I am familiar with registax, but it is quite buggy. I will check out Giotto. And of course I will try the power spectrum measurement suggestions.
root, as being nonlinear. You may consider the power spectrum worse
> Ah, the square root jogs my memory, and of course all bets are off
> when you perform nonlinear functions. I really need to reread this
> stuff.
>
> The thermal distortion is the time variant warping you see when
> using a telescope in the daylight looking over land. A fluttering
> in the low Hertz (say 10Hz). A camera at a reasonable shutter speed
> (say 1/125 second) with multiple exposures records many images of
> the same target with different warping as the live image flutters.
>
> It seems like there should be a way to combine these images to get
> a more accurate image, that is the unwarped image.
>
> Now if the is not the case, I guess second best would be a motion
> flow scheme where the frame with the least motion would be picked.
> I essentially do this now by hand by picking the sharpest image.
>
> Failing those choices, is there a way to have imagej quantify the
> sharpness of an image, that is a measure of the highest frequency
> component in the FFT?
>
>
>
> -----Original Message-----
> From: Michael Schmid <
[hidden email]>
> Date: Fri, 23 Apr 2010 11:19:27
> To: <
[hidden email]>
> Subject: Re: FFT averaging
>
> Hi Gary,
>
> according to the Wikipedia site, a periodogram plots the square root
> of the power spectrum, not the real and imaginary values. So it is a
> nonlinear operation, and there is a difference between averaging
> before and after the 'periodgram' operation.
>
> Thermal distortion - I am not sure that I understand you correctly.
> Do you have thermal drift of the image, and you want to register the
> images and then average over them? In that case, I'd use one of the
> image registration plugins. Registration via the Fourier domain works
> best in case of a uniform background (such as images of planets with
> a black background in astronomy; the program Registax is designed for
> this and uses the Fourier transform for registration). Otherwise you
> have to get rid of edge effects; a smooth window function will be
> helpful, but not full solve the problem.
>
> Michael
> ________________________________________________________________
>
> On 23 Apr 2010, at 05:31, gary wrote:
>
>
>> Ok. Thanks to both of you.
>>
>> I guess I have to dust off my Oppenhein and Schafer. Still I have
>> to wonder why periodograms are averaged in the frequency domain if
>> the time domain would work as well.
>>
>> What I was wondering is would stacking FFTs of images of one target
>> that contain thermal distortion would yield a sharper image, but if
>> the operation is linear in either domain, then this is a dead end
>> to explore. I know that stacking where parts of the image have
>> wiggled will just create a blur at those spots.
>>
>> Incidentally, I had some issues getting imagej working on my
>> windows 7 64 bit machine. It worked fine under X64. No big deal
>> since I have a few linux boxes at my disposal and it is trivial to
>> run imagej under linux. [The are not many multiplatform programs
>> where linux is the easiest port!] I suspect a permission problem
>> with windows 7 since it bombed when trying to write the
>> configuration file.
>>
>> On 4/22/2010 8:10 PM, Robert Dougherty wrote:
>>
>>> Gary,
>>>
>>> I agree with Bob (the other Bob), as long as what you want to
>>> average is the original images on the one hand and the complex FFT
>>> (or the FHT) on the other hand. Averaging and transforming are
>>> both linear operations, so it does not matter what order you do
>>> them in: average(transform(images)) = transform(averages
>>> (images)). There are types of processing in which you want to
>>> average the power spectra of the various images. (At least there
>>> are times you want to do this in regular signal processing of a
>>> Short Time Fourier Transform. I'm not sure when it applies in
>>> image processing.) Squaring to get the power spectra levels is a
>>> nonlinear operation, so it would not work to average the images
>>> first in this case.
>>>
>>> Bob D.
>>>
>>> On Apr 22, 2010, at 4:50 PM, Gary Sellani wrote:
>>>
>>>
>>>> Are you positive? This wouldn't work in the one dimensional case.
>>>> -----Original Message-----
>>>> From: Bob<
[hidden email]>
>>>> Date: Thu, 22 Apr 2010 17:21:41
>>>> To:<
[hidden email]>
>>>> Subject: Re: FFT averaging
>>>>
>>>> Average the images first, then do the FFT. Yes, you will get the
>>>> same
>>>> result, regardless of the order of the two operations.
>>>>
>>>>
>>>> --------------------------------------------------
>>>> From: "gary"<
[hidden email]>
>>>> Sent: Thursday, April 22, 2010 4:53 PM
>>>> To:<
[hidden email]>
>>>> Subject: FFT averaging
>>>>
>>>>
>>>>> I did a search on the list archive and fft yielded nothing,
>>>>> something I
>>>>> seriously doubt is the case. I used
>>>>>
https://list.nih.gov/cgi-bin/wa.exe>>>>>
>>>>> In any event, I can use Imagej to take the FFT of an image
>>>>> without issue.
>>>>> Both the "FFT window" and "complex FFT" work. But what I'd like
>>>>> to do is
>>>>> to average a few FFTs of some images, then take the inverse of
>>>>> that
>>>>> result.
>>>>>
>>>>> You can put the "FFT Window" images into a stack, but it just
>>>>> saves the 2D
>>>>> magitude, so when you average the slices, the result cannot be
>>>>> put through
>>>>> the inverse FFT.
>>>>>
>>>>> Using the complex FFT, I cam create a stack of real and a stack of
>>>>> imaginary, average each stack individually, but then the inverse
>>>>> FFT
>>>>> doesn't recognize it as a complex image.
>>>>>
>>>>>
>>>
>>> Robert Dougherty, Ph.D.
>>> President, OptiNav, Inc.
>>> 4176 148th Ave. NE
>>> Redmond, WA 98052
>>> (425)891-4883
>>> FAX (425)467-1119
>>> www.optinav.com
>>>
[hidden email]
>>>