Morphological Image ProcessingMorphological Image Processing

Dr.U.S.N.Raju

Morphology

•The word morphology commonly denotes a branch of biology that

deals with the form and structure of animals and plants.

•We use the same word here in the context of mathematical

morphology as a tool for extracting image components that are

useful in the representation and description of region shape, such as

boundaries, skeletons, and the convex hull.

•We are also interested in morphological techniques for pre- and

post processing, such as morphological filtering, thinning and

pruning.

From now onwards, it begins a transition from a focus on

purely image processing methods, whose input and output are

images, to processes in which the inputs are images, but the

outputs are attributes extracted from those images.

Common Usages include Edge detection, Noise removal, Image enhancement and Image segmentation.

Forcing shapes onto region edges

To count regions (or granules in morphological terms)

To estimate sizes of regions (or granules).

Applications of Morphology

The language of mathematical morphology is set theory.

All are binary images

Binary images may contain numerous imperfections. In

particular, the binary regions produced by simple thresholding

are distorted by noise and texture.

Morphological image processing pursues the goals of removing

these imperfections by accounting for the form and structure of

the image. These techniques can be extended to gray scale

images.

•Binary Morphology

•Gray Level Morphology

Dilation(⊕)

Erosion( )

Basic Morphological operations:

Morphological operations on Binary images

For a binary image, white pixels are normally taken to

represent foreground regions, while black pixels denote

background. (Note that in some implementations this

convention is reversed)

Binary Dilation:

The basic effect of the operator on a binary image is to

gradually enlarge the boundaries of regions of foreground pixels

(i.e. white pixels, typically). Thus areas of foreground pixels

grow in size while holes within those regions become smaller.

It will ‘Expand’ the image.

Binary Dilation:

Template: 1 1 1 1 1 1 1 1 1

Original Image Dilated Image

There are many specialist uses for dilation. For instance it

can be used to fill in small spurious holes (`pepper noise')

in images. The image

Common Names: Dilate, Grow, Expand

Erosion:

The basic effect of the operator on a binary image is to

erode away the boundaries of regions of foreground

pixels (i.e. white pixels, typically). Thus areas of

foreground pixels shrink in size, and holes within those

areas become larger.

Binary Erosion: Template: 1 1 1 1 1 1 1 1 1

Original Image Eroded Image

Erosion can also be used to remove small spurious

bright spots (`salt noise') in images. The image

Common Names: Erode, Shrink, Reduce

Results of Binary Dilation and Erosion:Original Image Dilated Image

Eroded Image

The other Binary Morphological Operations are:

•Opening

•Closing

•Boundary extraction

•Region filling

•Connected components

•Hit-or-miss

•Thinning

•Thickening

•Skeletons

The basic effect of an opening is somewhat like erosion in that

it tends to remove some of the foreground (bright) pixels from

the edges of regions of foreground pixels. However it is less

destructive than erosion in general. As with other

morphological operators, the exact operation is determined by a

structuring element. The effect of the operator is to preserve

foreground regions that have a similar shape to this structuring

element, or that can completely contain the structuring element,

while eliminating all other regions of foreground pixels.

Opening:

The opening of image I by using sub image (structuring

element T) is

I T= (I T) ⊕ T

i.e. opening is nothing but erosion followed by dilation.

Binary Opening: Template: 1 1 1 1 1 1 1 1 1

Original Image Opening Image

Common Names: Opening

The image shown below is a binary image containing a

mixture of circles and lines.

Suppose that we want to separate out the circles from

the lines, so that they can be counted. Opening with a

disk shaped structuring element 11 pixels in diameter

gives

The image shown below is a binary image containing a

mixture of circles and lines.

Suppose that we want to separate out the circles from

the lines, so that they can be counted. Opening with a

disk shaped structuring element 11 pixels in diameter

gives

Suppose that this time we wish to separately extract the

horizontal and vertical lines. The result of an opening with

a 3×9 vertically oriented structuring element is shown in

Closing:

Closing is similar in some ways to dilation in that it tends to

enlarge the boundaries of foreground (bright) regions in an

image (and shrink background color holes in such regions),

but it is less destructive of the original boundary shape. The

effect of the operator is to preserve background regions that

have a similar shape to this structuring element, or that can

completely contain the structuring element, while eliminating

all other regions of background pixels.

Closing:

The opening of image I by using structuring element T is

I T= (I ⊕ T) T

i.e. opening is nothing but dilation followed by erosion.

Binary Closing: Template: 1 1 1 1 1 1 1 1 1

Original Image Closing Image

Common Names: Closing

Closing can sometimes be used to selectively fill in

particular background regions of an image. Whether or not

this can be done depends upon whether a suitable

structuring element can be found that fits well inside

regions that are to be preserved, but doesn't fit inside

regions that are to be removed.

The image shown below is an image containing

large holes and small holes.

If it is desired to remove the small holes while retaining the

large holes, then we can simply perform a closing with a

disk-shaped structuring element with a diameter larger than

the smaller holes, but smaller than the large holes. The

image is the result of a closing with a 22 pixel diameter disk.

Note that the thin black ring has also been filled in as a

result of the closing operation.

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Original Binary Image Structuring Element

Boundary Extraction: β(A)=A- (A B)

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Boundary Extraction: β(A)=A- (A B)

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Original Binary Image Structuring Element

A B Boundary of Image: β(A)

Boundary Extraction: β(A)=A- (A B)

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Hole Filling:

Extraction of Connected Components:

Extraction of Connected Components:

Extraction of Connected Components:

Region (or) Hole filling:

Apply connected components labeling to an image counting problem.

