundary, and Connectedness of a Fuzzy Set -- 3.3.1 Fuzzy Neighborhood -- 3.3.2 Boundary of a Fuzzy Set -- 3.3.3 Connectedness -- 3.4 Fuzzy Geometry -- 3.4.1 Fuzzy Points and Lines -- 3.4.2 Fuzzy Rectangles and Fuzzy Convex Polygons -- 3.4.3 Fuzzy Disks -- 3.4.4 Fuzzy Geometrical Measures -- Area of a Fuzzy Set -- Perimeter of a Fuzzy Set -- Compactness of a Fuzzy Set -- Height, Width, and Diameter of a Fuzzy Set -- Intersection and Parallelism Between Fuzzy Lines -- Geometrical Measures as Fuzzy Numbers -- 3.5 Fuzzy Geometric Transformations -- 3.5.1 Transformation of a Fuzzy Set by a Crisp Operation -- 3.5.2 Transformation of a Fuzzy Set by a Fuzzy Operation -- References -- 4 Fuzzy Mathematical Morphology -- 4.1 Lattice Structure of ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper F) /StPNE pdfmark [/StBMC pdfmarkFps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 4.2 Algebraic Operators -- 4.3 Structuring Elements and Basic Morphological Operators -- 4.4 An Example in Medical Imaging -- 4.5 Towards a Fuzzy Mathematical Morphology Toolbox -- 4.5.1 Neighborhood and Boundary from Fuzzy Dilation and Erosion -- 4.5.2 Fuzzy Morphological Filters -- 4.5.3 Conditioning and Fuzzy Geodesic Operators -- 4.5.4 Fuzzy Skeleton and Skeleton by Influence Zones -- Distance-Based Approaches -- Morphological Approaches to Compute the Centers of Maximal Balls -- Morphological Thinning."]
[{"$nulls":4},"Fuzzy Skeleton of Influence Zones -- Discussion -- 4.5.5 Fuzzy Median, Application to Interpolation Between Fuzzy Sets -- 4.5.6 Extensions -- References -- 5 Fusion -- 5.1 Definitions -- 5.2 Fusion Systems and Architectures Types -- 5.3 Fuzzy Modeling in Fusion -- 5.4 Defining and Estimating Membership Functions -- 5.5 Fuzzy Combination -- 5.6 Decision in Fuzzy Fusion -- 5.7 Exploiting Spatial Information -- 5.8 Illustrative Examples -- References -- 6 Spatial Relations -- 6.1 Set Theoretical and Topological Relations -- 6.1.1 Adjacency -- 6.1.2 Fuzzy Region Connection Calculus -- 6.2 Distances Between Image Regions or Objects -- 6.2.1 Representations -- 6.2.2 Comparison of Membership Functions -- 6.2.3 Combination of Spatial and Membership Comparisons -- 6.2.4 Discussion and Examples -- 6.3 Fuzzy Hamming Distance -- 6.4 Directional Relations -- 6.4.1 Fuzzy Relations Describing Relative Position -- 6.4.2 Centroid Method -- 6.4.3 Histogram of Angles: Compatibility Method -- 6.4.4 Aggregation Method -- 6.4.5 Histogram of Forces -- 6.4.6 Projection Based Approach -- 6.4.7 Morphological Approach -- 6.4.8 Discussion and Examples -- 6.5 Complex Relations: Surround, Between, Along, Across, Parallel, Aligned -- 6.5.1 Surround -- 6.5.2 Between -- 6.5.3 Across -- 6.5.4 Along -- 6.5.5 Aligned -- 6.5.6 Parallel -- 6.6 Fuzzy Perceptual Organization for Image Understanding -- 6.6.1 Fuzzy Grouping Operator to Produce Straight LineSegments -- 6.6.2 Discrimination: Overlap of Two Segments -- 6.6.3 Obtaining Junctions -- 6.6.4 Obtaining Symmetric Line Structures -- Symmetry of Non-parallel Line Segments -- Symmetry of Parallel Line Structures -- 6.6.5 Obtaining Curves and Closed Regions -- 6.7 Comparison of Spatial "]
[{"$nulls":4},"Relations -- 6.7.1 Relations Represented as Numbers or Intervals -- 6.7.2 Relations Represented as Distributions."]
[{"$nulls":4},"6.7.3 Relations Represented as Spatial Fuzzy Sets -- References -- 7 Fuzzy Sets and Machine Learning -- 7.1 Fuzzy IF-THEN Rules -- 7.2 Unsupervised Learning -- 7.2.1 Fuzzy Clustering -- 7.2.2 Spatial Information and Bias -- 7.3 Fuzzy Sets and Connectionist Approaches -- 7.3.1 Conventional 2D Hopfield Neural Network -- 7.3.2 Fuzzy Sets and Deep Learning -- References -- 8 Structural and Linguistic Representations -- 8.1 Fuzzy Representation of Image Information and of Related Knowledge -- 8.1.1 Image Features -- 8.1.2 Knowledge and Semantics -- 8.1.3 Semantic Gap -- 8.2 Linguistic Representations -- 8.2.1 Description of Some Properties or Characteristics -- 8.2.2 Quantifiers -- 8.2.3 Associating Linguistic Representations and the Spatial Domain -- 8.3 Knowledge-Based Systems -- 8.4 Fuzzy Graphs and Hypergraphs -- 8.5 Fuzzy Logics and Fuzzy Rules -- 8.6 Ontologies -- 8.7 Fuzzy Decision Trees -- 8.8 Fuzzy Association Rules -- 8.9 Fuzzy Formal Concept Analysis -- References -- 9 Structural and Linguistic Reasoning for Image Understanding -- 9.1 From Linguistic Descriptions to Image Understanding -- 9.1.1 Representations of Structural Information -- 9.1.2 Fusion -- 9.1.3 Scene Understanding -- 9.2 From Image Analysis to Image Content Descriptions -- 9.3 A Few Examples in Medical Image Understanding -- 9.3.1 Interpretation as Graph Reasoning -- 9.3.2 Interpretation as Constraint Satisfaction Problem -- 9.3.3 Recognition Based on Ontological Reasoning -- 9.3.4 Interpretation as Abductive Reasoning -- 9.3.5 Deriving Linguistic Descriptions -- 9.4 Interpretability and Explainability -- References -- Index."]