curvature along the outline of a thresholded object

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Re: curvature along the outline of a thresholded object

Herbie
Good day Thomas,

I'm far from sure what you mean by "sensitivity" and "noise" in the context
of curvature.

Obviously, the main problem with general curvature measurements from
spatially discrete images, is the discreteness of the signal. Consequently
and in order to increase accuracy and precision (not the same), we need
reasonable interpolation and I see no chance that this can be performed post
hoc.

With ImageJ I'd use "Interpolation" fom the "Selection"-menu with a
reasonable interval setting. This may provide sufficiently small and perhaps
even equal intervals for the computation of the required difference
quotients. Not perfectly sure yet, but I'd then favour the curvature
computation from polar coordinates as formulated here:
<https://en.wikipedia.org/wiki/Curvature#Polar_coordinates>

I think you could achieve this yourself by writing a little macro.

Regards

Herbie
::::::::::::::::::::::::::::::::::::

Dear Bob,

My reply is late because I had computer problems. The result of the plugin
looks nice. In order to use it I would need two features
1) A parameter to tune the sensitivity. Right now it is not sensitive
enough for my purpose. I am aware that an increase in sensitivity would
make the result more noisy. But as with the plugin of Thomas I would do the
smoothing afterwards.
2) A list of the curvature values along the circumference. Just looking at
the nice result is not enough in my case. I have to extract numbers from
this list.

I am content with the plugin of Thomas. But as we say in German: the better
is the enemy of the good.

Best regards, Thomas



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Re: curvature along the outline of a thresholded object

Robert Dougherty
Herbie,I have a post hoc processing step in my code. I smooth the reciprocal of the radius of curvature. I actually use a weighted power mean for that, as it seemed like the right thing to do, without much evidence.Bob

Sent from Smallbiz Yahoo Mail for iPhone


On Monday, July 6, 2020, 1:20 AM, Herbie <[hidden email]> wrote:

Good day Thomas,

I'm far from sure what you mean by "sensitivity" and "noise" in the context
of curvature.

Obviously, the main problem with general curvature measurements from
spatially discrete images, is the discreteness of the signal. Consequently
and in order to increase accuracy and precision (not the same), we need
reasonable interpolation and I see no chance that this can be performed post
hoc.

With ImageJ I'd use "Interpolation" fom the "Selection"-menu with a
reasonable interval setting. This may provide sufficiently small and perhaps
even equal intervals for the computation of the required difference
quotients. Not perfectly sure yet, but I'd then favour the curvature
computation from polar coordinates as formulated here:
<https://en.wikipedia.org/wiki/Curvature#Polar_coordinates>

I think you could achieve this yourself by writing a little macro.

Regards

Herbie
::::::::::::::::::::::::::::::::::::

Dear Bob,

My reply is late because I had computer problems. The result of the plugin
looks nice. In order to use it I would need two features
1) A parameter to tune the sensitivity. Right now it is not sensitive
enough for my purpose. I am aware that an increase in sensitivity would
make the result more noisy. But as with the plugin of Thomas I would do the
smoothing afterwards.
2) A list of the curvature values along the circumference. Just looking at
the nice result is not enough in my case. I have to extract numbers from
this list.

I am content with the plugin of Thomas. But as we say in German: the better
is the enemy of the good.

Best regards, Thomas



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Re: curvature along the outline of a thresholded object

Herbie
In reply to this post by Robert Dougherty
Dear Bob and all others interested in this topic,

meanwhile I've coded a little macro that appears working reasonably well.

As expected, the interpolation is crucial and it turns out that a reasonable
angle increment, i.e. number of local curvature values, for the sample
images (450x450) provided by Thomas Fischer is about one degree or better
less.

My present interpolation strategy for the sample images is:

//
run( "Create Selection" );
run( "Interpolate", "interval=4 smooth" );
run( "Fit Spline" );
run( "Interpolate", "interval=2 adjust" );
//

Finally I decided not to use polar coordinates but parametrized coordinates:
<https://en.wikipedia.org/wiki/Curvature#In_terms_of_a_general_parametrization>

For the sample image "0453.tif" I get 390 values.
Attached please find the results table as a text file.
Results_0453.txt
<http://imagej.1557.x6.nabble.com/file/t380516/Results_0453.txt>  

For comparison, I really should like to see the corresponding results of
your approach.

