On Jul 17, 11:57 am, "stefanba...@[EMAIL PROTECTED]
" <stefanba...@[EMAIL PROTECTED]
>
wrote:
> 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 =3D> 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.
One correction: my statement above is an accurate if assume that
=93original signal=94 means the density-scalar field before digitizing; CT
data is one of such examples of digitized scalar field.
> > 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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