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Presentation On Mathematical Morphology

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Published in: Mathematics
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A short project ppt on Mathematical Morphology

Sumayya H / Dubai

2 years of teaching experience

Qualification: B.Ed (pursuing : 2020 - 2022), MSc Mathematics

Teaches: Maths, Mathematics

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  1. MAIHEMATICAL MORPHOLOGY
  2. INTRODUCTION 'MORPHOLOGY' What is The Word MORPHOLOGY' denotes a branch of Biology that deals with the form and structure of Animals and Plants.
  3. Now, what is 'Mathematical morphology' Here we use the same word Morphology in the context of Mathematical Morphology,which means as a Tool for extracting image components that are useful in the representation and Description of region,shape such as boundaries,skeletons etc. The Language of Mathematical morphology is SET THEORY. Sets in Mathematical Morphology represents objects in an image. Motive is to extract useful features from shape.
  4. *STORY Stem from the study of porous media. Developed in 1964 by G Matheron and J Serra. During 1960's and 1970's M.M deals with binary images and generated large number of binary operators During 1970's and 1980's M.M was generalised by Greyscale functions and images. In 1980's and 1990's M.M gained a wider recognization. • In 1986, Serra further generalised M.M based on complete lattices. Later it began to applied to large number of image problem.
  5. Basic Concepts From Set theory Let A and B be sets. To indicate a is an element of A write a e A. To indicate a is not an element of A write a A. Ais a subset of B, written A B, if for every a e A, a e B. The union of A and B, A UB = {x I x e A or x e B}. The intersection of A and B, A n B = {x I x e A and x e B}. The complement of A, A c = {x I x e A}. The difference of A and B, A —B = {x I x e A and x B}.
  6. Dilation and Erosion x Opening and Closing x x Hit-or-miss transform x Granulometry x Skeletonization,Medial axis transform x Thinning and Thickening
  7. BINARY DILATION To expand or to increase something. Basic effect Gradually enlarge the boundaries of regions of x foreground pixels on a binary image. x It is denoted by, be B
  8. DEFINITION ; x Dilation is the operation that combines two sets using vector addition of set elements. c=a+b for some a e A, be B}
  9. To delete or to reduce something Pixels matching a given pattern are deleted from the image. It is denoted by, AeB=ßlA -b beB
  10. DEFINITION : x Erosion is the operation that combines two sets using vector substraction of set elements. x Erosion is the morphological dual to dilation = {xe Z 21 for every be B, exist an a e A s.t.x=a—b} x+beA for every be B)
  11. PROPERTIES: DILATION 449B = BOA Commutative Associative AC(BCC) Extensivity if 0 e B, A A C B Dilation is increasing A c B implies A CD c BCD Translation Invariance Containment Decomposition of structuring element Linearity EROSION BOA not commutative not associative Extensivity if O e A Erosion is decreasing AcCimplies Translation Invariance Decomposition of structuring element Li nearity (BOC)
  12. EXAMPLE: ORIGINAL DILATED (a) (b) ERODED (c)
  13. Duality Relationship between erosion and dilation Dilation and Erosion transformation bear a marked similarity, in that what one does to image foreground and the other does for the image background. the reflection of B, is defined as Bez2 B = {xl for some b e B, x = —b} Erosion and Dilation Duality Theorem Similar but not identical to Demorgan rule in Boolean Algebra
  14. Open • An erosion followed by a dilation • It serves to elimi te noise Does not si Icantly change an object's size
  15. Close Dilation followed by erosion • Serves to close up cracks in objects and holes due to pepper noise Does not significantly ange object size
  16. Properties of Opening and Closing > Translation invariance >Antiextensivity of opening >Extensivity of closing > Duality AcA•B
  17. APPLICATIONS Fingerprint Feature Extraction Recognition of Handwriting Digits License Plate Detection Denoising using Morphological Filters Border Extraction & Text Extraction Detection of Imperfection in printed Circuit Boards
  18. Mathematical Morphology can be used for a variety of purposes, Entertainment Medical imaging Business and industry Military Civil Security Scientific analyses Digital image processing

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