Posted by
Rebecca Keller on
Oct 02, 2014; 6:48pm
URL: http://imagej.273.s1.nabble.com/Representing-Phases-and-Doing-Calculations-with-them-in-Images-tp5009868p5009874.html
Okay, sorry, let me be a little clearer: I've used Jay Unruh's excellent
plugin (I will never stop complimenting his amazing plugins!) for temporal
FFTs of timelapses, and since my signal is periodic and of known frequency
and phase, I can use that information to filter out tons of noise,
analogous to so-called "lock-in" amplifiers--manuscript in preparation, so
stay tuned if you're interested! Since to my knowledge there is no way to
"notch filter" the signal over time, I use the phase and amplitude values
(represented as images) at stimulus frequency from the Fourier stack to do
this (there are two other plugins to extract the amplitude and phase info
from the FFT stack). The problem is, however, that often the desired phases
are some arbitrary, non-zero value, which makes combination with the
amplitude information difficult. Ideally, I would like to be able to have
an image representing "phase difference from x" (where x is the signal
phase) to combine with the amplitude info, or approximately similarly,
shift the phase of my signal to, say, 0, and shift all other phases
accordingly.
JPK
On Thu, Oct 2, 2014 at 1:15 PM, Michael Schmid <
[hidden email]>
wrote:
> Hi Jacob,
>
> It is not really clear to me what you want: Filter the image with the
> phase?
>
> Then, one way might be converting the phase to two channels, sin(phase)
> and cos(phase).
> Then you can e.g. filter both the sin and cos channels, and use the atan2
> function to recover the phase from the two filtered images.
>
> Or do you just want to rotate the phase such that the 'typical' value is 0?
> Then take the average over the sin(phase) and cos(phase) values, use atan2
> on the result to get the 'typical phase', and subtract it from all phases.
> Thereafter loop through all pixels, subtract 2*pi from those above pi, and
> add 2*pi to those below -pi.
>
> Michael
> ________________________________________________________________
> On Oct 2, 2014, at 18:46, Rebecca Keller wrote:
>
> > Dear ImageJ Community,
> >
> > I've recently come across an interesting issue: representing phases an
> > image. I've got phase-images with ranges -pi to +pi radians, but the
> trick
> > is how to make this continuous range into a linear one. I.e., although
> the
> > phases (3.13 and -3.13) are actually very close in terms of phase, they
> are
> > far arithmetically, whereas (0.1 and -0.1) are just as close in phase but
> > are very close arithmetically. I am not sure how to combine the phases,
> > then, with non-cyclic information, like amplitude.
> >
> > My goal here is to use the phases as a filter, presumably simply by
> > multiplying by the corresponding amplitudes, but for this, the closeness
> in
> > phase to some given value should be represented by the values in the
> image,
> > perhaps with the set value being the maximum? I guess this is equivalent
> to
> > rotating the phases, such that the preferred value is at the "top" of the
> > circle? But I can't think how to do this mathematically in the images.
> >
> > All the best,
> >
> > Jacob Keller
>
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