http://imagej.273.s1.nabble.com/Hyperstack-with-nz-1-problem-tp5019980p5020066.html
thanks for chiming in and of course I know this paper. However and
<www.gluender.de/Writings/WritingsTexts/WritingsDownloads/2016_Diskretisierung.zip>
> 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>>>
>>>
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