Topic 8 - Image Filtering - II

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Topic 8 - Image Filtering - II
Department of Physics and Astronomy
DIGITAL IMAGE PROCESSING Course 3624
Professor Bob Warwick
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8. Image Filtering II - Fourier Domain Filtering
Filtering is the suppression or enhancement of
particular spatial frequency components in a
dataset.
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Types Of Fourier Domain Filter
(i) LOW-PASS FILTERS -- Noise
Suppression (high freq. suppression, low freq.
enhancement) (ii) HIGH-PASS FILTERS - Edge
enhancement/detection (low freq. suppression,
high freq. enhancement) (iii) BAND-STOP FILTERS
- Interference Suppression (mid-frequency
suppression)
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8.1 Low-Pass Filters
In many applications the noise has a much wider
frequency spread than the signal. For example in
1-d
Signal
White noise
In these circumstances an effective method of
noise suppression is to apply a low-pass Fourier
domain filter
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Types of Low-Pass Filters
(a) Rectangular or "Top-Hat" Filter
But this type of filter introduces both
BLURRING and RINGING!
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The Top-Hat Filter
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The Gaussian Filter
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8.2 High-Pass Filters
Abrupt edges and/or sharp boundaries of objects
generally produce most of the high frequency
signal in the image. It follows that to sharpen
an image it is necessary to enhance the high
frequency components. Types of HIGH-PASS
FILTER (a) Rectangular (b)
Trapezoidal (c) Gaussian
H(u)
u
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The High-Pass Filter
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High-Pass Filtering Example
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8.3 Band-Stop Filtering
Band-stop filters are used to suppress
interference signals in a specific frequency
range
Band-Stop Filtering Example I
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Band-Stop Filtering Example II
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8.4 Equivalent Filters
The effect of a spatial domain filter can be
investigated by considering the equivalent
Fourier domain filter (and vica-versa).
Consider the 1-d case of an N element image
spatially filtered with 1 x 3 mask. The first
step is to pad out the mask with N-3 zeros.
Example 1-d Smoothing Filter
1 1 1 ? 1 1 1 0 0 0 0 0
.. Then
In the Fourier domain the smoothing filter has a
low-pass response (rather as expected)
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Equivalent Filters cont.
Example 3 1-d Laplacian operator -1 2 -1
? -1 2 -1 0 0 0 0 0 .. Then
Scale Phase Amplitude Factor Terms
Response
A high-pass response
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2-D Equivalent Filters
For a 2-D spatial filter, the equivalent Fourier
domain filter can be calculated as
If the 2-d filter is separable, then the same
result can be achieved by the application of two
1-d filters
Example 1
Example 2