Questions about equations of Shape Descriptors

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Questions about equations of Shape Descriptors

 Hello, I think I'm asking trivial questions again, but I better be sure about this. http://rsbweb.nih.gov/ij/docs/menus/analyze.html says: *Round* (roundness): 4*area/(π*sqr(major axis)), or the inverse of the aspect ratio. So... does area in this equation mean "area of best fit ellipse" ? I suppose it does, as we're talking about "major axis" in the denominator. Also, does sqr mean pow(major axis, 2) aka (major axis)^2 ? In that case, how'd you write square root? Regards, Ákos
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Re: Questions about equations of Shape Descriptors

 On Thursday 25 February 2010 21:10:46 you wrote: > http://rsbweb.nih.gov/ij/docs/menus/analyze.html says: > > *Round* (roundness): 4*area/(π*sqr(major axis)), or the inverse of the > aspect ratio. > > So... does area in this equation mean "area of best fit ellipse" ? No, it is area of the blob, which in IJ is the number of pixels. Note that other plugins (such as the particles8 and 4 plugins) compute area differently than IJ, and so the result values might not be exactly the same. > suppose it does, as we're talking about "major axis" in the denominator. Major axis, here means "maximum Feret diameter" of the blob. > Also, does sqr mean pow(major axis, 2) aka (major axis)^2 ? > In that case, how'd you write square root? pow (n, 2) is n^2. sqrt(n) is the square root of n, see the macro functions. G.
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Re: Questions about equations of Shape Descriptors

 On 25 February 2010 23:34, Gabriel Landini <[hidden email]> wrote: > On Thursday 25 February 2010 21:10:46 you wrote: > > http://rsbweb.nih.gov/ij/docs/menus/analyze.html says: > > > > *Round* (roundness): 4*area/(π*sqr(major axis)), or the inverse of the > > aspect ratio. > > > > So... does area in this equation mean "area of best fit ellipse" ? > > No, it is area of the blob, which in IJ is the number of pixels. > Note that other plugins (such as the particles8 and 4 plugins) compute area > differently than IJ, and so the result values might not be exactly the > same. > > Ok, thank you, that sounds reasonable. However... > Major axis, here means "maximum Feret diameter" of the blob. > Then it's either very misleading, or even worse, not true at all. For Aspect ratio, the site says: *AR* (aspect ratio): major axis/minor axis. Enable "Fit Ellipse" in *Analyze>Set Measurements* to have the major and minor axis displayed. As far as I know, AR is calculated by the other way around: minor/major. Or am I false here again? I'm aware of the thing that it simply shows how elongated the area I measure, and it only has real relevance if I have predefined axis's which I compare to,  but somehow eg. 3:4 is just doesn't feel the same like 4:3. > > Also, does sqr mean pow(major axis, 2) aka (major axis)^2 ? > > In that case, how'd you write square root? > > pow (n, 2) is n^2. > sqrt(n) is the square root of n, see the macro functions. > Umm... are we exactly sure that circularity is 4π*area/sqr(perimeter) ? Because http://www.ncbi.nlm.nih.gov/pubmed/17933272 tells me circularity is: 4π*area/(perimeter)^2 which is != 4π*area/sqr(perimeter) ! Another misleading thing for me: if AR is calculated from the fit ellipse axis's (either way why would the descriptin say  **Enable "Fit Ellipse" in *Analyze>Set Measurements* to have the major and minor axis displayed), why does it say "major axis" again in * Round* (roundness): 4*area/(π*sqr(major axis)), or the inverse of the aspect ratio. ? To be exactly sure, I've double checked with graphical experiment, and Feret diamater is != Major axis of best fit ellipse. I hope it's not only my brain that can't add things up here, sorry if I'm annoying or too much incomprehent. Regards, Ákos
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Re: Questions about equations of Shape Descriptors

 The area of an irregular roi, and that its of best-fitting ellipse, are the same (so are their moments of inertia). Unfortunately, the equation >> roundness = 4*area/(π*sqr(major axis)) has slipped into the documentation ages ago. It is correct, but it simply says:  roundness = minor/major. The "sqr" in the above equation does mean "square" (though it's not macro syntax). Major axis and max Feret diameter are not the same. The best-fitting ellipse is a much more robust measurement than the Feret diameter, as all pixels inside an object are taken into account, not only the perimeter pixels. Norbert Vischer
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Re: Questions about equations of Shape Descriptors

