particle analysis-Feret diameter

[K. Kachrimanis]

Dear all,

I have a question or rather a feature request related to the particle analysis, which so far has limited functionality copared to commercial software packages in regard to particle size and shape analysis. I have noticed that there is a Feret diameter included in the module, but it is not clear at which orientation is this Feret measured. Since Feret diameters depend on particle orientation, a Feret at a single orientation is virtually useless, particularly when one has to deal with elongated particles. Would it be possible to include more Ferets, at different angles, and also add an automatic selection of maximum and minimum Ferets? This would enable the calculation of the aspect ratio and other relevant shape descriptors.

Regards,

K.Kachrimanis.

[Philippe Grosjean]

Hi all,

If my understanding of Feret diameter in ImageJ is correct, this is the
*maximum* one, calculated at various angles. But how many angles are
considered? I browse the source code rapidly, and found several
getFeretsDiameter() functions (ij.gui.OvalRoi, PolygonRoi, Roi &
ShapeRoi). In particular, in ShapeRoi, you also have a getMinFeret()
function, but it is commented out. Apparently, shape is rotated every
degree in these function?

Anyway, I join Mr Kachrimanis in a request for reporting also the
*minimum* (and possibly the *mean*) Feret diameter. A lot of derived
measurements can be done if you have those additional measurements. My
plan for the future is to patch ImageJ to report those. This should not
be too difficult... unfortunatelly, I am not a Java programmer and have
little free time now. So, this is a pain for me, and I will not do it
before one year, or so (I still hope to see it added in a future version
of ImageJ).

Best,

Philippe Grosjean

P.S.: by the way, many thanks for adding 'Skew' and 'Kurt' in the
particle analyzer in the latest version of ImageJ!

..............................................<°}))><........
  ) ) ) ) )
( ( ( ( (    Prof. Philippe Grosjean
  ) ) ) ) )
( ( ( ( (    Numerical Ecology of Aquatic Systems
  ) ) ) ) )   Mons-Hainaut University, Pentagone (3D08)
( ( ( ( (    Academie Universitaire Wallonie-Bruxelles
  ) ) ) ) )   8, av du Champ de Mars, 7000 Mons, Belgium
( ( ( ( (
  ) ) ) ) )   phone: + 32.65.37.34.97, fax: + 32.65.37.30.54
( ( ( ( (    email: [hidden email]
  ) ) ) ) )
( ( ( ( (    web:   http://www.umh.ac.be/~econum
  ) ) ) ) )          http://www.sciviews.org
( ( ( ( (
..............................................................

K. Kachrimanis wrote:
> Dear all,
>
> I have a question or rather a feature request related to the particle analysis, which so far has limited functionality copared to commercial software packages in regard to particle size and shape analysis. I have noticed that there is a Feret diameter included in the module, but it is not clear at which orientation is this Feret measured. Since Feret diameters depend on particle orientation, a Feret at a single orientation is virtually useless, particularly when one has to deal with elongated particles. Would it be possible to include more Ferets, at different angles, and also add an automatic selection of maximum and minimum Ferets? This would enable the calculation of the aspect ratio and other relevant shape descriptors.
>
> Regards,
>
> K.Kachrimanis.
>
>

[K. Kachrimanis]

If this is the maximum Feret and it is selected from all Ferets measured, then the only thing missing is to report the minimum and a mean Feret also. Then the system would be complete and better than any commercial image analysis package. By the way, about shape descriptors based on Ferets, I realized that the aspect ratio (among maany other shape descriptors), as well as the projected area or circle equivalent diameter is available in the 'Shape descriptors" plugin by Gary Chinga. So, perhaps it would be a good idea to incorporate that plugin in the basic package.
It seems that so far, the "macroshape" descriptors are more or less complete in ImageJ, a "microshape" descriptor is also available (fractal dimension), and visual texture is also possible to measure. The only thing missing is some "mesoshape" descriptors (like robustness and largest concavity index) as descriped in: Pons et al., Particle morphology: from visualization to measurement, Powder Technol., 103 (1999) 44-57.

Regards,

K.Kachrimanis.


