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

Posted by Rebecca Keller on Oct 02, 2014; 10:10pm
URL: http://imagej.273.s1.nabble.com/Representing-Phases-and-Doing-Calculations-with-them-in-Images-tp5009868p5009880.html

Hah! Awesome! Thanks so much Stephan--this ought to do it! If I understand
the code right (I've never used beanshell) you're taking the minimum of the
two distances around the phase circle, correct? If so, very elegant!

But there is one thing:

I'd like to enter a value for the phase manually, such as 0.726, then find
phase differences from this value. I could use your code, but need to make
an image with all pixels at this value, I guess, which I don't know how to
do--never had to do this weird sort of thing. I figured out a clever
(kludgy) way to make one, but there must be some simple way to make an
image with appropriate constant pixel value. Alternatively, I guess the
code could be modified to just take a constant value instead of the second
image, but I am not sure how to modify this correctly. I will take a shot
at it if I don't hear from you.

It would be really cool to have a little dial or slider which would
calculate this on the fly (pixel-wise phase difference between phase image
and reference phase), but I am not sure who would really use it besides me!

All the best, and thanks a lot for this!

Jacob





On Thu, Oct 2, 2014 at 3:39 PM, Stephan Saalfeld <[hidden email]
> wrote:

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