Regards

Herbie
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Robert Dougherty wrote

> Herbie,I have a post hoc processing step in my code. I smooth the
> reciprocal of the radius of curvature. I actually use a weighted power
> mean for that, as it seemed like the right thing to do, without much
> evidence.Bob
>
>
> Thomas,Thanks for the feedback and context.  There are several things I
> want to do with this, but I need to focus on my day job for a while.Bob
>
>
> Sent from Smallbiz Yahoo Mail for iPhone
>
>
> On Sunday, July 5, 2020, 10:14 AM, Thomas Fischer &lt;

> thmfischer@

> &gt; wrote:
>
> Dear Bob,
>
> My reply is late because I had computer problems. The result of the plugin
> looks nice. In order to use it I would need two features
> 1) A parameter to tune the sensitivity. Right now it is not sensitive
> enough for my purpose. I am aware that an increase in sensitivity would
> make the result more noisy. But as with the plugin of Thomas I would do
> the
> smoothing afterwards.
> 2) A list of the curvature values along the circumference. Just looking at
> the nice result is not enough in my case. I have to extract numbers from
> this list.
>
> I am content with the plugin of Thomas. But as we say in German: the
> better
> is the enemy of the good.
>
> Best regards, Thomas
>
>
>
>
>
> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty &lt;

> rpd@

> &gt;:
>
>>  Gabriel,
>> Thanks.  In case it matters, there is a new version with smoother
>> calculation and a black background.
>> Bob
>>
>>    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
>>

> g.landini@.ac

>> wrote:
>>
>>  Thanks Bob, I can confirm that it works fine.
>> I think colourblind observers (red-green type) would see the green as
>> some
>> shades of yellow and blue as blue. At lease that is what the Dichromacy
>> plugin
>> shows.
>> Regards
>>
>> Gabriel
>>
>>
>> On Saturday, 4 July 2020 18:05:09 BST you wrote:
>> >  Gabriel,
>> > In the meantime, I tried and failed to track down how ImageJ is
>> supposed
>> to
>> > load the Phase LUT. Giving up, I changed the code to use another
>> > sign-friendly LUT that I coded explicitly.  Now Curvature displays the
>> > results in green-blue. Going forward, it may be a question of which
>> color
>> > scheme is better.  One could experiment by running the new version of
>> > Curvature and then manually changing the LUT to Phase to simulate the
>> old
>> > version.  Perhaps green-blue is better for colorblindness than the
>> red-blue
>> > scheme of Phase?
>> >
>> > Bob
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html





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Re: curvature along the outline of a thresholded object

foxtango
Dear Herbie,

enclosed are two plots one with Thomas' the other one with your code. The
circles are the data. The line is a spline. With one little exception both
codes find the same number of locations with negative curvatures. Your code
produces much smoother data but does not run smoothly across the junction
between begin and end of the data file. Please note that this junction is
in the middle of the plot.

Best, Thomas

Am Mo., 6. Juli 2020 um 18:30 Uhr schrieb Herbie <[hidden email]>:

