The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Isabelle Bloch - One of the best experts on this subject based on the ideXlab platform.
-
On approximating Mathematical Morphology operators via deep learning techniques
2019Co-Authors: Santiago Velasco-forero, Jesus Angulo, Bastien Ponchon, Samy Blusseau, Isabelle BlochAbstract:Mathematical Morphology (MM) is a well-established discipline whose aim is mainly to provide tools to characterise complex object via their shape/size features. This study addresses the problem of robust approximation of Mathematical Morphology (MM) operators by deep learning methods. We present two cases, (a) Asymmetric autoencoders for part-based approximations of classical MM in the sense of [1] and, (b) image-to-image translation networks [2] to produce robust MM operators in presence of noise.
-
some relationships between fuzzy sets Mathematical Morphology rough sets f transforms and formal concept analysis
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2016Co-Authors: Jamal Atif, Isabelle Bloch, Celine HudelotAbstract:In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some Mathematical Morphology operators to fuzzy concept analysis. We also propose to use Mathematical Morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.
-
Robust similarity between hypergraphs based on valuations and Mathematical Morphology operators
Discrete Applied Mathematics, 2015Co-Authors: Isabelle Bloch, Alain Bretto, Aurélie LeborgneAbstract:Abstract This article aims at connecting concepts of similarity, hypergraph and Mathematical Morphology. We introduce new measures of similarity and study their relations with pseudo-metrics defined on lattices. More precisely, based on various lattices that can be defined on hypergraphs, we propose some similarity measures between hypergraphs based on valuations and Mathematical Morphology operators. We also detail new examples of these operators. The proposed similarity measures can be used in particular to introduce some robustness, up to some morphological operators. Some examples based on various dilations, erosions, openings and closings on hypergraphs illustrate the relevance of our approach. Potential applications to image comparison are suggested as well.
-
Mathematical Morphology operators over concept lattices
International Conference on Formal Concept Analysis, 2013Co-Authors: Jamal Atif, Isabelle Bloch, Felix Distel, Celine HudelotAbstract:Although Mathematical Morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic Mathematical Morphology framework. In particular we define Mathematical Morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.
-
Mathematical Morphology on hypergraphs, application to similarity and positive kernel
Computer Vision and Image Understanding, 2013Co-Authors: Isabelle Bloch, Alain BrettoAbstract:The focus of this article is to develop Mathematical Morphology on hypergraphs. To this aim, we define lattice structures on hypergraphs on which we build Mathematical Morphology operators. We show some relations between these operators and the hypergraph structure, considering in particular transversals and duality notions. Then, as another contribution, we show how Mathematical Morphology can be used for classification or matching problems on data represented by hypergraphs: thanks to dilation operators, we define a similarity measure between hypergraphs, and we show that it is a kernel. A distance is finally introduced using this similarity notion.
Celine Hudelot - One of the best experts on this subject based on the ideXlab platform.
-
some relationships between fuzzy sets Mathematical Morphology rough sets f transforms and formal concept analysis
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2016Co-Authors: Jamal Atif, Isabelle Bloch, Celine HudelotAbstract:In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some Mathematical Morphology operators to fuzzy concept analysis. We also propose to use Mathematical Morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.
-
Mathematical Morphology operators over concept lattices
International Conference on Formal Concept Analysis, 2013Co-Authors: Jamal Atif, Isabelle Bloch, Felix Distel, Celine HudelotAbstract:Although Mathematical Morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic Mathematical Morphology framework. In particular we define Mathematical Morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.
-
abduction in description logics using formal concept analysis and Mathematical Morphology application to image interpretation
Concept Lattices and their Applications, 2011Co-Authors: Jamal Atif, Celine Hudelot, Isabelle BlochAbstract:We propose an original way of enriching Description Logics with ab- duction reasoning services by computing the best explanations of an observation through Mathematical Morphology (using erosions) over the Concept Lattice of a background theory. The intended application is scene understanding and spatial
-
integrating bipolar fuzzy Mathematical Morphology in description logics for spatial reasoning
European Conference on Artificial Intelligence, 2010Co-Authors: Celine Hudelot, Jamal Atif, Isabelle BlochAbstract:Bipolarity is an important feature of spatial information, involved in the expression of preferences and constraints about spatial positioning or in pairs of opposite spatial relations such as left and right. Another important feature is imprecision which has to be taken into account to model vagueness, inherent to many spatial relations (as for instance vague expressions such as close to, to the right of), and to gain in robustness in the representations. In previous works, we have shown that fuzzy sets and fuzzy Mathematical Morphology are appropriate frameworks, on the one hand, to represent bipolarity and imprecision of spatial relations and, on the other hand, to combine qualitative and quantitative reasoning in description logics extended with fuzzy concrete domains. The purpose of this paper is to integrate the bipolarity feature in the latter logical framework based on bipolar and fuzzy Mathematical Morphology and description logics with fuzzy concrete domains. Two important issues are addressed in this paper: the modeling of the bipolarity of spatial relations at the terminological level and the integration of bipolar notions in fuzzy description logics. At last, we illustrate the potential of the proposed formalism for spatial reasoning on a simple example in brain imaging.
