http://imagej.273.s1.nabble.com/Hyperstack-with-nz-1-problem-tp5019980p5020067.html
be a nice introduction to the discussed problem for the whole list. The
not having a surface or a slice not having a thickness. Sadly I don't read
> 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>>>>>
>>>>>
>>>>> --
>>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>>
>>>>
>>>> --
>>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>>
>>>
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>> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html>>
>>
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