ITK
4.10.0
Insight Segmentation and Registration Toolkit
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#include <itkAnalyticSignalImageFilter.h>
Generates the analytic signal from one direction of an image.
This filter generates the complex valued analytic signal along one direction of an image. This input is a real valued image, and the output is a complex image.
The analytic signal is given by
f_a(x) = f(x) - i f_H(x)
Where i is the square root of one and f_H(x) is the Hibert transform of f(x).
Since the Hilbert transform in the Fourier domain is
F_H(k) = F(k) i sign(k),
f_a(x) is calculated by
f_a(x) = F^{-1}( F(k) 2 U(k) )
where U(k) is the unit step function.