----- Original Message -----
From: "Philippe Grosjean" <[hidden email]>
To: <[hidden email]>
Sent: Sunday, November 27, 2005 8:22 AM
Subject: Re: particle analysis-Feret diameter

> Hi all,
>
> If my understanding of Feret diameter in ImageJ is correct, this is the
> *maximum* one, calculated at various angles. But how many angles are
> considered? I browse the source code rapidly, and found several
> getFeretsDiameter() functions (ij.gui.OvalRoi, PolygonRoi, Roi &
> ShapeRoi). In particular, in ShapeRoi, you also have a getMinFeret()
> function, but it is commented out. Apparently, shape is rotated every
> degree in these function?
>
> Anyway, I join Mr Kachrimanis in a request for reporting also the
> *minimum* (and possibly the *mean*) Feret diameter. A lot of derived
> measurements can be done if you have those additional measurements. My
> plan for the future is to patch ImageJ to report those. This should not
> be too difficult... unfortunatelly, I am not a Java programmer and have
> little free time now. So, this is a pain for me, and I will not do it
> before one year, or so (I still hope to see it added in a future version
> of ImageJ).
>
> Best,
>
> Philippe Grosjean
>
> P.S.: by the way, many thanks for adding 'Skew' and 'Kurt' in the
> particle analyzer in the latest version of ImageJ!
>
> ..............................................<°}))><........
>  ) ) ) ) )
> ( ( ( ( (    Prof. Philippe Grosjean
>  ) ) ) ) )
> ( ( ( ( (    Numerical Ecology of Aquatic Systems
>  ) ) ) ) )   Mons-Hainaut University, Pentagone (3D08)
> ( ( ( ( (    Academie Universitaire Wallonie-Bruxelles
>  ) ) ) ) )   8, av du Champ de Mars, 7000 Mons, Belgium
> ( ( ( ( (
>  ) ) ) ) )   phone: + 32.65.37.34.97, fax: + 32.65.37.30.54
> ( ( ( ( (    email: [hidden email]
>  ) ) ) ) )
> ( ( ( ( (    web:   http://www.umh.ac.be/~econum
>  ) ) ) ) )          http://www.sciviews.org
> ( ( ( ( (
> ..............................................................
>

[Gabriel Landini]

On Sunday 27 November 2005 08:57, K. Kachrimanis wrote:
> If this is the maximum Feret and it is selected from all Ferets measured,
> then the only thing missing is to report the minimum and a mean Feret also.

My plugin Particles8_Plus at
http://www.dentistry.bham.ac.uk/landinig/software/software.html

does most of the descriptors mentioned and includes the angle of the maximum
feret diameter. It also calculates the Breadth, which I think is a better
parameter than the minimum feret, but it uses a different way to estimate
perimeter (it uses Freeman's algorithm) so sometimes the results are not
exactly the same as the built-in analyser.

How do you propose to place the other feret diameters at n angles?
Is this based on the image frame of reference or angles offset from the
direction of the largest one?
And what should one use, the centroid or the centre of mass of the particle?
Note that when using the centre of mass, holes in the particle make it
difficult to standardise the measurements (the same particle filled and with
holes has different feret legths because the "centre" is in a different
location.

> a "microshape" descriptor is also available (fractal dimension),

Fractal dimension is not a microshape descriptor, but a global one which has
no scale (and therefore is not micro, meso or macro). However I have been
always suspicious of other commercial programs that "estimate" the f dim of
particles, for two reasons:
1."particles" I guess are image objects that are most of the time not large
enough to satisfy the requirement of an order of magnitude in the range of
scales analysed.
2. fractal dimension is a bit of a statistical measure, it depends of a
goodness of fit to a particular model, so the "goodness" of the result needs
to be monitored by some other means (for instance the r-squared of a log-log
plot linear fit). When particles are all different sizes, these goodness of
fit are not comparable (it is not the same to look at a 30 pixel particle
than to a 30000 pixel one, in the latter there will be much larger scales
that are not present in the former, and so one is not measuring the same
property unless we already know that the objects are strictly fractal). I do
not think that it is a good idea to do this blindly.
I think that if f dim is incorporated in the Particle Analyzer, it is going to
be misused extensively. If there were a vote I would go for "no".