Solution:• Starting from produce a suitable binary image (i.e. threshold the image).

• And then apply connected components labeling with the aim of obtaining a distinct label for each penguin. (Note, this may require some experimentation with threshold values.)

Reflection

Duality of Dilation and Erosion w.r.t. set complement and reflection

Duality of Opening and Closing w.r.t. set complement and reflection

Skeletonization:

(a) Is the result using square structuring element. (b) Is the result using cross structuring element.

Reconstruction

The hit-and-miss transform is a general binary morphological

operation that can be used to look for particular patterns of

foreground and background pixels in an image.

It is actually the basic operation of binary morphology since

almost all the other binary morphological operators can be

derived from it.

As with other binary morphological operators it takes as input

a binary image and a structuring element, and produces another

binary image as output.

Hit-or-Miss /Hit-and-Miss :

If the foreground and background pixels in the structuring

element exactly match foreground and background pixels in

the image, then the pixel underneath the origin of the

structuring element is set to the foreground color. If it doesn't

match, then that pixel is set to the background color.

The structuring element used in the hit-and-miss is a slight

extension to the type that has been introduced

for erosion and dilation, in that it can contain both foreground

and background pixels, rather than just foreground

pixels, i.e. both ones and zeros.

Note that the simpler type of structuring element used with

erosion and dilation is often depicted containing both ones and

zeros as well, but in that case the zeros really stand for `don't

care's', and are just used to fill out the structuring element to a

convenient shaped kernel, usually a square. In all our

illustrations, these `don't care's' are shown as blanks in the

kernel in order to avoid confusion.

As usual we denote foreground pixels using ones, and

background pixels using zeros.

The hit-and-miss operation is performed in much the same

way as other morphological operators, by translating the

origin of the structuring element to all points in the image, and

then comparing the structuring element with the underlying

image pixels. If the foreground and background pixels in the

structuring element exactly match foreground and background

pixels in the image, then the pixel underneath the origin of the

structuring element is set to the foreground color. If it doesn't

match, then that pixel is set to the background color.

Four structuring elements used for corner finding in

binary images using the hit-and-miss transform. Note

that they are really all the same element, but rotated by

different amounts.

After obtaining the locations of corners in each orientation,

We can then simply ‘OR’ all these images together to get the

final result showing the locations of all right angle convex

corners in any orientation.

Figure shows the effect of this corner detection on a simple

binary image.

The operations of erosion, dilation, opening, closing,

thinning and thickening can all be derived from the hit-and-

miss transform in conjunction with simple set operations.

Figure 4 illustrates some structuring elements that can be

used for locating various binary features.

Figure : Some applications of the hit-and-miss transform. 1 is used to locate isolated points in a binary image.

2 is used to locate the end points on a binary skeleton Note that this structuring element must be used in all its

rotations so four hit-and-miss passes are required. 3a and 3b are used to locate the triple points (junctions) on

a skeleton. Both structuring elements must be run in all orientations so eight hit-and-miss passes are required.

The 1-valued elements make up the domain of SE1, the -1-valued elements make up

the domain of SE2, and the 0-valued elements are ignored (don’t cares).

Thinning:

Thickening:

Convexhull

Hit or miss: used for image pattern matching and marking

Thinning- structured erosion using image pattern matching

Thickening-structured dilation using image pattern matching

Skeletonization/ Medial Axis Transform: finding skeletons of binary regions

Gray level morphology

Gray Level Dilation:

Original Image

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Dilated Image

Gray Level Erosion:

Original Image

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Eroded Image

Opening and Closing:

Opening suppresses the bright details smaller than the specified SE and Closing suppresses the dark details.

Some basic gray-scale morphological Algorithms:

Morphological Smoothing

Morphological gradient

Top-hat and Bottom-hat transformations

Granulometry

Textural Segmentations

Morphological Smoothing

Morphological Gradient

Top-hat transformation

Result of Grey Level Dilation:

Result of Grey Level Dilation:

Result of Grey Level Erosion:

Result of Grey Level Erosion:

The other gray level morphological operations are :

•Opening•Closing•Morphological smoothing•Morphological Gradient•Top-hat transformation

Opening:

The opening of image I by using sub image (structuring element T) is

I T= (I T) ⊕ T

i.e. opening is nothing but erosion followed by dilation.

Opening operation decreases the sizes of small, bright details with no appreciable effect on the darker gray levels.

Result of Opening:

The opening of image I by using sub image (structuring element T) is

I T= (I ⊕ T) T

i.e. opening is nothing but dilation followed by erosion.

Closing operation decreases the sizes of small, dark details with relatively little effect on the bright features.

Closing:

Result of Closing:

Opening Vs Closing

After opening After closing

Morphological Smoothing:

(I T) T

•It remove or attenuate both bright and dark artifacts or noise.

Results of Morphological Smoothing:

Before After

Morphological Gradient:

Morphological gradient of an image is defined as,

g= (I⊕T)- (I T)

the morphological gradient highlights sharp gray level transformations in the input image.

Result of Morphological Gradient:

Top-Hat Transformation:

( )TIIh −=The top-hat transformation of an image denoted by h, is defined as,

This is useful for enhancing detail in the presence of shading.

Result of Top-Hat Transformation: