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# Chapter 9 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Chapter 9' - kylan-chan

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### Chapter 9

Morphological Image Processing

• 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.

• Will focus on binary images.

• Applicable to other situations. (Higher-dimensional space)

• Empty set

• Subset

• Union

• Intersection

• Disjoint sets

• Complement

• Difference

• Reflection of set B:

• Translation of set A by point z=(z1,z2):

• AND

• OR

• NOT

• 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.

• With A and B as sets in Z2, the erosion of A by B is defined as:

• Dilation and erosion are duals:

• Opening of set A by structuring element B:

• Erosion followed by dilation

• Closing of set A by structuring element B:

• Dilation followed by erosion

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

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

• Shape detection tool

• Definition:

• Beginning with a point p inside the boundary, repeat:

with X0=p

• Until Xk=Xk-1

• Conditional dilation

• Beginning with a point p of the connected component, repeat:

with X0=p

• Until Xk=Xk-1

• The connected component Y=Xk

• 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.

• 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:

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

• Dilation Max

• Erosion Min