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 Osobn? ?daje: Informace o zpracov?n? a ochran? osobn?ch ?daj? obchodn?ch partner? PRECHEZA a.s. jsou zve?ejn?ny na: https://www.precheza.cz/zasady-ochrany-osobnich-udaju/ | Information about processing and protection of business partner's personal data are available on website: https://www.precheza.cz/en/personal-data-protection-principles/ D?v?rnost: Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a podl?haj? tomuto pr?vn? z?vazn?mu prohl??en? o vylou?en? odpov?dnosti: https://www.precheza.cz/01-dovetek/ | This email and any documents attached to it may be confidential and are subject to the legally binding disclaimer: https://www.precheza.cz/en/01-disclaimer/ -------------- next part -------------- A non-text attachment was scrubbed... Name: particle.pdf Type: application/pdf Size: 43446 bytes Desc: particle.pdf URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20190220/59b4dc10/attachment.pdf>
On 2/21/19 12:16 AM, PIKAL Petr 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?This is fundamentally a stereology problem (or so it seems to me) and as such twists my head. Stereology is tricky and can be full of apparent paradoxes. "Generally speaking" it surely must be the case that larger particles have a larger probability of intersecting the complement of the window, but to say something solid, some assumptions would have to be made. I'm not sure what. To take a simple case: If the particles are discs whose centres are uniformly distributed on the window W which is an (a x b) rectangle, the probability that a particle, whose radius is R, intersects the complement of W is 1 - (a-R)(b-R)/ab for R <= min{a,b}, and is 1 otherwise. I think! (I could be muddling things up, as I so often do; check my reasoning.) This is an increasing function of R for R in [0,min{a,b}]. I hope this helps a bit. Should you wish to learn more about stereology, may I recommend:> @Book{baddvede05, > author = {A. Baddeley and E.B. Vedel Jensen}, > title = {Stereology for Statisticians}, > publisher = {Chapman and Hall/CRC}, > year = 2005, > address = {Boca Raton}, > note = {{ISBN} 1-58488-405-3} > }cheers, Rolf -- Honorary Research Fellow Department of Statistics University of Auckland Phone: +64-9-373-7599 ext. 88276
Okay, suppose the viewing field is circular and we consider two particles as in the attached image. Probability of being within the field: R0 > sqrt((x1+R1-x0)^2 + (y1+R1-y0)^2) Probability of being outside the field: R0 < sqrt((x2-R1-x0)^2 + (y2-R1-y0)^2) Since these are the limiting cases, it looks like the averaging I suggested will work. Jim On Thu, Feb 21, 2019 at 9:23 AM Rolf Turner <r.turner at auckland.ac.nz> wrote:> > On 2/21/19 12:16 AM, PIKAL Petr 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? > > This is fundamentally a stereology problem (or so it seems to me) and as > such twists my head. Stereology is tricky and can be full of apparent > paradoxes. > > "Generally speaking" it surely must be the case that larger particles > have a larger probability of intersecting the complement of the window, > but to say something solid, some assumptions would have to be made. I'm > not sure what. > > To take a simple case: If the particles are discs whose centres are > uniformly distributed on the window W which is an (a x b) rectangle, > the probability that a particle, whose radius is R, intersects the > complement of W is > > 1 - (a-R)(b-R)/ab > > for R <= min{a,b}, and is 1 otherwise. I think! (I could be muddling > things up, as I so often do; check my reasoning.) > > This is an increasing function of R for R in [0,min{a,b}]. > > I hope this helps a bit. > > Should you wish to learn more about stereology, may I recommend: > > > @Book{baddvede05, > > author = {A. Baddeley and E.B. Vedel Jensen}, > > title = {Stereology for Statisticians}, > > publisher = {Chapman and Hall/CRC}, > > year = 2005, > > address = {Boca Raton}, > > note = {{ISBN} 1-58488-405-3} > > } > > cheers, > > Rolf > > -- > Honorary Research Fellow > Department of Statistics > University of Auckland > Phone: +64-9-373-7599 ext. 88276 > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-------------- next part -------------- A non-text attachment was scrubbed... Name: particles.png Type: image/png Size: 2402 bytes Desc: not available URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20190221/52104c6a/attachment.png>