http://imagej.273.s1.nabble.com/Hyperstack-with-nz-1-problem-tp5019980p5020068.html
contradictory to signal / systems theory. Personally, I find the
whole story, i.e. "signal discretization and reconstruction of the
be reconstructed from it. However, if one has sufficient discrete
the samples of each slice). If one calls this reconstruction "thickness
> Hi Herbie,
>
> I didn't dare to send this often-posted link for you, Kenneth or the other
> knowledgable people already discussing in this thread - I figured it could
> be a nice introduction to the discussed problem for the whole list. The
> argument made is along the line of your earlier statements about a pixel
> not having a surface or a slice not having a thickness. Sadly I don't read
> German to really understand if your underlying reasons or explanation
> differ from Alvy Ray Smith - in any case it's always interesting to learn
> more about the "philosophical" aspect of what we're dealing with every day.
>
> Best Regards,
>
> Christophe
>
> 2018-02-10 11:09 GMT+01:00 Herbie <
[hidden email]>:
>
>> Bonjour Christophe,
>>
>> thanks for chiming in and of course I know this paper. However and
>> although it is to the point, a more thorough view would be desirable.
>>
>> For those who read German, here is a link to an article written for those
>> who prefer thorough scientific explanations that require only moderate
>> mathematical knowledge:
>> <www.gluender.de/Writings/WritingsTexts/WritingsDownloads/20
>> 16_Diskretisierung.zip>
>>
>> Best
>>
>> Herbie
>>
>> ::::::::::::::::::::::::::::::::::::::::::::::::::
>> Am 10.02.18 um 10:47 schrieb Christophe Leterrier:
>>
>> Hi everyone,
>>>
>>> I think the discussion has reached the "post the Alvy Ray Smith paper"
>>> point:
>>>
https://news.ycombinator.com/item?id=8614159>>> "A Pixel Is Not A Little Square, A Pixel Is Not A Little Square, A Pixel
>>> Is
>>> Not A Little Square! (And a Voxel is Not a Little Cube)"
>>>
>>> As a biologist-microscopist I can't say I understand everything in it, but
>>> I got the part about pixels not being little squares :)
>>>
>>> Christophe
>>>
>>>
>>>
>>> 2018-02-10 10:11 GMT+01:00 Herbie <
[hidden email]>:
>>>
>>> Good day Fred,
>>>>
>>>> no problem with your statements. They are compatible with signal theory
>>>> (see my answer to Kenneth).
>>>>
>>>> Mathematical fact is that samples are numbers (or in RGB number triplets)
>>>> that have no spatial or temporal extension.
>>>>
>>>> If you consider the physical process of sampling, the question may arise
>>>> of how an extended little area, or in your tomographic case, an extended
>>>> little volume eventually leads to a number. The answer is easy:
>>>>
>>>> By spatial integration.
>>>>
>>>> Consequently, it is not the little integration area or the little
>>>> integration volume that is later (after pictorial or tomographic
>>>> reconstruction) displayed as little area or little volume. It is the
>>>> number
>>>> (gray value) that resulted from integration during signal acquisition
>>>> that
>>>> is smeared out or interpolated in some fashion on a display or by a
>>>> projector and presented as a light intensity.
>>>>
>>>> Of course the integration area or volume during signal acquisition may be
>>>> much larger than the sampling distance. In tomography (CT and MRI) this
>>>> is
>>>> not only the case regarding the z-direction but also, usually not as
>>>> pronounced, in the xy-directions. The classic example however, is the
>>>> flying spot scanner in which the spot represents the integration area and
>>>> the sampling distance may be chosen independently from the spot size.
>>>>
>>>> Hopefully I could clarify the topic a bit.
>>>>
>>>> Regards
>>>>
>>>> Herbie
>>>>
>>>> ::::::::::::::::::::::::::::::::::::::::
>>>> Am 10.02.18 um 02:54 schrieb Fred Damen:
>>>>
>>>> Greetings,
>>>>
>>>>>
>>>>> Beauty is in the eyes of the beholder... and my beauty is MRI.
>>>>>
>>>>> In MRI a slice is a 3D entity with length, width and depth -- which we
>>>>> call
>>>>> slice thickness. A voxel, i.e., volume element, represents a single
>>>>> value for
>>>>> a location in 3D space. Voxels are contiguous within the slice and
>>>>> depending
>>>>> on how data was collected may be contiguous in z also -- you can have
>>>>> what we
>>>>> call an interslice gap. In MRI there is no way to acquire a slice with
>>>>> infinitesimally thin slice thickness. Usually the slice thickness is
>>>>> more
>>>>> than twice that of the in-slice voxel size.
>>>>>
>>>>> Thanks for the info,
>>>>>
>>>>> Fred
>>>>>
>>>>> On Fri, February 9, 2018 11:03 am, Herbie 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
>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> Sent from:
http://imagej.1557.x6.nabble.com/>>>>>>
>>>>>> --
>>>>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>>>>
>>>>>>
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>>>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>>>
>>>>>
>>>>> --
>>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>>
>>>>
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