Neutrosophic approach for mathematical morphology. Presented By : Eman marzouk el_hassaaneen el_nakeb Supervisors Dr. Ahmed Salama (A. A. Salama) Department of Mathematics and Computer Science, Faculty of Science , Port Said University , Egypt Dr. Hewayda El-Ghawalby Department of Mathematics, Faculty of Engineering , Port Said University , Egypt

Motivation: :Mathematical morphology Is a theory and technique for the analysis and processing of geometrical structures, based on set theory, topology, and random functions. It is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids etc. .

Topological and geometrical continuous -space concepts such as size, shape , convexity , connectivity , and geodesic distance, were introduced on both continuous and discrete spaces.

Mathematical morphology is also the foundation of morphological , image processing which consists of a set of operators that transform images according to the above characterizations.

The basic morphological operations: (a) Original set, extracted as a subset from the turbinate image (b) structuring element: a square of side 3. The reference pixel is at the centre.

morphological operators erosion dilation opening closing

Binary morphology dilation

erosion

For example: Is the hit-or-miss transform , which uses a pier of structuring element . Let A and B be tow disjoint subset of E ; A will be the foreground structuring element and B the background structuring element we then define :

This will give the locus of all points where A fits the foreground and B fits the background This operation corresponds to what is usually called template matching .

Fuzzy mathematical morphology Fuzzy mathematical morphology provides an alternative extension of the binary morphological operations to gray-scale images based on the theory of fuzzy set . The operation of intersection and union used in binary mathematical morphology are replaced by minimum and maximum operation respectively .

dilation

erosion

Thesis Plan: A survey on mathematical morphology. Standard morphology. Fuzzy mathematical morphology. Neutrosophic sets in literature. Introduce and study anew mathematical morphology. Crisp Neutrosophic mathematical morphology. Neutrosophic mathematical morphology. Application in image processing applying Neutrosophic mathematical morphology in image processing.