# [R] particle count probability

Jim Lemon drj|m|emon @end|ng |rom gm@||@com
Wed Feb 20 22:43:57 CET 2019

```Hi Petr,
This is off the top of my head, but I assume that the shape of the
particle is not considered in counting. Assume particles are uniformly
distributed in the viewing field. If all particles entirely within the
field are counted, large particles will be undercounted. If all
particles within or intruding on the field are counted, large
particles will be overcounted. I do not have an analytic proof of
this, but the average of the two counts may provide a true count.

Hi Roger,
The Wicksell problem looks fascinating, although I don't think it
solves Petr's problem. I will study it further.

Jim

On Wed, Feb 20, 2019 at 10:34 PM Roger Koenker <rkoenker using illinois.edu> wrote:
>
>
> Somewhere, buried in the vast literature on the Wicksell problem, there is probably an answer, or at least a hint.
>
> > On Feb 20, 2019, at 11:16 AM, PIKAL Petr <petr.pikal using precheza.cz> wrote:
> >
> > Dear all
> >
> > Sorry, this is probably the most off-topic mail I have ever sent to this help list. However maybe somebody could point me to right direction or give some advice.
> >
> > In microscopy particle counting you have finite viewing field and some particles could be partly outside of this field. My problem/question is:
> >
> > Do bigger particles have also bigger probability that they will be partly outside this viewing field than smaller ones?
> >
> > Saying it differently, although there is equal count of bigger (white) and smaller (black) particles in enclosed picture (8), due to the fact that more bigger particles are on the edge I count more small particles (6) than big (4).
> >
> > Is it possible to evaluate this feature exactly i.e. calculate some bias towards smaller particles based on particle size distribution, mean particle size and/or image magnification?
> >
> > Best regards
> > Petr Pikal
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