Spatial Filtering
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Transcript of Spatial Filtering
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5/19/2018 Spatial Filtering
1/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial Image Filtering
Some Basics
Dr Muhammad Sarim
http://find/ -
5/19/2018 Spatial Filtering
2/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)
http://find/ -
5/19/2018 Spatial Filtering
3/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.
http://find/ -
5/19/2018 Spatial Filtering
4/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.
http://find/ -
5/19/2018 Spatial Filtering
5/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.
http://find/ -
5/19/2018 Spatial Filtering
6/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.
Linear Filter
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5/19/2018 Spatial Filtering
7/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.
Linear Filter
A filter G is said to be linear if, for any two images f andh and any two scalars a and b,
G(af +bh) =aG(f) +bG(h). (1)
http://find/ -
5/19/2018 Spatial Filtering
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Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.
Linear Filter
A filter G is said to be linear if, for any two images f andh and any two scalars a and b,
G(af +bh) =aG(f) +bG(h). (1)
Filter responseIn general, linear filtering of an image f of size M Nwith a filter mask of size m n is given by the expression:
http://find/ -
5/19/2018 Spatial Filtering
9/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
2D Spatial image Filtering
Filter( Mask, Kernel, Window, Template.)A mathematical operation / function.Applied locally on an image.A 2D matrix.
Linear Filter
A filter G is said to be linear if, for any two images f andh and any two scalars a and b,
G(af +bh) =aG(f) +bG(h). (1)
Filter responseIn general, linear filtering of an image f of size M Nwith a filter mask of size m n is given by the expression:
h(x, y) =c
s=c
d
t=d
(s, t)f(x+s, y+t). (2)
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5/19/2018 Spatial Filtering
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Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Filter response
http://find/ -
5/19/2018 Spatial Filtering
11/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
12/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/http://goback/ -
5/19/2018 Spatial Filtering
13/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
14/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
15/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/http://goback/ -
5/19/2018 Spatial Filtering
16/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/http://goback/ -
5/19/2018 Spatial Filtering
17/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
18/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
19/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Box Filtering
http://find/ -
5/19/2018 Spatial Filtering
20/42
Image
Filtering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
http://find/ -
5/19/2018 Spatial Filtering
23/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
http://find/ -
5/19/2018 Spatial Filtering
24/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
P i
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
P i
http://find/ -
5/19/2018 Spatial Filtering
26/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
P i
http://find/ -
5/19/2018 Spatial Filtering
27/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
P ti
http://find/ -
5/19/2018 Spatial Filtering
28/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Practice
G i Filt
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Gaussian Filter
Weight contributions of neighboring pixels by nearness
G = 1
22e
x2+y2
22
(3)
Gaussian Vs Box Filter
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Gaussian Vs Box Filter
Gaussian Vs Box Filter
http://find/ -
5/19/2018 Spatial Filtering
31/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Gaussian Vs Box Filter
Important Properties
http://goforward/http://find/http://goback/ -
5/19/2018 Spatial Filtering
32/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Remove high-frequency components from the image(low-pass filter).
Important Properties
http://goforward/http://find/http://goback/ -
5/19/2018 Spatial Filtering
33/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Remove high-frequency components from the image(low-pass filter).
Images become more smooth.
Important Properties
http://goforward/http://find/http://goback/ -
5/19/2018 Spatial Filtering
34/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Remove high-frequency components from the image(low-pass filter).
Images become more smooth.
Convolution with self is another Gaussian.
Important Properties
http://goforward/http://find/http://goback/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Remove high-frequency components from the image(low-pass filter).
Images become more smooth.
Convolution with self is another Gaussian.
So can smooth with small-width kernel, repeat, and get
same result as larger-width kernel would have.
Important Properties
http://find/ -
5/19/2018 Spatial Filtering
36/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Remove high-frequency components from the image(low-pass filter).
Images become more smooth.
Convolution with self is another Gaussian.
So can smooth with small-width kernel, repeat, and get
same result as larger-width kernel would have.Convolving two times with Gaussian kernel of width issame as convolving once with kernel of width
2
Important Properties
http://find/http://goback/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Separable kernel.
Important Properties
http://find/ -
5/19/2018 Spatial Filtering
38/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Important Properties
Separable kernel.
Factors into product of two 1D Gaussians.
Important Properties
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
po ta t ope t es
Separable kernel.
Factors into product of two 1D Gaussians.
G = 1
22e
x2+y2
22
(4)
= 1
22e
x2
22
+
1
22e
y2
22
Separability Examples
http://find/ -
5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
p y p
Separabilitiy
http://find/ -
5/19/2018 Spatial Filtering
41/42
ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
p y
Why separability is useful?
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5/19/2018 Spatial Filtering
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ImageFiltering
Dr. Sarim
2D Spatial
image
Filtering
Box Filtering
Practice
Gaussian Filter
Gaussian Vs BoxFilter
ImportantProperties
SeparabilityExamples
Q & A
Q & A
http://find/