[vtkusers] bounds argument in vtkBox::IntersectWithLine()

[David Gobbi]

On Thu, Mar 19, 2015 at 7:38 AM, Maarten Beek <beekmaarten at yahoo.com> wrote:

> But voxels of a CT (MRI) image cannot be considered infinitesimal thin,
> can they?
>

Er.. well, yes, they can be.  The data that makes up a CT image can be
considered to be a set of point samples of a continuous function.  The
"continuous function" is generally the underlying "true image" convolved
with the detector response.  The detector response might have some "natural
width", though it's always more of a distribution (e.g. the slice
profile).  But after the image has been discretized, a single slice in
isolation really does not have any thickness.  You could look at the
full-width half-maximum of the slice profile and say that the "real" slice
(as opposed to its discrete representation) has a certain thickness.  But
even then, that thickness unlikely to be exactly equal to the slice spacing.

Here is another way that I look at it, again considering the digital image
to be a discrete sampling of a continuous function.  If you want to
estimate the continuous function (i.e. the "real" image) from your discrete
samples, you do so by interpolating between the samples.  By definition,
you cannot interpolate in the region beyond the samples (that would be
extrapolation, which is another name for "wandering off into the unknown").

The one time where I find it useful to break this rule is when the image is
displayed with nearest-neighbor interpolation (otherwise known as "draw
each sample point as a solid-colored rectangle").  But even then, it should
be understood that only the inside half of each border pixel is being
interpolated.  The outside half is actually an extrapolation.

I'm rambling a bit here.  In summary, I generally consider individual
slices to be infinitesimally thin, unless the problem that I'm working on
requires me to consider the slice profile of the image acquisition system.
But the slice profile rarely figures into the visualization of the data.

 - David
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