[iaihwt] [Up] [ialogfilter] Image Transformation

iaisdftsym
Check for conjugate symmetry

Synopsis

b = iaisdftsym( F )

Implemented in Python.

Input

F	Image. Gray-scale (uint8 or uint16) or binary image (logical). Complex image.

Output

Boolean.

Description

Verify if a complex array show the conjugate simmetry. Due to numerical precision, this comparison is not exact but with within a small tolerance (10E-4). This comparison is useful to verify if the result of a filtering in the frequency domain is correct. Before taking the inverse DCT, the Fourier transform must be conjugate symmetric so that its inverse is a real function (an image).

Examples

>>> import FFT, MLab

>>> print iaisdftsym(FFT.fft2d(MLab.rand(100,100)))

>>> print iaisdftsym(FFT.fft2d(MLab.rand(101,100)))

>>> print iaisdftsym(FFT.fft2d(MLab.rand(101,101)))

>>> print iaisdftsym(iabwlp([10,10], 8, 5))

>>> print iaisdftsym(iabwlp([11,11], 8, 5))

Equation

Source Code
        def iaisdftsym(F):
    from Numeric import asarray, Complex64, NewAxis, reshape, take, ravel, conjugate, alltrue
    F = (asarray(F)).astype(Complex64)
    if len(F.shape) == 1: F = F[NewAxis,:]
    global rows, cols
    (rows, cols) = F.shape
    (x, y) = iameshgrid(range(cols), range(rows))
    yx = iasub2ind(F.shape, y, x)
    aux1 = reshape(map(lambda k:k%rows, -ravel(y)), (rows, cols))
    aux2 = reshape(map(lambda k:k%cols, -ravel(x)), (rows, cols))
    myx = iasub2ind(F.shape, aux1, aux2)
    is_ = abs( take(ravel(F), yx) - \
          conjugate(take(ravel(F), myx)) ) < 10E-4
    b = alltrue(ravel(is_))
    return b
    
      

iadft	Discrete Fourier Transform.
iaidft	Inverse Discrete Fourier Transform.

iaisdftsym Check for conjugate symmetry