Re: Representing Phases and Doing Calculations with them in Images?

Posted by Saalfeld, Stephan on Oct 02, 2014; 7:39pm
URL: http://imagej.273.s1.nabble.com/Representing-Phases-and-Doing-Calculations-with-them-in-Images-tp5009868p5009876.html

This Beanshell script calculates the pixel-wise absolute radial
difference of a stack with two slices, each of them storing 32bit angle
values in radians in the range [-Pi, Pi], with ImageJ's built in image
calculators:


import ij.*;
import ij.process.*;
import java.lang.Math;

imp = IJ.getImage();
a = imp.getStack().getProcessor(1).convertToFloatProcessor();
b = imp.getStack().getProcessor(2).convertToFloatProcessor();

/* sort large values to b, small values to a */
c = a.duplicate();
a.copyBits(b, 0, 0, Blitter.MIN);
b.copyBits(c, 0, 0, Blitter.MAX);

/* b - a */
c = b.duplicate();
c.copyBits(a, 0, 0, Blitter.SUBTRACT);

/* a + PI - b */
d = a.duplicate();
d.add(2 * Math.PI);
d.copyBits(b, 0, 0, Blitter.SUBTRACT);

/* min */
d.copyBits(c, 0, 0, Blitter.MIN);

/* show */

new ImagePlus("radial difference", d).show();


Best,
Stephan



On Thu, 2014-10-02 at 14:48 -0400, Rebecca Keller wrote:

> 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
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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