Posted by
Herbie on
URL: http://imagej.273.s1.nabble.com/Hyperstack-with-nz-1-problem-tp5019980p5020063.html
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
>>
>>
>>
>> --
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http://imagej.nih.gov/ij/list.html>>
>
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