Cheers,

Gabriel

[Philippe Grosjean]

Gabriel Landini wrote:

> On Sunday 27 November 2005 08:57, K. Kachrimanis wrote:
>
>>If this is the maximum Feret and it is selected from all Ferets measured,
>>then the only thing missing is to report the minimum and a mean Feret also.
>
>
> My plugin Particles8_Plus at
> http://www.dentistry.bham.ac.uk/landinig/software/software.html
>
> does most of the descriptors mentioned and includes the angle of the maximum
> feret diameter. It also calculates the Breadth, which I think is a better
> parameter than the minimum feret, but it uses a different way to estimate
> perimeter (it uses Freeman's algorithm) so sometimes the results are not
> exactly the same as the built-in analyser.
>
> How do you propose to place the other feret diameters at n angles?
> Is this based on the image frame of reference or angles offset from the
> direction of the largest one?

No, you just calculate Feret diameter for each angle. You have a vector
of Feret diameters. Maximum is the max value in this vector. Minimum is
min value. Mean is the average of all values. This is how Matrox Imaging
Library calculates the three values. According to MIL, breadth is max
Feret/min Feret. So, no mather if you have max and min Feret or max
feret and Breadth... you can calculate the third parameter easily. May
be do you calculate breadth in a different way?

> And what should one use, the centroid or the centre of mass of the particle?
> Note that when using the centre of mass, holes in the particle make it
> difficult to standardise the measurements (the same particle filled and with
> holes has different feret legths because the "centre" is in a different
> location.

Sorry, but I don't understand how this affects calculation of Feret
diameter. Obviously, choosing a different centre for rotation affects
the way the rotated particle is represented (well, just a translation
depending on the choosen centre). However, as far as I know, Feret
diameter is not constrained to pass by a given centre. So, no mather
which centre you use for the rotation, once your particle is rotated,
you should get the same Feret diameter. This is true also for holes:
Feret is calculated on the outline of the particle. So, holes have no
effect on it.

>>a "microshape" descriptor is also available (fractal dimension),
>
>
> Fractal dimension is not a microshape descriptor, but a global one which has
> no scale (and therefore is not micro, meso or macro). However I have been
> always suspicious of other commercial programs that "estimate" the f dim of
> particles, for two reasons:
> 1."particles" I guess are image objects that are most of the time not large
> enough to satisfy the requirement of an order of magnitude in the range of
> scales analysed.

I agree totally! Even something simple like circularity is measured with
a large error, due to pixellisation of the particle outline and other
systematic errors introduced in the image, like shadows (just try to
digitize spherical objects and analyze them... you would be surprised of
the results: sometimes circularity is very far from one!)

> 2. fractal dimension is a bit of a statistical measure, it depends of a
> goodness of fit to a particular model, so the "goodness" of the result needs
> to be monitored by some other means (for instance the r-squared of a log-log
> plot linear fit). When particles are all different sizes, these goodness of
> fit are not comparable (it is not the same to look at a 30 pixel particle
> than to a 30000 pixel one, in the latter there will be much larger scales
> that are not present in the former, and so one is not measuring the same
> property unless we already know that the objects are strictly fractal). I do
> not think that it is a good idea to do this blindly.
> I think that if f dim is incorporated in the Particle Analyzer, it is going to
> be misused extensively. If there were a vote I would go for "no".

Same to me!

Best,

Philippe Grosjean

> Cheers,
>
> Gabriel
>
>

[K. Kachrimanis]

> How do you propose to place the other feret diameters at n angles?
> Is this based on the image frame of reference or angles offset from the
> direction of the largest one?
> And what should one use, the centroid or the centre of mass of the particle?
> Note that when using the centre of mass, holes in the particle make it
> difficult to standardise the measurements (the same particle filled and with
> holes has different feret legths because the "centre" is in a different
> location.

Feret diameter is affected by particle orientation and the only way to
minimize
variations due to particle orientation is to measure it at many different
angles. It doesn't matter how you rotate the particle, the dependency on
initial orientation will not go away completely. But the variation will be
minimal if many angles are used. Typically, commercial systems use from 32 to
sometimes more 72 angles, but usually 72 are sufficient.

