Morphological Image Processing - PowerPoint PPT Presentation

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Morphological Image Processing

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Convex Hull ... The convex hull H of an arbitrary set S is the smallest convex set containing S. ... C(A): convex hull of a set A. Algorithm. Four structuring ... – PowerPoint PPT presentation

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Title: Morphological Image Processing


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 X0p
  • Until XkXk-1
  • Conditional dilation

20
Example
21
Extraction of Connected Component
  • Beginning with a point p of the connected
    component, repeat
  • with X0p
  • Until XkXk-1
  • The connected component YXk

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, i1,2,3,4
  • Repeat
  • with X0i A until XkiXk-1i to obtain Di
  • The convex 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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