iabwlp

iabwlp
Low-Pass Butterworth frequency filter.

Synopsis

H = iabwlp( fsize, tc, n, option = 'circle' )

Implemented in Python.

Input

fsize	Image. Gray-scale (uint8 or uint16) or binary image (logical). Filter size: a col vector: first element: rows, second: cols, etc. uses same convention as the return of size.
tc	Double. Cutoff period.
n	Double. Filter order.
option	String. Filter options. Possible values: 'circle' or 'square'. Default: `'circle'`

Output

H	Image. Gray-scale (uint8 or uint16) or binary image (logical). DFT mask filter, with H(0,0) as (u,v)=(0,0)

Description

This function generates a frequency domain Low Pass Butterworth Filter with cutoff period tc and order n. At the cutoff period the filter amplitude is about 0.7 of the amplitude at H(0,0). This function returns the mask filter with H(0,0). As the larger the filter order, sharper will be the amplitude transition at cutoff period. The minimum cutoff period is always 2 pixels, despite of the size of the frequency filter.

Examples

Different filters

>>> H2_10 = iabwlp([100,100],2,10) # cutoff period: 2 pixels, order: 10

>>> iashow(iadftview(H2_10))

(100, 100) Min= 0 Max= 255 Mean=213.734 Std=73.38

>>> H4_1 = iabwlp([100,100],4,1) # cutoff period: 4, order: 1

>>> iashow(iadftview(H4_1))

(100, 100) Min= 76 Max= 255 Mean=154.060 Std=43.27

>>> H8_100 = iabwlp([100,100],8,100) # cutoff period: 8, order: 100

>>> iashow(iadftview(H8_100))

(100, 100) Min= 0 Max= 255 Mean=12.650 Std=55.11

>>> H4_1box = iabwlp([100,100],4,1,'square') # cutoff period: 4, order: 1

>>> iashow(iadftview(H4_1box))

(100, 100) Min= 117 Max= 255 Mean=168.055 Std=38.03


iadftview(H2_10)	iadftview(H4_1)	iadftview(H8_100)	iadftview(H4_1box)

Filtering example, cutoff period of 16 pixels, order 6

>>> import Numeric

>>> import FFT

>>> f = iaread('cookies.pgm')

>>> iashow(f)

(174, 314) Min= 16 Max= 205 Mean=94.752 Std=57.61

>>> F = FFT.fft2d(f)

>>> iashow(iadftview(F))

(174, 314) Min= 25 Max= 255 Mean=111.508 Std=15.92

>>> H = iabwlp(F.shape,16,6)

>>> iashow(iadftview(H))

(174, 314) Min= 0 Max= 255 Mean=3.996 Std=28.86

>>> G = F * H

>>> iashow(iadftview(G))

(174, 314) Min= 0 Max= 255 Mean=4.862 Std=23.62

>>> g = FFT.inverse_fft2d(G)

>>> g = abs(g).astype(Numeric.UnsignedInt8)

>>> iashow(g)

(174, 314) Min= 16 Max= 192 Mean=94.254 Std=56.85


f	iadftview(F)


iadftview(H)	iadftview(G)


g

Equation

Source Code

def iabwlp(fsize, tc, n, option='circle'):
    from Numeric import arange, sqrt, maximum, ravel, reshape
    import string
    def test_exp(x, y):
        try:
            return x**(2*y)
        except:
            return 1E300 # Infinito!
    rows, cols = fsize[0], fsize[1]
    mh, mw = rows/2, cols/2
    y, x = iameshgrid(arange(-mw,cols-mw), arange(-mh,rows-mh)) # center
    if string.find(string.upper(option), 'SQUARE') != -1:
        H=1./(1.+(sqrt(2)-1)*(maximum(abs(1.*x/rows) , abs(1.*y/cols))*tc)**(2*n))
    else:
        aux1 = ravel(sqrt(((1.*x)/rows)**2 + ((1.*y)/cols)**2)*tc)
        aux2 = 0.*aux1 + n
        aux = reshape(map(test_exp, aux1, aux2), x.shape)
        H=1./(1+(sqrt(2)-1)*aux)
    H=iafftshift(H)
    return H

iacos	Create a cossenoidal image.
iagaussian	Generate a 2D Gaussian image.
ialog	Laplacian of Gaussian image.

iabwlp Low-Pass Butterworth frequency filter.