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Chapter 9

Chapter 9. Morphological Image Processing. Preview. Morphology: denotes a branch of biology that deals with the form and structure of animals and plants. Mathematical morphology: tool for extracting image components that are useful in the representation and description of region shapes.

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Chapter 9

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  1. Chapter 9 Morphological Image Processing

  2. Preview • Morphology: denotes a branch of biology that deals with the form and structure of animals and plants. • Mathematical morphology: tool for extracting image components that are useful in the representation and description of region shapes. • Filtering, thinning, pruning.

  3. Scope • Will focus on binary images. • Applicable to other situations. (Higher-dimensional space)

  4. Set Theory • Empty set • Subset • Union • Intersection • Disjoint sets • Complement • Difference • Reflection of set B: • Translation of set A by point z=(z1,z2):

  5. Logic Operations • AND • OR • NOT

  6. Dilation • With A and B as sets in Z2, the dilation of A by B is defined as: • Or, equivalently, • B is commonly known as the structuring element.

  7. Illustration

  8. Example

  9. Erosion • With A and B as sets in Z2, the erosion of A by B is defined as: • Dilation and erosion are duals:

  10. Illustration

  11. Example: Removing image components

  12. Opening and Closing • Opening of set A by structuring element B: • Erosion followed by dilation • Closing of set A by structuring element B: • Dilation followed by erosion

  13. Opening • Opening generally smoothes the contour of an object, breaks narrow isthmuses, eliminate thin protrusions.

  14. Closing • Closing tends to smooth contours, fuse narrow breaks and long thin gulfs, eliminate small holes, fill gaps in the contour.

  15. Illustration

  16. Example

  17. Hit-or-Miss Transform • Shape detection tool

  18. Boundary Extraction • Definition:

  19. Region Filling • Beginning with a point p inside the boundary, repeat: with X0=p • Until Xk=Xk-1 • Conditional dilation

  20. Example

  21. Extraction of Connected Component • Beginning with a point p of the connected component, repeat: with X0=p • Until Xk=Xk-1 • The connected component Y=Xk

  22. Illustration

  23. Example

  24. Convex Hull • A set A is said to be convex if the straight line segment joining any two points in A lies entirely within A. • The convex hull H of an arbitrary set S is the smallest convex set containing S. • H-S is called the convex deficiency of S. • C(A): convex hull of a set A.

  25. Algorithm • Four structuring elements: Bi, i=1,2,3,4 • Repeat with X0i =A until Xki=Xk-1i to obtain Di • Theconvex hull of A is:

  26. Illustration

  27. Thinning • The thinning of a set A by a structuring element B is defined as:

  28. Illustration

  29. Thickening

  30. Skeleton

  31. Skeleton: Definition

  32. Illustration

  33. Pruning

  34. Extension to Gray-Scale Images • Dilation Max • Erosion Min

  35. Illustration

  36. Opening and Closing

  37. Smoothing and Gradient

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