Regards,

K.Kachrimanis.

[Robert Dougherty]

There are some utilities at
http://www.optinav.com/ImageJplugins/Measure-Roi.htm

Bob

Robert P. Dougherty, Ph.D.
President, OptiNav, Inc.
Phone [phone]
Fax [phone]
www.optinav.com
 

> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of K.
> Kachrimanis
> Sent: Saturday, November 26, 2005 1:45 PM
> To: [hidden email]
> Subject: particle analysis-Feret diameter
>
> Dear all,
>
> I have a question or rather a feature request related to the particle
> analysis, which so far has limited functionality copared to commercial
> software packages in regard to particle size and shape analysis. I have
> noticed that there is a Feret diameter included in the module, but it is
> not clear at which orientation is this Feret measured. Since Feret
> diameters depend on particle orientation, a Feret at a single orientation
> is virtually useless, particularly when one has to deal with elongated
> particles. Would it be possible to include more Ferets, at different
> angles, and also add an automatic selection of maximum and minimum Ferets?
> This would enable the calculation of the aspect ratio and other relevant
> shape descriptors.
>
> Regards,
>
> K.Kachrimanis.

[Gabriel Landini]

Hi Philippe,

On Sun, 27 Nov 2005, Philippe Grosjean wrote:

> Gabriel Landini wrote:
> No, you just calculate Feret diameter for each angle. You have a vector
> of Feret diameters.

Ok, the confusion comes from how I have implemented it (and I wonder if IJ
uses a similar method, I have not checked). I have followed what other
imaging programs seem to do too (Nexus and I think Optimas too): to detect
the furthest 2 points along the convex hull. Of course this does
not guarantee that this line pases through the centre of mass.
This longest distance does not depend of the orientation of the particle
because the way it is calculated.

> Maximum is the max value in this vector. Minimum is
> min value. Mean is the average of all values. This is how Matrox Imaging
> Library calculates the three values. According to MIL, breadth is max
> Feret/min Feret. So, no mather if you have max and min Feret or max
> feret and Breadth... you can calculate the third parameter easily. May
> be do you calculate breadth in a different way?

I use "breadth" as the shortest distance orthogonal to the longest
diameter (as defined above). This distance is not necessarily on the same
line on both sides of the longest diameter. (a macro is included in the
morphology.zip that draws this.

> > Note that when using the centre of mass, holes in the particle make it
> > difficult to standardise the measurements (the same particle filled and with
> > holes has different feret legths because the "centre" is in a different
> > location.
>
> Sorry, but I don't understand how this affects calculation of Feret
> diameter. Obviously, choosing a different centre for rotation affects
> the way the rotated particle is represented (well, just a translation
> depending on the choosen centre). However, as far as I know, Feret
> diameter is not constrained to pass by a given centre. So, no mather
> which centre you use for the rotation, once your particle is rotated,
> you should get the same Feret diameter. This is true also for holes:
> Feret is calculated on the outline of the particle. So, holes have no
> effect on it.

Hmm... I am confused how the algorithm should work. Can you give an
example (just a description)on how is the whole set of Feret diameters
calculated?

Cheers,

Gabriel

[Philippe Grosjean]

Gabriel Landini wrote:
> [...]
> Hmm... I am confused how the algorithm should work. Can you give an
> example (just a description)on how is the whole set of Feret diameters
> calculated?
>
> Cheers,
>
> Gabriel

A naive approach (may be too naive?) is simply to rotate the particle at
given angles and then to use the width of the bounding box around the
rotated particule as the Feret diameter at that orientation. In Matrox
Imaging library, the default number of rotation angles is 6 (if my
memory is correct). I guess that a few tens of rotations would be more
accurate... but obviously much slower to calculate. Thus, a trade-off is
required.

