Image Enhancement in Frequency Domain
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Transcript of Image Enhancement in Frequency Domain
© 2002-2003 by Yu Hen Hu 1ECE533 Digital Image Processing
Image Enhancement in Frequency Domain
© 2002-2003 by Yu Hen Hu 2ECE533 Digital Image Processing
Image and Its Fourier Spectrum
© 2002-2003 by Yu Hen Hu 3ECE533 Digital Image Processing
Filtering in Frequency Domain: Basic Steps
Basic Steps1. Multiply pixel f(x,y) of the
input image by (-1)x+y. 2. Compute F(u,v), the DFT3. G(u,v)=F(u,v)H(u,v)4. g1(x,y)=F-1{G(u,v)}5. g(x,y) = g1(x,y)*(-1)x+y
© 2002-2003 by Yu Hen Hu 4ECE533 Digital Image Processing
Notch Filter
The frequency response F(u,v) has a notch at origin (u = v = 0).
Effect: reduce mean value.
After post-processing where gray level is scaled, the mean value of the displayed image is no longer 0.
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vuvuF
© 2002-2003 by Yu Hen Hu 5ECE533 Digital Image Processing
Low-pass & High-pass Filtering
© 2002-2003 by Yu Hen Hu 6ECE533 Digital Image Processing
Gaussian Filters
Fourier Transform pair of Gaussian function
Depicted in figures are low-pass and high-pass Gaussian filters, and their spatial response, as well as FIR masking filter approximation.
High pass Gaussian filter can be constructed from the difference of two Gaussian low pass filters.
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© 2002-2003 by Yu Hen Hu 7ECE533 Digital Image Processing
Gaussian Low Pass Filters
D(u,v): distance from the origin of Fourier transform
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vuDvuH
© 2002-2003 by Yu Hen Hu 8ECE533 Digital Image Processing
Ideal Low Pass Filters
The cut-off frequency Do determines % power are filtered out.
Image power as a function of distance from the origin of DFT (5, 15, 30, 80, 230)
© 2002-2003 by Yu Hen Hu 9ECE533 Digital Image Processing
Effects of Ideal Low Pass Filters
Blurring can be modeled as the convolution of a high resolution (original) image with a low pass filter.
© 2002-2003 by Yu Hen Hu 10ECE533 Digital Image Processing
Ringing and Blurring
© 2002-2003 by Yu Hen Hu 11ECE533 Digital Image Processing
Butterworth Low Pass Filters
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© 2002-2003 by Yu Hen Hu 12ECE533 Digital Image Processing
Ideal high pass filter
Butterworth high pass filter
Gaussian high pass filter
High Pass Filters
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© 2002-2003 by Yu Hen Hu 13ECE533 Digital Image Processing
Applications of HPFs Ideal HPF
» Do = 15, 30, 80
Butterworth HPF» n = 2,» Do = 15, 30, 80
Gaussian HPF» Do = 15, 30, 80
© 2002-2003 by Yu Hen Hu 14ECE533 Digital Image Processing
Laplacian HPF 3D plots of the Laplacian
operator, its 2D images, spatial domain response
with center magnified, and Compared to the FIR mask
approximation
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