Differences between revisions 7 and 8
 ⇤ ← Revision 7 as of 2006-08-04 17:46:02 → Size: 1900 Editor: penczek Comment: ← Revision 8 as of 2007-06-20 16:46:39 → ⇥ Size: 1893 Editor: bmb24 Comment: Deletions are marked like this. Additions are marked like this. Line 6: Line 6: output = filt_btwo(input, low, high, value) params = filt_btwo(e, freql, freqh, value) Line 9: Line 9: par1:: input image (can be either real or Fourier)    par2:: low - stop-band frequency    par3:: high - pass-band frequency    par4:: value - value of the filter at zero freqeuncy e:: input image (can be either real or Fourier)    freql:: low - stop-band frequency    freqh:: high - pass-band frequency    value:: value of the filter at zero freqeuncy Line 17: Line 17: out1:: output - filtered image. Output image is real when input image is real or Fourier when input image is Fourier params:: output - filtered image. Output image is real when input image is real or Fourier when input image is Fourier

# Name

filt_btwo - Butterworth homomorphic Fourier filter

# Usage

params = filt_btwo(e, freql, freqh, value)

## Input

e
input image (can be either real or Fourier)
freql
low - stop-band frequency
freqh
high - pass-band frequency
value
value of the filter at zero freqeuncy
• Numerical parameters are (unless otherwise noted) in [:absolute_frequency_units:absolute frequency units] `f_a` and their valid range is ]0:0.5].

## Output

params
output - filtered image. Output image is real when input image is real or Fourier when input image is Fourier

# Method

Fourier transform of the input image is multiplied by a radially symmetric filter:

• `1-(1-value)**B(f)`

• where `B(f)` is the Butterworth filter

• `B(f) = 1.0/sqrt(1.0+(f/(RAD))^(ORDER))`

Value of ORDER determines the filter falloff and RAD corresponds to the cut-off frequency. RAD and ORDER are calculated from the parameters specified by the user using following equations:

• `ORDER = [2*log((eps)/sqrt(a^2-1))]/[log((low)/(high))]`

• `RAD = (low)/((eps)^(2/(ORDER)))`

where low and high are the pass-band and stop-band frequencies, respectively, and parameters eps and a are set to 0.882 and 10.624, respectively. Note values of the filter B(f) deviate from 1.0 at frequency low by about 0.2 and from 0.0 at frequency high by about 0.09 (for a low-pass filter.)

# Reference

Gonzalez, R. F., Woods, R. E., 2002. Digital Image Processing. Prentice Hall, Upper Saddle River, NJ.

Pawel A. Penczek

category 1
FILTER
category 2
FOURIER

filter.cpp

# Maturity

stable
works for most people, has been tested; test cases/examples available.

# Bugs

None. It is perfect.

filt_btwo (last edited 2013-07-01 13:12:56 by localhost)