Best,

Philippe Grosjean

[Gabriel Landini]

On Sun, 27 Nov 2005, Kyriakos Kachrimanis wrote:

> > How do you propose to place the other feret diameters at n angles?
> > Is this based on the image frame of reference or angles offset from the
> > direction of the largest one?
> > And what should one use, the centroid or the centre of mass of the particle?
> > Note that when using the centre of mass, holes in the particle make it
> > difficult to standardise the measurements (the same particle filled and with
> > holes has different feret legths because the "centre" is in a different
> > location.
>
> Feret diameter is affected by particle orientation and the only way to
> minimize
> variations due to particle orientation is to measure it at many different
> angles. It doesn't matter how you rotate the particle, the dependency on
> initial orientation will not go away completely. But the variation will be
> minimal if many angles are used. Typically, commercial systems use from 32 to
> sometimes more 72 angles, but usually 72 are sufficient.

Hi,

The maximum feret diameter calculated with the method described in
my previous message is independent on the particle orientation. But
perhaps I am missing something.


Is the definition you are using the maximun difference in (let's say) the
x direction, then rotate the particle and find again this difference, and
measure the length of the particle in the same x directions and so on?
This would mean that the same particle if analysed by 2 people
using a different number of rotations would possibly give different
results.
Furthermore, I suspect that the true particle longest diameter cannot be
guaranteed to be found this way either?

Cheers,

Gabriel

[K. Kachrimanis]

> Is the definition you are using the maximun difference in (let's say) the
> x direction, then rotate the particle and find again this difference, and
> measure the length of the particle in the same x directions and so on?
> This would mean that the same particle if analysed by 2 people
> using a different number of rotations would possibly give different
> results.
> Furthermore, I suspect that the true particle longest diameter cannot be
> guaranteed to be found this way either?
>

According to the user manuals, this is the way the Quantimet 500 is calculating the Feret diameter. And you are right, you need to search an infinite number of rotations to make sure that you get the maximum particle dimension. But with a large number of rotations, you stand a good chance of getting an accurate estimate.

Regards,

K.Kachrimanis.

[Gabriel Landini]

On Sun, 27 Nov 2005, Philippe Grosjean wrote:

> A naive approach (may be too naive?) is simply to rotate the particle at
> given angles and then to use the width of the bounding box around the
> rotated particule as the Feret diameter at that orientation. In Matrox
> Imaging library, the default number of rotation angles is 6 (if my
> memory is correct). I guess that a few tens of rotations would be more
> accurate... but obviously much slower to calculate. Thus, a trade-off is
> required.

Thanks Philippe,
I see. I think that if the maximum diameter is the purpose, then the
method I described is more accurate as it always finds the largest
distance.
Now I see that I was incorrect about holes in the particle. I thought that
this diameters necessarily had to pass through the centre of mass.

Thanks again.
Cheers,

Gabriel

[audrey karperien]

I needed similar data a few years ago, and added a feature to a plugin to calculate distances to the convex hull from various centres, using the min, max, mean, and coefficient of variation amongst all possibles.  

Philippe Grosjean <[hidden email]> wrote:Hi all,

If my understanding of Feret diameter in ImageJ is correct, this is the
*maximum* one, calculated at various angles. But how many angles are
considered? I browse the source code rapidly, and found several
getFeretsDiameter() functions (ij.gui.OvalRoi, PolygonRoi, Roi &
ShapeRoi). In particular, in ShapeRoi, you also have a getMinFeret()
function, but it is commented out. Apparently, shape is rotated every
degree in these function?

Anyway, I join Mr Kachrimanis in a request for reporting also the
*minimum* (and possibly the *mean*) Feret diameter. A lot of derived
measurements can be done if you have those additional measurements. My
plan for the future is to patch ImageJ to report those. This should not
be too difficult... unfortunatelly, I am not a Java programmer and have
little free time now. So, this is a pain for me, and I will not do it
before one year, or so (I still hope to see it added in a future version
of ImageJ).

Best,

Philippe Grosjean

P.S.: by the way, many thanks for adding 'Skew' and 'Kurt' in the
particle analyzer in the latest version of ImageJ!

