Digital Image Processing Morphological Image Processing.

luguangm@gmail.com

Digital Image Processing

Morphological Image Processing

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What Is Morphology?

Presented by J. Serra in 1964.Morphological image processing (or morphology)

describes a range of image processing techniques that deal with the shape (or morphology) of features in an image

The basic ideal of Morphology is to use a special structuring element to measure or extract the corresponding shape or characteristics in the input images for further image analysis and object recognition.

The mathematical foundation of morphology is the set theory.

In this chapter, the input images are binary images.

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0, 1, Black, White?

Throughout all of the following slides whether 0 and 1 refer to white or black is a little interchangeable

All of the discussion that follows assumes that images are made up of 0s for background pixels (off pixels) and 1s for object pixels (foreground=on pixels)

After this it doesn’t matter if 0 is black, white, yellow, green…….

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A is a set, if a=(a1,a2) is an element of A, then,

aAIf not, then, aA

: null (empty) set

Typical set specification: C={w|w=-d, for d D}

Basic Concepts of Set Theory

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A subset of B: AB

Union of A and B: C=AB

Intersection of A and B: D=AB

Disjoint sets: AB=

Complement of A: Ac={w|wA}

Difference of A and B:

A-B={w|wA, wB}=A Bc

Basic Concepts of Set Theory

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Basic Concepts of Set Theory

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Logic Operations involving Binary Image

The principal logic operations AND OR and NOTPerform on a pixel by pixel basis

Basic Concepts of Set Theory

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Basic Concepts of Set Theory

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Structuring Elements, Hits, Fits, & Missing

B

AC

Structuring Element

Fit: All on pixels in the structuring element cover on pixels in the imageHit: Any on pixel in the structuring element covers an on pixel in the imageMiss: no pixel in the structuring element covers an on pixel in the image

All morphological processing operations are based on these simple ideas

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Structuring Elements

Structuring elements can be any size and make any shapeHowever, for simplicity we will use rectangular structuring elements with their origin at the middle pixel

1 1 1

1 1 1

1 1 1

0 0 1 0 0

0 1 1 1 0

1 1 1 1 1

0 1 1 1 0

0 0 1 0 0

0 1 0

1 1 1

0 1 0

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Fitting, Hitting, &Missing

0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 0 0 0

0 0 1 1 1 1 1 0 0 0 0 0

0 1 1 1 1 1 1 1 0 0 0 0

0 1 1 1 1 1 1 1 0 0 0 0

0 0 1 1 1 1 1 1 0 0 0 0

0 0 1 1 1 1 1 1 1 0 0 0

0 0 1 1 1 1 1 1 1 1 1 0

0 0 0 0 0 1 1 1 1 1 1 0

0 0 0 0 0 0 0 0 0 0 0 0

B C

A

1 1 1

1 1 1

1 1 1Structuring Element 1

0 1 0

1 1 1

0 1 0Structuring Element 2

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Fundamental Operations

Fundamentally morphological image processing is very like spatial filtering

The structuring element is moved across every pixel in the original image to give a pixel in a new processed image

The value of this new pixel depends on the operation performed

There are two basic morphological operations: erosion and dilation

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Dilation

Dilation of image f by structuring element s is given by f sThe structuring element s is positioned with its origin at (x, y) and the new pixel value is determined using the rule:

otherwise 0 hits s if 1),( fyxg

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Dilation Example

Structuring Element

Original Image Processed Image

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Dilation Example

Structuring Element

Original Image Processed Image With Dilated Pixels

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}])ˆ[(|{ AABxBA x B is the structuring element in dilation.

Dilation

})ˆ[(|{ ABxBA x

Dilation:B is often called the “structuring element”Process consists of obtaining the reflection of B,

about its originThen shifting this reflection, B, by xThe dilation of A by B is the set of all x,

displacements such that B and A overlap by at least one element

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Dilation Example

Structuring Element

Original Image Processed Image

B̂B

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Dilation Example

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What Is Dilation For?

Dilation can repair breaks

Dilation can repair intrusions

Watch out: Dilation enlarges objects