Applies an exponential frequency domain filter to a frequency domain image. The effect is to convolve a filter with the image in the spatial domain. The frequency domain representation of the filter is as follows:
H(u,v) = Alpha + Beta *
exp {Gamma*[(a11 u + a12 v)2 + (a21 u + a22 v)2 ]}


H( )   = transfer function of the filter
u,v    = 2D frequency coordinates
Alpha  = high frequency asymptote
Beta   = decay coefficient
Gamma  = exponential decay coefficient
Eccent = Eccentricity of equal contours of the filter
         in the frequency domain
Theta  = angle in degrees of the filter's orientation
xSize  = x dimension of the source image
ySize  = y dimension of the source image
sigmaL = 1.0 / sqrt (1.0 -(Eccent*Eccent))
sigmaS = 1.0
phi    = 0.017453 * Theta
a11    =  sigmaS * cos(phi) / xSize
a12    =  sigmaS * sin(phi) / ySize
a21    = -sigmaL * sin(phi) / xSize
a22    =  sigmaL * cos(phi) / ySize

The input must be a frequency domain image in the packed format produced by the ForwardFFTImg module (see format description in ForwardFFTImg documentation). The Fourier transformation and the cross correlation are discussed in:

Digital Image Processing, Gonzales, R.C., Wintz, P., Addison Wesley, Second Edition, 1987, pp 61--137.


Port: Img In
Type: Lattice
Constraints: 1..3-D
Source frequency domain image.


Port: Alpha
Type: Dial
Alpha constant value.

Port: Beta
Type: Dial
Beta constant value.

Port: Gamma
Type: Dial
Gamma constant value.

Port: Eccent
Type: Dial
Eccent constant value.

Port: Theta
Type: Dial
Theta constant value.


Port: Img Out
Type: Lattice
Constraints: 1..3-D
Filtered frequency domain image.



ForwardFFTImg, InverseFFTImg, FourierGaussFltImg.
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© The Numerical Algorithms Group Ltd, Oxford UK. 2000