..............................................<°}))><........
) ) ) ) )
( ( ( ( ( Prof. Philippe Grosjean
) ) ) ) )
( ( ( ( ( Numerical Ecology of Aquatic Systems
) ) ) ) ) Mons-Hainaut University, Pentagone (3D08)
( ( ( ( ( Academie Universitaire Wallonie-Bruxelles
) ) ) ) ) 8, av du Champ de Mars, 7000 Mons, Belgium
( ( ( ( (
) ) ) ) ) phone: + 32.65.37.34.97, fax: + 32.65.37.30.54
( ( ( ( ( email: [hidden email]
) ) ) ) )
( ( ( ( ( web: http://www.umh.ac.be/~econum
) ) ) ) ) http://www.sciviews.org
( ( ( ( (
..............................................................

K. Kachrimanis wrote:
> Dear all,
>
> I have a question or rather a feature request related to the particle analysis, which so far has limited functionality copared to commercial software packages in regard to particle size and shape analysis. I have noticed that there is a Feret diameter included in the module, but it is not clear at which orientation is this Feret measured. Since Feret diameters depend on particle orientation, a Feret at a single orientation is virtually useless, particularly when one has to deal with elongated particles. Would it be possible to include more Ferets, at different angles, and also add an automatic selection of maximum and minimum Ferets? This would enable the calculation of the aspect ratio and other relevant shape descriptors.
>
> Regards,
>
> K.Kachrimanis.
>
>

[r.ghezzo]

Hello,
I think that you have only one feret diameter, the maximum.
draw the convex hull and then compute all the distances between the points in
the hull.
What is the minimum? The smallest size hole through which the particle can pass?
How about a banana? Does anybody know of an algorithm that can compute the
smalles feret for an egg and for a banada?
Juist my monday morning thoughts
Heberto Ghezzo
Meakins-Christie Labs
Montreal - canada

[Gabriel Landini]

On Monday 28 November 2005 13:47, [hidden email] wrote:
> I think that you have only one feret diameter, the maximum.
> draw the convex hull and then compute all the distances between the points
> in the hull.

Yes, that is what I described earlier and what is implemented in the
Particles8_Plus plugin.

> What is the minimum? The smallest size hole through which the particle can
> pass?

Well, not according to the definition of Feret diameter given yesterday.

> How about a banana? Does anybody know of an algorithm that can
> compute the smalles feret for an egg and for a banada?

The algorithm should be the same, but the smallest hole through which the
particle can pass is not necessarily the same as the minimum Feret.
The breadth is not the same either, although it is the smallest hole neded to
pass the particle if you push the particle in the direction of the maximum
Feret.

Cheers,

Gabriel

[audrey karperien]

Regarding the banana, for a few years, I've been doing analyses on cells that change their morphology dramatically, sometimes being shaped very much like banana and others like an egg, as well as some other very different shapes.  I need info on the smallest and largest "diameters", the degree of variability, roundness, etc., and have found the convex hull and the various radii defining it to be a useful way of distinguishing amongst the shapes and relating them to their biological correlates.  I've been using FracLac for this, which also gives fractal, multifractal, and lacunarity values that are useful in defining the cell shapes.  As to the banana, I looked at breakfast and measured the roundness and radii of the convex hull, lacunarity, and density within the convex hull.  The banana had a fractal dimension of 1, though-boring, eh?

Audrey

[Robert Dougherty]

"Measure ROI Curve" on http://www.optinav.com/ImageJplugins/Measure-Roi.htm
can compute the width of a banana, as well as the Feret diameter.  It uses
an ad-hoc algorithm that works well enough most of the time.

A limitation of Measure ROI Curve has recently been pointed out to me.  If
the banana is so sharply bent that its interior angle is less than about 53
degrees (where 180 degrees would be a straight banana), then the algorithm
can get confused.  This happens because the Feret diameter is not what a
human analyst would regard as the length in this case.  I've been asked to
address the limitation and have not yet found a solution.

Bob

Robert P. Dougherty, Ph.D.
President, OptiNav, Inc.
Phone [phone]
Fax [phone]
www.optinav.com
 

> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> [hidden email]
> Sent: Monday, November 28, 2005 5:47 AM
> To: [hidden email]
> Subject: Re: particle analysis-Feret diameter
>
> Hello,
> I think that you have only one feret diameter, the maximum.
> draw the convex hull and then compute all the distances between the points
> in
> the hull.
> What is the minimum? The smallest size hole through which the particle can
> pass?
> How about a banana? Does anybody know of an algorithm that can compute the
> smalles feret for an egg and for a banada?
> Juist my monday morning thoughts
> Heberto Ghezzo
> Meakins-Christie Labs
> Montreal - canada

[Gabriel Landini]

On Monday 28 November 2005 16:14, audrey karperien wrote:
> The banana had a
> fractal dimension of 1, though-boring, eh?

