On Jul 17, 12:05=A0pm, "stefanba...@[EMAIL PROTECTED]
" <stefanba...@[EMAIL PROTECTED]
>
wrote:
> 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
t=
he
> > > > 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
signa=
l
> > > 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;
C=
T
> data is one of such examples of digitized scalar field.
>
>
>
> > > For a 3D CT case, I assume you are talking about resampling an
alread=
y
> > > 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
fo=
r
> > > 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]- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
What you say is a special case where one would want to estimate
optical properties from image information, with an additional
assumption that the image data, in some form, depicts the density of
the material imaged (for direct volume rendering of CT data for
example).
The original post does not say anything about rendering, hence my
reply was very general, focussed only on resampling of an already
digitized signal.
Your point taken, however, for the special case in VR where you would
want to interpolate first then classify.
Anyways, its just a matter of what you treat as 'original' data, and
how you measure the accuracy of resampling. The basic concept behind
'sample a signal enough to retain high frequency features' remains the
same.. theres nothing more to it. Its up to us if/how we have to
complicate its interpretation based on our needs.
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