 Hello, On 26 February 2010 01:39, Norbert Vischer <[hidden email]> wrote: > The area of an irregular roi, and that its of best-fitting ellipse, are the > same (so are their moments of inertia). > > > The "sqr" in the above equation does mean "square" (though it's not macro > syntax). > So I can assume "square" here truly means x^2 Major axis and max Feret diameter are not the same. The best-fitting ellipse > is a much more robust measurement than the Feret diameter, as all pixels > inside an object are taken into account, not only the perimeter pixels. > So the A for Area is best fitting ellipse area and major minor axis of best fitting ellipse in AR, Round? And what about Circularity? (I'm rewriting those parts in my thesis that describe what's what in the equation now for at least the 4th time :D ) Regards Ákos
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Re: Questions about equations of Shape Descriptors

 In reply to this post by vischer On Friday 26 Feb 2010  09:06:33 you wrote: > The "sqr" in the above equation does mean "square" (though it's not macro > syntax). That is right. > Major axis and max Feret diameter are not the same. The > best-fitting ellipse is a much more robust measurement than the Feret > diameter, as all pixels inside an object are taken into account, not only > the perimeter pixels. Well it depends of what one is trying to characterise. For instance if one needs to know something related to their length for very thin particles like a latin cross, the fitted ellipse (that has the same area as the cross) has a very small maximum diameter and so it underestimates the extent of the shape (I know, it correlates with the area, but we already know that!). For convex particles with no holes the fitted ellipse might approach the particle other stats. So it really depends. Just in case, I think that most "major" and "minor axis" instances of morphological parameters (such as those in Russ' book) relate to the maximum Feret and breadth (and should not be confused with the Major, Minor of the fitted ellipse found in the IJ results table when one uses "Fit ellipse"). Otherwise one would end up measuring the shape descriptors of ellipses. I mention this because it might become confusing when computing parameters like the "equivalent ellipse area" that represents the area of an ellipse that has the same long and short axis (ie Max Feret and breadth) as the particle. As mentioned in Russ' book there are tons of morphological parameters  which are small variations of others, sometimes with different names or just factored by a constant. Cheers G.
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Re: Questions about equations of Shape Descriptors

 In reply to this post by Ruszkai Ákos On Thursday 25 Feb 2010  10:17:02 you wrote: > Then it's either very misleading, or even worse, not true at all. For > Aspect ratio, the site says: > > *AR* (aspect ratio): major axis/minor axis. Enable "Fit Ellipse" in > *Analyze>Set > Measurements* to have the major and minor axis displayed. In Particles8 I compute the aspect ratio as the ratio of Maximum Feret to the Breadth of the particle. In IJ, that seems to be done on the fitted ellipse. They are measuring different things. > As far as I know, AR is calculated by the other way around: minor/major. As far as I am aware that is not written  in stone, so it is a matter of definition. > Or > am I false here again? I'm aware of the thing that it simply shows how > elongated the area I measure, and it only has real relevance if I have > predefined axis's which I compare to,  but somehow eg. 3:4 is just doesn't > feel the same like 4:3 As you know, since you will be computing all your ARs with the same procedure it should not make a difference in the result. If you want them the way round do 1.0/AR.  That is why one has to be aware to the definition of the parameters. Sometimes these do not match across different packages (or plugins). The advantage here is that you can check the source to see exactly how things are done. Try that in any "commercial" package. > Umm... are we exactly sure that circularity is 4π*area/sqr(perimeter) ? > Because http://www.ncbi.nlm.nih.gov/pubmed/17933272 tells me circularity > is: > > 4π*area/(perimeter)^2 which is != 4π*area/sqr(perimeter) ! Perhaps I confused you in my reply. The formula is correct 4π*area/(perimeter)^2 I just pointed out that "sqrt" (no "t") is the square root in the macro language. But I now realise that this was not what you were asking. > Another misleading thing for me: if AR is calculated from the fit ellipse > axis's (either way why would the descriptin say  **Enable "Fit > Ellipse" in *Analyze>Set  Measurements* to have the major and minor axis > displayed), why does it say "major axis" again in > *Round* (roundness): 4*area/(π*sqr(major axis)), or the inverse of the > aspect ratio. This is confusing but only because the way IJ computes AR. As mentioned before, AR in IJ is for the fitted ellipse, not the particle. You need to write your own AR or use Particles8 to compute the AR of the particle instead. Cheers G.
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Re: Questions about equations of Shape Descriptors

