9 Morphological Image Processing Angela Chih-Wei Tang Department of Communication Engineering National Central University JhongLi, Taiwan 2009 Fall
9 Morphological Image Processing
Angela Chih-Wei Tang
Department of Communication Engineering
National Central University
JhongLi, Taiwan
2009 Fall
Outline
� Preliminaries
� Dilation and erosion
� Opening and closing
� Some basic morphological algorithms
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 2
� Some basic morphological algorithms
� Extensions to gray-scale images
Basic Concepts from Set Theory� Sets: objects in an image
� Set theory: the language of mathematical
morphology
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 33
Translation and Reflection
� They are extended from morphology but not
found in basic texts on set theory
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 9
Outline
� Preliminaries
� Dilation and erosion
� Opening and closing
Some basic morphological algorithms
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 10
� Some basic morphological algorithms
� Extensions to gray-scale images
Use of Morphological Erosion for
Removing Image Components
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 14
Outline
� Preliminaries
� Dilation and erosion
� Opening and closing
Some basic morphological algorithms
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 15
� Some basic morphological algorithms
� Extensions to gray-scale images
Opening and Closing
� Opening: smooth the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions
� Closing: smooth sections of contours, but it
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 16
� Closing: smooth sections of contours, but it generally fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour
Use of Opening and Closing for
Morphological Filtering
20C.E., NCU, Taiwan 20Angela Chih-Wei Tang, 2009
Outline
� Preliminaries
� Dilation and erosion
� Opening and closing
Some basic morphological algorithms
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 21
� Some basic morphological algorithms
� Extensions to gray-scale images
Extraction of Connected Components
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�Converge!!!
1 If
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kXY =⇒ Let
Outline
� Preliminaries
� Dilation and erosion
� Opening and closing
Some basic morphological algorithms
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 27
� Some basic morphological algorithms
� Extensions to gray-scale images
2-D Dilation
� General effects:
� If all the values of the structuring
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 28
� If all the values of the structuring
element are positive, the output image
tends to be brighter than the input
� Dark details either are reduced or
eliminated, depending on how their
values and shapes relate to the
structuring element used for dilation
2-D Erosion
� General effects
If all the elements of the structuring
C.E., NCU, Taiwan Angela Chih-Wei Tang, 2009 30
� If all the elements of the structuring
element are positive, the output image
tends to be darker than the input image
� The effect of bright details in the input
image that are smaller in area than the
structuring element is reduced