Posted by
Herbie on
URL: http://imagej.273.s1.nabble.com/Hyperstack-with-nz-1-problem-tp5019980p5020062.html
Dear Kenneth,
we had this discussion before...
In short:
The answer is in signal theory, especially in signal discretisation,
vulgo sampling, and in signal reconstruction (from discrete signals).
The little areas or volumes you are referring to represent the easiest
or cheapest way of interpolation of discrete signals (reconstruction)
and of course, as we all know, it is not the correct way.
The issue in question is only indirectly related to this signal
theoretical fact and partly even a matter of taste. The way I've argued
is closely related to signal theory, favoring the sampling distances as
the essential entity because it is independent of the way discrete
signals are represented or displayed.
"do you consider a SINGLE pixel to be a 1x1 image?"
Of course it is not a discretisation of an image, it is number and as
such is not related to a (pictorial) signal, except it is known that it
was taken from a (spatially) discrete signal.
I don't insist on discussing this topic any further because this would
mean to rewrite the respective chapters of signal/l and systems theory.
The view of informatics or computer science may be different but not
necessarily correct.
(Because it appears important for you to mention your academic teaching
experience, I've been a university prof. in both fields, signal /
systems theory and informatics.)
Best
Herbie
:::::::::::::::::::::::::::::::::::::::::::
Am 09.02.18 um 22:57 schrieb Kenneth Sloan:
> I respectfully disagree.
>
> First, I think it's preferable to consider pixels as having area, and voxels as having volume (this view is supported by the display shown when images are zoomed). Indeed - this was usually part of the content in the first class meeting for every course in image processing (or raster graphics) that I taught over the course of 40 years.
>
> Second, I think it's preferable for it to be possible to view a slice as a volume which simply has zero extent in the z-direction. I'd actually prefer it to be considered to have some finite depth (when viewed as a volume) rather than 0.0, but, alas, there is no easy way to assign that finite depth. Once you have two slices, and a spacing between them, I prefer to think of each slice as having a finite depth (a slab, rather than a plane).
>
> Most of the time, it's reasonable to take the point of view that a pixel = a point (rather than an area) and a voxel = a point (rather than a volume), but I think it's preferable to ALLOW both points of view.
>
> I see nothing problematic about a 3d volume consisting of a single slice.
>
> If you think a pixel is a point - do you consider a SINGLE pixel to be a 1x1 image? or it that "not an image"?
>
> I, for one, would be pleased if ImageJ were to allow this point of view (A volume with x*y*1 voxels). But, for now, the answer for the OP is: ImageJ just doesn't allow that point of view. I think it's a deficiency.
>
>
> --
> Kenneth Sloan
>
[hidden email]
> Vision is the art of seeing what is invisible to others.
>
>
>
>
>
>> On 9 Feb 2018, at 12:03 , Herbie <
[hidden email]> wrote:
>>
>> Good day!
>>
>> "[...] so that ImageJ treats a single slice as a volume?"
>>
>> A slice is an image!
>>
>> A slice has no extension orthogonal to itself.
>> A pixel also has no extension in any direction because it is a mathematical
>> point in 2D, i.e. a number or sample value.
>> A voxel also has no extension in any direction because it is a mathematical
>> point in 3D, i.e. a number or sample value.
>>
>> Pixels, i.e. values at points in 2D, are arranged in a 2D grid and the
>> sometimes equidistant *spacing* of the grid points is often confused with
>> the pixel size, that actually doesn't exist.
>> (A pixel doesn't have a size.)
>>
>> Voxels, i.e. values at points in 3D, are arranged in a 3D grid and the
>> sometimes equidistant *spacing* of the grid points is often confused with
>> the voxel size, that actually doesn't exist.
>> (A voxel doesn't have a size.)
>>
>> In short:
>> A slice has no neighbors orthogonal to itself, i.e. there is no (defined)
>> spacing in the third dimension.
>>
>> That said, you may indeed use dummy slices to define the missing spacing!
>>
>> HTH
>>
>> Herbie
>>
>>
>>
>> --
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http://imagej.1557.x6.nabble.com/>>
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http://imagej.nih.gov/ij/list.html>
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