iadftexamples

The DFT of a constant image is a single point at F(0,0), which gives the sum of all pixels in the image.

>>> import Numeric, FFT

>>> f = 50 * Numeric.ones((10, 20))

>>> F = FFT.fft2d(f)

>>> aux = F.real > 1E-5

>>> r, c = iaind2sub([10, 20], Numeric.nonzero(Numeric.ravel(aux)))

>>> print r

[0]

>>> print c

[0]

>>> print F[r[0],c[0]]/(10.*20.)

(50+0j)

The DFT of a square image is a digital sync.

>>> f = Numeric.zeros((128, 128))

>>> f[63:63+5,63:63+5] = 1

>>> iashow(f)

(128, 128) Min= 0 Max= 1 Mean=0.002 Std=0.04

>>> F = FFT.fft2d(f)

>>> Fv = iadftview(F)

>>> iashow(Fv)

(128, 128) Min= 0 Max= 255 Mean=73.791 Std=59.51


f	Fv

The DFT of a pyramid is the square of the digital sync.

>>> f = Numeric.zeros((128, 128))

>>> k = Numeric.array([[1,2,3,4,5,6,5,4,3,2,1]])

>>> k2 = Numeric.matrixmultiply(Numeric.transpose(k), k)

>>> f[63:63+k2.shape[0], 63:63+k2.shape[1]] = k2

>>> iashow(f)

(128, 128) Min= 0 Max= 36 Mean=0.079 Std=1.14

>>> F = FFT.fft2d(f)

>>> Fv = iadftview(F)

>>> iashow(Fv)

(128, 128) Min= 0 Max= 255 Mean=51.718 Std=59.31


f	Fv

The DFT of a Gaussian image is a Gaussian image.

>>> f = iagaussian([128,128],[65,65],[[3*3,0],[0,5*5]])

>>> fn = ianormalize(f,[0,255])

>>> iashow(fn)

(128, 128) Min= 0.0 Max= 255.0 Mean=1.467 Std=13.60

>>> F = FFT.fft2d(f)

>>> Fv = iadftview(F)

>>> iashow(Fv)

(128, 128) Min= 0 Max= 255 Mean=3.168 Std=20.45


fn	Fv

The DFT of an impulse image is an impulse image.

>>> f = iacomb((128,128), (4,4), (0,0))

>>> fn = ianormalize(f, (0,255))

>>> iashow(fn)

(128, 128) Min= 0.0 Max= 255.0 Mean=15.938 Std=61.73

>>> F = FFT.fft2d(f)

>>> Fv = iadftview(F)

>>> iashow(Fv)

(128, 128) Min= 0 Max= 255 Mean=0.249 Std=7.97


fn	Fv

iadftexamples
Demonstrate the DFT spectrum of simple synthetic images.