On Some Associations Between Mathematical Morphology and Artificial Intelligence

Bloch, Isabelle; Blusseau, Samy; Pérez, Ramón Pino; Puybareau, Élodie; Tochon, Guillaume

doi:10.1007/978-3-030-76657-3_33

Cited by 6 publications

(6 citation statements)

References 43 publications

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“…) is a modal algebra. Hence, under this interpretation, modal logic is a tool for talking about spatial transformation, and in this setting, modal logic has been applied efficiently to symbolic artificial intelligence [5,13,16].…”

Section: Bmentioning

confidence: 99%

“…Following the approach developed in [16], the idea is then to dilate the class of models of ϕ until meeting the class of models of ψ. Then, as this has been defined in [16] for the propositional logic, let us define the operator • as follows:…”

Section: Belief Revisionmentioning

confidence: 99%

“…As shown in [5,13,16], morpho-logic, as defined in this paper, provides a simple axiomatization of some of these relations.…”

Section: E-conmentioning

confidence: 99%

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Morpho-logic from a Topos Perspective: Application to symbolic AI

Aiguier¹,

Bloch²,

Salim³

et al. 2023

Preprint

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Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis of structures, that was widely developed and applied in image analysis. Its mathematical bases rely on algebra, complete lattices, topology. Strong links have been established between MM and mathematical logics, mostly modal logics. In this paper, we propose to further develop and generalize this link between mathematical morphology and modal logic from a topos perspective, i.e. categorial structures generalizing space, and connecting logics, sets and topology. Furthermore, we rely on the internal language and logic of topos. We define structuring elements, dilations and erosions as morphisms. Then we introduce the notion of structuring neighborhoods, and show that the dilations and erosions based on them lead to a constructive modal logic, for which a sound and complete proof system is proposed. We then show that the modal logic thus defined (called morpho-logic here), is well adapted to define concrete and efficient operators for revision, merging, and abduction of new knowledge, or even spatial reasoning.

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Section: Bmentioning

confidence: 99%

Section: Belief Revisionmentioning

confidence: 99%

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Morpho-logic from a Topos Perspective: Application to symbolic AI

Aiguier¹,

Bloch²,

Salim³

et al. 2023

Preprint

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show abstract

“…The basic idea of mathematical morphology is to measure and extract the corresponding shape in the image with structural elements of a certain shape, laying the basis for image analysis and recognition. Its application can simplify image data, keep their basic shape features, and remove irrelevant structures [17]. The expansion of grayscale image adopts the positive values of structural elements, and outputs an image brighter than the input.…”

Section: Back Contour Segmentationmentioning

confidence: 99%

Scoliosis Detection Based on Feature Extraction from Region-of-Interest

Yang¹,

Xi²,

Zhang³

et al. 2022

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In recent years, the incidence of scoliosis is rising among adolescents. Considering the radiation hazards of X-ray detection, this paper intends to develop an effective non-radiation detection method for scoliosis. The research method consists of the following steps: (1) Collect clear an image of the back of the patient with a high-resolution digital camera, and optimize the image through preprocessing; (2) Segment the region of interest (ROI) of the back and spine to reduce the complexity of subsequent calculations; (3) Extract the back contour and mark the feature points; (4) Extract features according to the grayscale change of the spine ROI, and fit the spine midline according to the feature points; (5) Evaluate the degree of scoliosis according to the symmetry of the posture features and the Cobb angle of the spine midline. Finally, experimental results were analyzed, which indicate that the proposed scoliosis detection method can preliminarily evaluate the posture features. The scoliosis detection error fell in the reasonable range (0-4 degrees), when the subjects had a Cobb angle between 0 and 30 degrees. Hence, our algorithm is accurate and effective, and provides a low-cost, efficient solution for scoliosis detection.

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“…Various other extensions of Mathematical Morphology (MM) have been contributed by many authors like Di Gesu, De Baets, Bloch [16][17][18][19]21], Maitre and Nachtegeal [30,31]. This includes extension of binary morphology to grayscale morphology based on fuzzy set theory [12,13,20], bipolar fuzzy set theory, intuitionistic fuzzy set theory and interval valued fuzzy set theory, which has many applications in different fields such as medical imaging and artificial intelligence.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Graph Mathematical Morphology and Some of its Properties

Jacob

Ramkumar

2022

Preprint

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This paper studies the mathematical morphology operators acting on a lattice of all intuitionistic fuzzy sub graphs of an intuitionistic fuzzy graph (IFG). pn-adjacency of vertices and edges are defined as neighbourhoods of vertices and edges. We define vertex dilation, vertex erosion, edge dilation, edge erosion and some of their properties on intuionistic fuzzy graph using pn-adjacency of vertices and edges. We propose elementary mathematical morphology operators, dilation and erosion, on intuionistic fuzzy graph using pn-adjacency of vertices and edges based on lattice theory and also prove following basic properties of the proposed intuitionistic fuzzy graph mathematical morphology operators, dilation and erosion. (1) Dilation and erosion on IFG are increasing (2) Dilation is extensive. (3) Erosion is anti-extensive. (4) Dilation is distributive with respect to union and Erosion on IFG is distributive with respect to intersection. These properties are analogous to the properties of dilation and erosion in the classical Mathematical Morphology. So this paper is a theoretical extension of mathematical morphology on graphs to mathematical morphology on intuitionistic fuzzy graph. MSC Classification: 68U10 , 05C72

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On Some Associations Between Mathematical Morphology and Artificial Intelligence

Cited by 6 publications

References 43 publications

Morpho-logic from a Topos Perspective: Application to symbolic AI

Morpho-logic from a Topos Perspective: Application to symbolic AI

Scoliosis Detection Based on Feature Extraction from Region-of-Interest

Intuitionistic Fuzzy Graph Mathematical Morphology and Some of its Properties

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