Morphological Image Processing - PowerPoint Presentation

Slide1

Morphological Image Processing

By

Dr. Rajeev SrivastavaSlide2

What is Morphology?Slide3

DefinitionSlide4
Slide5

The filters can be described using set theoretic notation . A set is a collection of pixels in the context of an image.Slide6

Morphological OperationsSlide7

OperationsSlide8

Let A and B be sets. If a is the index of a pixel in A, then we write

If a is not in A we write

If every element that is in A is also in B then A is a subset of B, written

This is equivalent to the

statement

.

 Slide9

In the morphological dilation and erosion operations, the state of any given pixel in the output image is determined by applying a rule to the corresponding pixel and its neighbors in the input image.

The rule used to process the pixels defines the operation as a dilation or an erosion. Slide10

Operation

Rule

Dilation

The value of the output pixel is the maximum value of all the pixels in the input pixels neighborhood. In

a binary image, if any of the pixels is set to the value 1, the output pixel is set to 1

Erosion

The value of the output pixel is the minimum value of all the pixels in the input pixels neighborhood. In

a binary image, if any of the pixels is set to the value 0, the output pixel is set to 0

The table lists the rules for both dilation and erosion.Slide11

Dilation

It can be applied to binary as well as grey-scale images

Effect of this operator on a binary image is , it gradually increases the boundaries of the region, while the small holes in image becomes smaller

Assume that A and B are two set of pixels, then the dilation of A by B is denoted by

 Slide12

It means that A is translated by every point of the set B.

Dilation can be considered as a union operation of all the translations of the image A caused by the elements specified in the structuring element B

 Slide13

Erosion

The objective of erosion is to make an object smaller by removing its outer layer of pixels.

This operator takes the image and structuring element as inputs and thins the object

 Slide14

Algorithms for dilation and erosion

Let the number of pixels in structuring element be k

Let the number of pixels of value 1 in the input image be z

Let the pixel coordinates beneath the origin of the structuring element be (

)

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For dilation, the output is given by

For erosion, the output is given by

These algorithms can also be extended to modified dilation and erosion, which involves the use of a threshold m.

The threshold is user-controlled, based on the requirement

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Modified dilation and erosion

The algorithm for dilation can be modified using the threshold value m

The mapping functions are given by

For modified erosion, the mapping function is given by

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An another approach to morphological operations is to consider them as binary correlation operations involving logical elements

The structuring element is placed on a binary imageSlide18

Properties of dilation and erosion

The dilation and erosion shows the following properties

Communicative property

Associative property

Distributive property

Duality property

Translation property

Decomposition propertySlide19

Combining Dilation and Erosion

Opening and ClosingSlide20

Opening and Closing Operations

The opening is defined as erosion followed by a dilation operator

The opening operation satisfies the following properties

1)

This is called idempotent property

Opening is useful for smoothing the edges, breaking the narrow joints and thinning the protrusions that are present in the image

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Closing is a dilation operation followed by an erosion operation

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Properties of Opening and Closing

They show the following properties

Dual transformation

Ordering relationship

Increasing transformation

Transform invariance

Idempotence

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Hit-or-Miss transform

It is a general binary morphological operation that can be used to look for particular patterns of fore-G and background pixels of an image

The algorithm is as shown below

Translate the

centre

of the structuring element to all the points of the input image

Compare the structuring element with the image pixelsSlide24

If there is a complete match, then

the pixel underneath the structuring element is set to foreground, its called a hit.

Else

the pixel underneath the structuring element is set to background color, its called a missSlide25

Uses of morphological operations

They are immensely useful in a variety of imaging applications which are discussed as…

Boundary extraction

Noise removal

Thinning

Thickening

Convex hull

Skeletonization

Medical axis transform and distance transform

Region filling

Extraction of connected component

PruningSlide26

Grey-Scale Morphology

Similar to binary morphological operations, the mask moves across the image

The pixel-by-pixel process is done and the resultant is produced in the output image.

The structuring element can be a square matrix of size 3*3, 5*5, or larger depending upon the applicationSlide27

The erosion mask is shown as

 Slide28

Comparison of grey-scale

erosion and dilation

Erosion

Dilation

Reduces the size of the objects

wrt

. background

Increases the six=

ze

of the objects

Eliminates noise spikes and ragged edges

It also eliminates noise spikes and ragged edges

Darkens the bright objects

Brighten the objects

Increases the size of holes and sharpen

cornersConnects objects, bridge gaps,smoothenes edges, fill holes and creates outline in an imageSlide29

The

morphological gradient highlights sharp transitions in the input image. It depends less on edge directionality than the

Sobel

operator and is useful for locating faint but large scale structures. The morphological gradient is defined by

,

 Slide30

Gradient…

It is thus the difference between a dilated image and an eroded image. Dilation removes small scale dark features and erosion removes small scale bright features. Dilation brightens the image and erosion darkens it.