IN both the regular and irregular case, you are making strong
assumptions about the 3rd dimension.
Your idea of slicing into discs seems reasonable (and directly
expresses your assumptions).
Here's another idea: you can easily compute the AREA of your
perimeter curve. In your sample picture, it
also seems reasonable to estimate a length and a width for the
object. Given these three numbers, you
can produce a perimeter somewhere between an ellipse and a
rectangle. I'd probably look at super-quadrics to do this.
Compute the volume of this object.
I would first try very simple (and possibly very wrong) versions of
estimating width and height. My first attempt would be to find the
major axis, call that the length, and find the width perpendicular to
that axis. This would tend to underestimate the length of an
irregular object, but overestimate the width (I'm assuming these
objects would be elongated ellipsoids except for the kinks in the
medial axis). I suspect that these two errors might cancel each
other out.
Clearly, ANY of these methods (even the one you use on "regular"
perimeters) will require lots of validation.
If my cheap tricks are good enough (as shown by validation), then
perhaps you can stop there.
If not, my next attempt would be to find a polyline describing the
axis of the perimeter (to estimate a length) and examine the width
perpendicular to that axis. Again, you have a length, width, and
area - generate a prototypical 3D object and use its volume.
Next, I might try constructing a generalized-cylinder representation
of the object (again, assuming that cross-sections perpendicular to
the axis look like discs) and integrating cross-sectional area along
the axis (a curve). There are two reasons I don't want to go here
first: a) it's difficult to do, b) there are problems in regions
where the axis has a very small radius of curvature.
Finally...I'll as if you *really* need "volume". Even in the easiest
cases, your volume estimates depend on assumptions that might not be
justified. Can you answer the higher-level questions using area
instead of volume?
And then...it occurs to me that "length" may not be necessary. I
suspect that area and width (measured somewhere in the middle of the
object) are sufficient to estimate the volume. But, this probably
does not allow you to tell the difference between ellipsoids and
cylinders.
I hope this helps.
On Mar 27, 2009, at 10:01 AM, Zottel wrote:
> Hi
>
> I was wondering if someone has any good ideas to the following
> problem:
> I do perimter measurements of liquid filled ojects. The general
> shape of the object varies between cylinder-like and oblate
> spheroid, but the perimeter line is irregular (first picture).
> The question now: Is there any plug-in around or does anyone have
> an idea how to get the best estimate for a volume of an object by
> it's perimeter?
> My idea of how this could work is to "stretch out" the irregular
> perimeter line to resemble e.g. a cylinder (of which it is easy to
> calculated volume from width and length).
> Or maybe have "slice" it into a number of discs and then sum up
> their volume?
>
> We did establish an equation already that calculates the volume
> fairly well when the object has sort of a regular shape (as in the
> second picture), but that equation grossly overestimated volume for
> very thin and elongated objects.
>
> I would be very grateful for any hints on how this could be done in
> a smart way...
>
> Thanks a lot
> /Daniel
>
>
>
> --
> View this message in context:
http://n2.nabble.com/Volume-
> calculation-by-perimeter-possible--tp2544704p2544704.html
> Sent from the ImageJ mailing list archive at Nabble.com.
--
Kenneth Sloan
[hidden email]
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