So are you saying that a banana is 1-dimensional?
Or are you implying that the projection of a banana into a plane defines a
shape with 1-D *boundary*? That is a different thing.

Cheers,

Gabriel

[Gabriel Landini]

On Mon, 28 Nov 2005, Krishnan Subramaniam wrote:
>    If I am right then we just need the diameter of the smallest circle that
> would fully circumscribe the ROI - the minimal circle where the ROI is fully
> contained within the circle (We will have at least two points of the ROI
> that have to be on the circumference of the circle). I think the "diam of
> the min circle" method should work - at least I can't see why it would not.

No, they are different things. Imagine an equilateral triangle. The
maximum feret diameter would be the length of one of its sides (i.e. the
longest distance between any 2 points in the perimeter), however the
diameter of the minimal bounding circle has to be larger than the feret
since it has to contain the 3 vertices.

Cheers,

Gabriel

[Robert Dougherty]

I should clarify that Measure ROI Curve computes the Feret diameter
internally as its starting point, but does not return it.  It returns an
estimate of the length of a curve that follows a centerline of the object.

For the topologists out there, what I think I need to start the calculation
properly for sharply bent objects is a generalization of the Feret diameter
that is something like this:  

Find the longest continuous curve that connects two points of the perimeter
of the ROI and satifies both of the following:

1. The curve must inside the ROI along its entire length.
2. The curve is a minimum-length curve for it endpoints; i.e., it cannot be
shortened by moving its interior points.

I'm visualizing a taught string that connects the endpoints and bends at the
interior kinks of the ROI that it is forced to go around to stay inside the
ROI.  This seems like it must be a standard concept.  Intuitively, this
curve should be unique if the ROI is simply connected.

My plan for updating Measure ROI Curve is to begin with the endpoints for
the above curve (assuming they can be found...) and use the left and right
boundary curves defined by these to find the centerline and its length and
the maximum width using the present algorithm.

Bob

> -----Original Message-----
> From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> Robert Dougherty
> Sent: Monday, November 28, 2005 8:29 AM
> To: [hidden email]
> Subject: Re: particle analysis-Feret diameter
>
> "Measure ROI Curve" on http://www.optinav.com/ImageJplugins/Measure-
> Roi.htm
> can compute the width of a banana, as well as the Feret diameter.  It uses
> an ad-hoc algorithm that works well enough most of the time.
>
> A limitation of Measure ROI Curve has recently been pointed out to me.  If
> the banana is so sharply bent that its interior angle is less than about
> 53
> degrees (where 180 degrees would be a straight banana), then the algorithm
> can get confused.  This happens because the Feret diameter is not what a
> human analyst would regard as the length in this case.  I've been asked to
> address the limitation and have not yet found a solution.
>
> Bob
>
> Robert P. Dougherty, Ph.D.
> President, OptiNav, Inc.
> Phone [phone]
> Fax [phone]
> www.optinav.com
>
> > -----Original Message-----
> > From: ImageJ Interest Group [mailto:[hidden email]] On Behalf Of
> > [hidden email]
> > Sent: Monday, November 28, 2005 5:47 AM
> > To: [hidden email]
> > Subject: Re: particle analysis-Feret diameter
> >
> > Hello,
> > I think that you have only one feret diameter, the maximum.
> > draw the convex hull and then compute all the distances between the
> points
> > in
> > the hull.
> > What is the minimum? The smallest size hole through which the particle
> can
> > pass?
> > How about a banana? Does anybody know of an algorithm that can compute
> the
> > smalles feret for an egg and for a banada?
> > Juist my monday morning thoughts
> > Heberto Ghezzo
> > Meakins-Christie Labs
> > Montreal - canada