Jamal Atif - One of the best experts on this subject based on the ideXlab platform.
-
some relationships between fuzzy sets Mathematical Morphology rough sets f transforms and formal concept analysis
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2016Co-Authors: Jamal Atif, Isabelle Bloch, Celine HudelotAbstract:In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some Mathematical Morphology operators to fuzzy concept analysis. We also propose to use Mathematical Morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.
-
Mathematical Morphology operators over concept lattices
International Conference on Formal Concept Analysis, 2013Co-Authors: Jamal Atif, Isabelle Bloch, Felix Distel, Celine HudelotAbstract:Although Mathematical Morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic Mathematical Morphology framework. In particular we define Mathematical Morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.
-
abduction in description logics using formal concept analysis and Mathematical Morphology application to image interpretation
Concept Lattices and their Applications, 2011Co-Authors: Jamal Atif, Celine Hudelot, Isabelle BlochAbstract:We propose an original way of enriching Description Logics with ab- duction reasoning services by computing the best explanations of an observation through Mathematical Morphology (using erosions) over the Concept Lattice of a background theory. The intended application is scene understanding and spatial
-
integrating bipolar fuzzy Mathematical Morphology in description logics for spatial reasoning
European Conference on Artificial Intelligence, 2010Co-Authors: Celine Hudelot, Jamal Atif, Isabelle BlochAbstract:Bipolarity is an important feature of spatial information, involved in the expression of preferences and constraints about spatial positioning or in pairs of opposite spatial relations such as left and right. Another important feature is imprecision which has to be taken into account to model vagueness, inherent to many spatial relations (as for instance vague expressions such as close to, to the right of), and to gain in robustness in the representations. In previous works, we have shown that fuzzy sets and fuzzy Mathematical Morphology are appropriate frameworks, on the one hand, to represent bipolarity and imprecision of spatial relations and, on the other hand, to combine qualitative and quantitative reasoning in description logics extended with fuzzy concrete domains. The purpose of this paper is to integrate the bipolarity feature in the latter logical framework based on bipolar and fuzzy Mathematical Morphology and description logics with fuzzy concrete domains. Two important issues are addressed in this paper: the modeling of the bipolarity of spatial relations at the terminological level and the integration of bipolar notions in fuzzy description logics. At last, we illustrate the potential of the proposed formalism for spatial reasoning on a simple example in brain imaging.
Frank Yeong-chyang Shih - One of the best experts on this subject based on the ideXlab platform.
-
Image Processing and Mathematical Morphology: Fundamentals and Applications
2009Co-Authors: Frank Yeong-chyang ShihAbstract:Introduction to Mathematical Morphology Basic Concept in Digital Image Processing Brief History of Mathematical Morphology Essential Morphological Approach to Image Analysis Scope of This Book Binary Morphology Set Operations on Binary Images Logical Operations on Binary Images Binary Dilation Binary Erosion Opening and Closing Hit-or-Miss Transformation Grayscale Morphology Grayscale Dilation and Erosion Grayscale Dilation Erosion Duality Theorem Grayscale Opening and Closing Basic Morphological Algorithms Boundary Extraction Region Filling Extraction of Connected Components Convex Hull Thinning Thickening Skeletonization Pruning Morphological Edge Operator Basic Morphological Filters Alternating Sequential Filters Recursive Morphological Filters Soft Morphological Filters OSSM Filters RSM Filters (RSMFs) ROSSM Filters Regulated Morphological Filters Fuzzy Morphological Filters Distance Transformation DT by Iterative Operations DT by Mathematical Morphology Approximation of Euclidean Distances Decomposition of Distance SEs Iterative Erosion Algorithm Two Scan-Based Algorithm Three-Dimensional Euclidean Distance Acquiring Approaches Deriving Approaches 7 Feature Extraction Edge Linking by MM Corner Detection by Regulated Morphology Shape Database with Hierarchical Features Corner and Circle Detection Size Histogram Object Representation Object Representation and Tolerances Skeletonization or MA Transformation Morphological Shape Description Decomposition of Morphological Structuring Elements Decomposition of Geometric-Shaped SEs Decomposition of Binary SEs Decomposition of Grayscale SEs Architectures for Mathematical Morphology Threshold Decomposition of Grayscale Morphology into Binary Morphology Implementing Morphological Operations Using Programmable Neural Networks MLP as Processing Modules A Systolic Array Architecture Implementation on Multicomputers General Sweep Mathematical Morphology Theoretical Development of General Sweep MM Blending of Sweep Surfaces with Deformations Image Enhancement Edge Linking Geometric Modeling and Sweep MM Formal Language and Sweep Morphology Grammars Parsing Algorithms Morphological Approach to Shortest Path Planning Relationships between Shortest Path Finding and MM Rotational MM The Shortest Path-Finding Algorithm Experimental Results and Discussions Dynamic Rotational MM The Rule of Distance Functions in Shortest Path Planning Index
-
adaptive Mathematical Morphology for edge linking
Information Sciences, 2004Co-Authors: Frank Yeong-chyang Shih, Shouxian ChengAbstract:In this paper, adaptive Mathematical Morphology and its application to edge linking are presented to fill in the gaps between edge segments. Broken edges are extended along their slope directions by using the adaptive dilation operation with the suitable sized elliptical structuring elements. The size and orientation of the structuring element are adjusted according to the local properties, such as slope and curvature. Postprocesses of thinning and pruning are also applied. The edge-linking operation is performed in an iterative manner, so that the broken edges can be linked up gradually and smoothly while the details of the object shape are preserved.
