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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.

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chapter 9

Chapter 9

Morphological Image Processing

preview
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
Scope
  • Will focus on binary images.
  • Applicable to other situations. (Higher-dimensional space)
set theory
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
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
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 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
  • Opening generally smoothes the contour of an object, breaks narrow isthmuses, eliminate thin protrusions.
closing
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
Hit-or-Miss Transform
  • Shape detection tool
region filling
Region Filling
  • Beginning with a point p inside the boundary, repeat:

with X0=p

  • Until Xk=Xk-1
  • Conditional dilation
extraction of connected component
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
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
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
Thinning
  • The thinning of a set A by a structuring element B is defined as:
extension to gray scale images
Extension to Gray-Scale Images
  • Dilation Max
  • Erosion Min
ad