Medical Images Edge Detection via Neutrosophic Mathematical Morphology Presented by Eman. M. EL-Nakeeb Physics and Engineering Mathematics Department Faculty of Engineering, Port Said University

Supervisors Dr. A. A. Salama Dr. Samy Ahmed Abd El-Hafeez Department of Mathematics and Computer Science, Faculty of Science, Port Said University Dr. Samy Ahmed Abd El-Hafeez Professor of Mathematics - Department of Mathematics and Computer Science Faculty of Science, Port said University, Egypt. Dr. Hewayda El Ghawalby Physics and Engineering Mathematics Department Faculty of Engineering , Port Said University.

  Abstract : Detection edges in medical images is a significant task for human organs recognition, moreover it is an essential pre-processing step in 3D reconstructing and in segment medical image. In the literature, there are several edge detection algorithms; for instance, the gradient-based algorithm and template-based algorithm. A min drawback of these algorithms is that they are not so efficient with noisy medical image. In this work, we propose a novel edge detection algorithm based on the concepts of neutrosophic set theory ad operations combined with mathematical morphology. experimenting the proposed method on lunge CT image, showed some promising results.

Neutrosophic Crisp Math Morph Math Morphology Fuzzy Math Morphology Neutrosophic Math Morph

Theory of Neutrosophy In 1991; Smarandache presented the concept of neutrosophy as the study of the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. In 2015; Salama introduced the concept of neutrosophic crisp sets, to represent any event by a triple crisp structure.

Mainly, some event. "A" is to be considered in relation to its opposite "Non-A", and to that which is neither "A" nor "Non-A", denoted by "Neut-A". As a powerful generalization of both the classic and fuzzy concepts, neutrosophy became fundamental of several disciplines such as: "Neutrosophic Set Theory, Neutrosophic Logic, Neutrosophic Probability, Neutrosophic Calculus and Neutrosophic Statistic"

Birth of Morphology from the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France. Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and topology.

In 1968, the Centre de Morphologie Mathématique was founded During the rest of the 1960s and most of the 1970s, Mathematical Morphology (MM) dealt essentially with binary images, treated as sets, and generated a large number of binary basic operators: dilation, erosion, opening, closing.

Mathematical Morphology Is a theory and technique for the analysis and processing the geometrical structures, based on set theory, topology, continuous-space concepts such as: size, shape and geodesic distance, It is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes and solids.

Mathematical Morphology Mathematical Morphology is also the foundation of morphological image processing which consists of a set of operators that transform images according to those concepts.

Binary Mathematical Morphology For morphology of binary images, the sets consist of pixels in an image.

Morphological Operators erosion dilation opening closing

Basic Morphological operations Original set, extracted as a subset from the turbinate image structuring element: a square of side 3. The reference pixel is at the centre.

Binary Mathematical Morphology Dilation The Dilation operation uses a structuring element for exploring and expanding the shapes contained in the input image.

c) the Dilation with SE(5) a) Binary image c) the Dilation with SE(5) b) the Dilation with SE(3)

Binary Mathematical Morphology Erosion Used to reduces objects in the image (Unlike Dilation)  

a) Binary image b) the Erosion with SE(3) c) the Erosion with SE(5)

Binary Mathematical Morphology Opening Used to remove small objects and connections between objects in the image    

a) Binary image b) the Opening with SE(3) c) the Opening with SE(5)

Binary Mathematical Morphology Closing Is used to merge or fill structures in an image (removes small holes).  

c) the Closing with SE(5) a) Binary Image b) the Closing with SE(3) c) the Closing with SE(5)

Neutrosophic Mathematical Morphology In this presentation we aim to use the concepts from Neutrosophic crisp set theory to Mathematical Morphology which will allow us to deal with not only Binary images but also the grayscale images.

Neutrosophic Crisp Image:  

a) Original image        

Neutrosophic Crisp Mathematical Morphological Operations: * Neutrosophic Crisp Dilation * Neutrosophic Crisp Erotion * Neutrosophic Crisp Opening * Neutrosophic Crisp Closing

Neutrosophic Crisp Dilation

Neutrosophic Crisp Erosion

Neutrosophic Crisp Opening

Neutrosophic Crisp Closing

Neutrosophic Crisp Mathematical Morphological Filters * Neutrosophic Crisp Outline Boundary * Neutrosophic Crisp Grad Boundary * Neutrosophic Crisp Div. Boundary

Neutrosophic Crisp Outline Boundary    

Neutrosophic Crisp Internal Boundary           Neutrosophic Crisp External Boundary          

Neutrosophic Crisp Grad Boundary    

Neutrosophic Crisp Div. Boundary    

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