-
Object Representation and Recognition Using Mathematical Morphology Model
Journal of Systems Integration, 1991Co-Authors: Frank Yeong-chyang ShihAbstract:The integration of representation and recognition of rigid solid objects is becoming increasingly important in computer-aided design (CAD), computer-aided manufacturing (CAM), computer graphics, computer vision, and other fields that deal with spatial phenomena. The Mathematical framework used for modeling solid objects is Mathematical Morphology, which is based on set-theoretic concept. The Mathematical characteristics of these operators are investigated in order to achieve a formal theory. Using Mathematical Morphology as a tool, our theoretical research aims at studying the representation schemes for the dimension and tolerance of the geometric structure. Object features can be also extracted by using the Mathematical Morphology approach. Through a distance transformation, we can obtain the shape number, significant points database, and skeleton. We have also developed the object recognition, localization, and corner and circle detection algorithms.
Peter Sussner - One of the best experts on this subject based on the ideXlab platform.
-
lattice fuzzy transforms from the perspective of Mathematical Morphology
Fuzzy Sets and Systems, 2016Co-Authors: Peter SussnerAbstract:The compositions of direct and inverse fuzzy transforms constitute powerful tools in knowledge extraction and representation that have been applied to a large variety of problems in computational intelligence as well as in image processing and computer vision. Fuzzy transforms (FTs) have linear as well as lattice-based versions. In this paper, we extend the latter FTs, known as lattice FTs, and relate these operators and their underlying Mathematical structures to the ones of Mathematical Morphology (MM), in particular to the ones of MM on complete lattices and L-fuzzy MM.
-
interval valued and intuitionistic fuzzy Mathematical morphologies as special cases of mathbb l fuzzy Mathematical Morphology
Journal of Mathematical Imaging and Vision, 2012Co-Authors: Peter Sussner, Mike Nachtegael, Tom Melange, Glad Deschrijver, Estevao Esmi, Etienne KerreAbstract:Mathematical Morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale Morphology. Extensions of classical binary Morphology to gray-scale Morphology include approaches based on fuzzy set theory that give rise to fuzzy Mathematical Morphology (FMM). From a Mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of $\mathbb{L}$ -fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov's intuitionistic fuzzy set. In addition, the class of $\mathbb{L}$ -fuzzy sets forms a complete lattice whenever the underlying set $\mathbb{L}$ constitutes a complete lattice. Based on these observations, we develop a general approach towards $\mathbb{L}$ -fuzzy Mathematical Morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy Mathematical morphologies that arise as special, isomorphic cases of $\mathbb{L}$ -fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing.
-
fuzzy associative memories from the perspective of Mathematical Morphology
IEEE International Conference on Fuzzy Systems, 2007Co-Authors: Marcos Eduardo Valle, Peter SussnerAbstract:Mathematical Morphology (MM) is a theory concerned with the processing and analysis of objects using operators based on topological and geometrical concepts. We speak of a fuzzy morphological associative memory (FMAM) when a fuzzy associative memory (FAM) model is equipped with neurons that correspond to an operator of Mathematical Morphology. This paper shows that several FAM models, including the FAMs of Kosko, most generalized FAMs of Chung and Lee, the FAM of Junbo et al., the max-min FAM with threshold, the fuzzy logic bidirectional associative memories, and the implicative fuzzy associative memories, belong to the FMAM class. Moreover, we present two strategies for deriving a new FMAM model from a given FMAM. These strategies are based on two duality relationship of Mathematical Morphology: duality with respect to negation and duality with respect to adjunction.