Chapter 9

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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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### 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.
• Filtering, thinning, pruning.
Scope
• Will focus on binary images.
• Applicable to other situations. (Higher-dimensional space)
Set Theory
• Empty set
• Subset
• Union
• Intersection
• Disjoint sets
• Complement
• Difference
• Reflection of set B:
• Translation of set A by point z=(z1,z2):
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.
Erosion
• With A and B as sets in Z2, the erosion of A by B is defined as:
• Dilation and erosion are duals:
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
Opening
• Opening generally smoothes the contour of an object, breaks narrow isthmuses, eliminate thin protrusions.
Closing
• Closing tends to smooth contours, fuse narrow breaks and long thin gulfs, eliminate small holes, fill gaps in the contour.
Hit-or-Miss Transform
• Shape detection tool
Region Filling
• Beginning with a point p inside the boundary, repeat:

with X0=p

• Until Xk=Xk-1
• Conditional dilation
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
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.
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:
Thinning
• The thinning of a set A by a structuring element B is defined as:
Extension to Gray-Scale Images
• Dilation Max
• Erosion Min