Morphological Image Processing. Chapter 9

Mirroring of an object
In asymmetric structure elements we don’t use the original structure element we mirror it around it’s origin.

Mirroring of an object

Mirroring of an object
This is the structure element will be used.

Mirroring of an object
In symmetric structure elements it will not matter to mirror or not.

We have 2 main morphological operations
Dilation Erosion
The rule is:
if the structure element has at least one pixel of binary 1, the origin will be 1
The rule is:
if the structure element has at least one pixel of binary 0, the origin will be 0. The structure element should be totally contained inside the body to give 1 at the origin.

For simplicity we imagine a moving origin on the boundary of the body and the whole structure element to be changed
Dilation Erosion
The rule is:
The origin moves on boundary and the structure element draw ones.
The rule is:
The origin moves on boundary and the structure element draw zeros.

Dilation Erosion
Dilating point ? structure element
Eroding a body with an structure element of the same shape ? point

Dilate
Object Structure
Element
Mirroring of Symmetric object, gives the same object.

Dilate
Structure
Object Element
Mirroring of Symmetric object, gives the same object.

Erode
Object Structure
Element
Mirroring of Symmetric object, gives the same object.

Structure
Object Element
Mirroring of Symmetric object, gives the same object.
Erode

Find object of size 15 “max size”
1- erode by structure element 15, will give pixel 1 at the origin of objects 15, and zero otherwise.

Find object of size 15 “max size”
2- dilate by structure element 15, will retrieve the objects of size 15.

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Open and Close
Open:
Erode first then Dilate.
Close:
Dilate first then Erode.

open
1- Erode

open
2- Dilate

Close
1- Dilate

Close
2- Erode

Hit or Miss
We want to identify specific object.
Make a structure element with the same shape of the required object,
Erode the image with the structure element,
The required object and bigger will be replaced by 1 pixel at the origin.
Complement the image , complement the structure element,
Erode the inverted image with the inverted structure element.

Image
Hit or Miss
Structure element
×
a
a
We want elements of cross of ones with 4 zeros at the corners not this
Output No.1

Image complement
Hit or Miss
Structure element
×
a
a
Here we will check the 4 zeros at the corners
Image
Structure element
complement
a
a
a
Output No.2

Hit or Miss
Anding the 2 output images
a
a

Hit or Miss
Find X
Erode by X
Complement
Erode by (W-X)
W is one pixel bigger than X in all directions

Hit or Miss
While eroding Z the structure element hit the gap of X creating the L shape

Boundary Extraction
Eroding an object by small structure element then substitute the original image – the result of erosion will give you the boundary of the object.
Erode by B
Anded with complement of the result of the prev. step

Region Filling
It needs many iterations to be done.
Starting by point inside the region, dilate with cross structure element (+) , And the output with the complement of original image.
Starting point
Complement

Dilate
Anding

Dilate
Anding

Dilate
Anding

Dilate
Anding

Dilate
Anding

Dilate
Anding

Dilate
Anding

The last 2 iterations are the same ? stop
Dilate
Anding

The Result is the union of the region fill and the boundary

Extraction of Connected Component
It needs many iterations to be done.
Starting by point inside the component, dilate with square structure element , And the output with the original image.
Select a starting point on the component

Extraction of Connected Component
Dilate
Anding

Extraction of Connected Component
Dilate
Anding

Extraction of Connected Component
After many iterations we will get this shape

Extraction of Connected Component
By dilating this shape then anding this shape with the original image we will get the same shape.
The last 2 iterations are the same ? stop

Fully contained will not erase

Not fully contained

Not fully contained

Not fully contained

(c) Only Non overlapping particles:
Hit or miss

(a) Only of particles that have merged with boundary of the image
1- make a boundary of the image.
2- And the image with the boundary.
3- Extract Connected Component by expansion starting with this seed.

(b) Only Overlapped particles:
Original Image – the 2 previous results , such that the image only contain 3 types of particles:
Overlapped.
non overlapped.
On boundary.