 In reply to this post by Gabriel Landini Hi Gabriel, of course I agree with you that Feret is less abstract, and often comes close to what one really wants to know. But any noise or other irregularities biases the Feret parameters to be overestimated. In our lab, we measure rod-shaped bacteria (cylinders with hemispherical caps), and if we would use Min Feret to classify the diameter of the cylinder (13..15 px), a single noise pixel or slightly bent cylinders would lead to large overestimation. So we better use the ellipse parameters and convert them with an equation into length and diameter. The converter equation assumes that the image of the rod has the same moments of inertia as the ellipse found by ImageJ. For any shape that has two axes of symmetry, and that can be described with two parameters, such a converter equation can possibly be found. regards, Norbert
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Re: Questions about equations of Shape Descriptors

 In the ratio, at times we've also used the perimeter instead of the Feret's diameter.  I think the rationale was that for very irregular objects the Feret's doesn't change much while the perimeter could continue to grow very large. -Michael C On Fri, Feb 26, 2010 at 8:01 AM, Norbert Vischer <[hidden email]> wrote: > Hi Gabriel, > > of course I agree with you that Feret is less abstract, and often comes close to what one really wants to know. > But any noise or other irregularities biases the Feret parameters to be overestimated. > > In our lab, we measure rod-shaped bacteria (cylinders with hemispherical caps), and if we would use Min Feret to classify the diameter of the cylinder (13..15 px), a single noise pixel or slightly bent cylinders would lead to large overestimation. > So we better use the ellipse parameters and convert them with an equation into length and diameter. The converter equation assumes that the image of the rod has the same moments of inertia as the ellipse found by ImageJ. > For any shape that has two axes of symmetry, and that can be described with two parameters, such a converter equation can possibly be found. > > regards, Norbert > -- Michael Cammer  *  http://coxcammer.com/[hidden email]  or  [hidden email] H 914-632-3044     Cell 914-309-3270
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Text on the Movie

 Dear List, in ImageJ, there a way to insert a text over a movie, a text that remains on all frames (or even some of the frames)? Thanks in advance for your help. _________________________________________________________________________________ Dr. Cesare Covino ALEMBIC Advanced Light and Electron Microscopy BioImaging Center San Raffaele Scientific Institute Milano - Italy
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Re: Text on the Movie

 ciao Cesare, try the Event Stamper Plugin in the "Movies" group Hope it helps Mario  Cesare -ALEMBIC- ([hidden email]) wrote:  >  > Dear List,  > in ImageJ, there a way to insert a text over a movie, a text that  > remains on all frames (or even some of the frames)?  >  > Thanks in advance for your help.  >  >  > _________________________________________________________________________________  > Dr. Cesare Covino  > ALEMBIC  > Advanced Light and Electron Microscopy BioImaging Center  > San Raffaele Scientific Institute  > Milano - Italy  > -- Mario Faretta Department of Experimental Oncology European Institute of Oncology c/o IFOM-IEO Campus for Oncogenomics via Adamello 16 20139 Milan Italy Phone: ++39-02574303054 email: [hidden email] http://www.ifom-ieo-campus.it[- Il Tuo 5 per Mille a favore della Ricerca dell'Istituto Europeo di Oncologia Tutti coloro che presentano il modello Unico, il modello 730 o più semplicemente che ricevono dal proprio datore di lavoro il modello CUD, hanno la facoltà di scegliere la destinazione del proprio 5 per mille. Nella casella riservata al Finanziamento agli Enti della Ricerca Sanitaria inserisci il codice fiscale dello IEO (08 69 14 40 153) ed apponi la Tua firma. Il Tuo 5 per Mille verrà destinato alla ricerca contro il cancro dell'Istituto Europeo di Oncologia NON COSTA NULLA E NON COMPORTA ALCUN AUMENTO DELLE IMPOSTE DA VERSARE NON È UN'ALTERNATIVA ALL'8 PER MILLE E' UN GESTO CONCRETO E DI GRANDE VALORE Per saperne di più vai al sito dello IEO www.ieo.it < http://www.ieo.it > oppure scrivi a [hidden email] < mailto:[hidden email]> Segnala ad un amico questa opportunità  -]
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Re: Text on the Movie

 In reply to this post by Cesare -ALEMBIC- On Mar 1, 2010, at 6:04 AM, Cesare -ALEMBIC- wrote: > Dear List, > in ImageJ, there a way to insert a text over a movie, a text that > remains on all frames (or even some of the frames)? You can do this using the image>Stacks>Label command. Set "Interval" to zero to display only the contents of the "Text" field. The daily build adds a "Slice range" option. -wayne