9 MORPHOLOGICAL IMAGE PROCESSING

Chih-Wei TangDepartment of Communication Engineering

National Central UniversityJhongLi, Taiwan

Outline• Preliminaries• Dilation and erosion• Opening and closing• Some basic morphological algorithms• Extensions to gray-scale images

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Basic Concepts from Set Theory

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• Sets: objects in an image• Set theory: the language of mathematical

morphology

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Translation and Reflection

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• They are extended from morphology but not found in basic texts on set theory.

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Outline

Preliminaries Dilation and erosion Opening and closing Some basic morphological algorithms Extensions to gray-scale images

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Translation

Use of Morphological Dilation for Bridging Gaps

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Use of Morphological Erosion for Removing Image Components

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Outline

Preliminaries Dilation and erosion Opening and closing Some basic morphological algorithms Extensions to gray-scale images

Opening and Closing• Opening

• smooth the contour of an object• breaks narrow isthmuses• eliminates thin protrusions

• Closing• smooth sections of contours• generally fuses narrow breaks and long thin gulfs• eliminates small holes• fills gaps in the contour

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Opening

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Closing

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Opening

Closing

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Use of Opening and Closing for Morphological Filtering

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Outline

Preliminaries Dilation and erosion Opening and closing Some basic morphological algorithms Extensions to gray-scale images

Boundary Extraction

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StructureElement

Erosion

Example – Boundary Extraction

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Region Filling

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Dilation

Complement

Example – Region Filling

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Extraction of Connected Components

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Converge!!!1 If kk XX

kXY Let

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Outline

Preliminaries Dilation and erosion Opening and closing Some basic morphological algorithms Extensions to gray-scale images

2-D Dilation

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• General effects• 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.

1-D Dilation

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Correct?

2-D Erosion

• General effects• 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.

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1-D Erosion

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Correct?

Dilation and Erosion on A Gray-Scale Image

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Gray-Scale Opening and Closing

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Gray-Scale Opening and Closing –Example

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