On Jul 16, 9:14 am, "Science.Medical.Imaging List"
<pixel.to.l...@[EMAIL PROTECTED]
> wrote:
> On Jul 16, 1:37 am, Mauro <mauro.ita...@[EMAIL PROTECTED]
> wrote:
>
> > Hi all,
> > I would like to understand better the idea of frequency (in the
> > spatial domain) of an image in relation with an imaged object. Is the
> > frequency measured in pixels/cm or cm/pixels?
> > Mainly becuase I would like to see whether the Nyquist frequency is
> > satisfied over an imaged object in a 3d volume (CT).
>
> > thanks,
> > Mauro
>
> Mauro,
>
> There can be several ways of estimating the frequency of a signal.
> Take a simple case of a 1 dimensional signal, a finite ****tion of
> which has been digitized (sampled along equal intervals using some
> spread function). Also, lets assume you know that width of the finite
> ****tion in some spatial units, lets say cm.
>
> In this case, then, the frequency of the signal as estimated in the
> digitized spatial domain will be: (number of pixels in digitized
> signal / length in cm of the signal ****tion).
>
> Meaning, higher the number of pixels in the 1D image, the finer you
> sampled over the original signal => higher frequency.
>
> To ensure your sampling method is using at least a Nyquist frequency
> or higher, you will first need to know the frequency of the original
> signal. Then you will nede to make sure you sample it enough times
> (enough pixels) that will capture even the finest detail in the signal
> that would occur in the smalles relative spatial region.
It is not so straightforward. It is correct only for Classification
Interpolation (CI) and if lighting does not use scalar field
gradients. It is plainly wrong for IC and lighting with original
gradients.
> For a 3D CT case, I assume you are talking about resampling an already
> digitized image data. Is that correct? If so, you will need to find
> out the highest frequency of a feature that you dont want to lose in
> the image after resampling. If the image is not isotropic (has
> different frequency along three dimensions), you will need to repeat
> this for all three directions and get the highest frequency of all for
> simplicity. Then you will need to make sure the frequency of the
> resampling kernel is higher than the Nyquist rate, given the highest
> frequency.
>
> Hope this helps.
>
> [http://groups.google.com/group/medicalimagingscience/web/smiviewer-
> download-page]
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