> Dear Bob and all others interested in this topic,
>
> meanwhile I've coded a little macro that appears working reasonably well.
>
> As expected, the interpolation is crucial and it turns out that a
> reasonable
> angle increment, i.e. number of local curvature values, for the sample
> images (450x450) provided by Thomas Fischer is about one degree or better
> less.
>
> My present interpolation strategy for the sample images is:
>
> //
> run( "Create Selection" );
> run( "Interpolate", "interval=4 smooth" );
> run( "Fit Spline" );
> run( "Interpolate", "interval=2 adjust" );
> //
>
> Finally I decided not to use polar coordinates but parametrized
> coordinates:
> <
> https://en.wikipedia.org/wiki/Curvature#In_terms_of_a_general_parametrization
> >
>
> For the sample image "0453.tif" I get 390 values.
> Attached please find the results table as a text file.
> Results_0453.txt
> <http://imagej.1557.x6.nabble.com/file/t380516/Results_0453.txt>
>
> For comparison, I really should like to see the corresponding results of
> your approach.
>
> Regards
>
> Herbie
> :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
>
> Robert Dougherty wrote
> > Herbie,I have a post hoc processing step in my code. I smooth the
> > reciprocal of the radius of curvature. I actually use a weighted power
> > mean for that, as it seemed like the right thing to do, without much
> > evidence.Bob
> >
> >
> > Thomas,Thanks for the feedback and context.  There are several things I
> > want to do with this, but I need to focus on my day job for a while.Bob
> >
> >
> > Sent from Smallbiz Yahoo Mail for iPhone
> >
> >
> > On Sunday, July 5, 2020, 10:14 AM, Thomas Fischer &lt;
>
> > thmfischer@
>
> > &gt; wrote:
> >
> > Dear Bob,
> >
> > My reply is late because I had computer problems. The result of the
> plugin
> > looks nice. In order to use it I would need two features
> > 1) A parameter to tune the sensitivity. Right now it is not sensitive
> > enough for my purpose. I am aware that an increase in sensitivity would
> > make the result more noisy. But as with the plugin of Thomas I would do
> > the
> > smoothing afterwards.
> > 2) A list of the curvature values along the circumference. Just looking
> at
> > the nice result is not enough in my case. I have to extract numbers from
> > this list.
> >
> > I am content with the plugin of Thomas. But as we say in German: the
> > better
> > is the enemy of the good.
> >
> > Best regards, Thomas
> >
> >
> >
> >
> >
> > Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty &lt;
>
> > rpd@
>
> > &gt;:
> >
> >>  Gabriel,
> >> Thanks.  In case it matters, there is a new version with smoother
> >> calculation and a black background.
> >> Bob
> >>
> >>    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> >>
>
> > g.landini@.ac
>
> >> wrote:
> >>
> >>  Thanks Bob, I can confirm that it works fine.
> >> I think colourblind observers (red-green type) would see the green as
> >> some
> >> shades of yellow and blue as blue. At lease that is what the Dichromacy
> >> plugin
> >> shows.
> >> Regards
> >>
> >> Gabriel
> >>
> >>
> >> On Saturday, 4 July 2020 18:05:09 BST you wrote:
> >> >  Gabriel,
> >> > In the meantime, I tried and failed to track down how ImageJ is
> >> supposed
> >> to
> >> > load the Phase LUT. Giving up, I changed the code to use another
> >> > sign-friendly LUT that I coded explicitly.  Now Curvature displays the
> >> > results in green-blue. Going forward, it may be a question of which
> >> color
> >> > scheme is better.  One could experiment by running the new version of
> >> > Curvature and then manually changing the LUT to Phase to simulate the
> >> old
> >> > version.  Perhaps green-blue is better for colorblindness than the
> >> red-blue
> >> > scheme of Phase?
> >> >
> >> > Bob
> >>
> >> --
> >> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >>
> >>
> >> --
> >> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >>
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
> >
> >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
>
>
>
> --
> Sent from: http://imagej.1557.x6.nabble.com/
>
> --
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>

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Re: curvature along the outline of a thresholded object

Herbie
Dear Thomas,

as far as I can see, the announced plots are missing.

"[...] does not run smoothly across the junction between begin and end
of the data"

Yes, there is a problem with the curvature-data around the start / end
position (presently at the rightmost point of the lowest object border)
and I'm not perfectly sure about its cause. Presently, I conjecture that
the selection process is responsible for it which can't easily be changed.

I have an idea how this problem can be circumvented, but hadn't time to
implement it. However, the first step will be to ensure that the
selection process is actually the main source of the problem.

"Your code produces much smoother data [...]"

The smoothness depends on the kind of spatial contour interpolation and
I'm not aware of exact mathematical approaches to contour interpolations.

My present and purely heuristic approach consists of the three operations:

//
run( "Interpolate", "interval=4 smooth" );
run( "Fit Spline" );
run( "Interpolate", "interval=2 adjust" );
//

The first two operations are dominant.
(Setting "interval" to a lower value means less smoothing...)

It's up to you to decide, or even better, you explain how contours of
spatially discrete and binary objects must be represented in order to
compute the correct local contour curvatures.

Regards

Herbie

::::::::::::::::::::::::::::::::::::::::::::
Am 07.07.20 um 11:48 schrieb Thomas Fischer:

> Dear Herbie,
>
> enclosed are two plots one with Thomas' the other one with your code. The
> circles are the data. The line is a spline. With one little exception both
> codes find the same number of locations with negative curvatures. Your code
> produces much smoother data but does not run smoothly across the junction
> between begin and end of the data file. Please note that this junction is
> in the middle of the plot.
>
> Best, Thomas
>
> Am Mo., 6. Juli 2020 um 18:30 Uhr schrieb Herbie <[hidden email]>:
>
>> Dear Bob and all others interested in this topic,
>>
>> meanwhile I've coded a little macro that appears working reasonably well.
>>
>> As expected, the interpolation is crucial and it turns out that a
>> reasonable
>> angle increment, i.e. number of local curvature values, for the sample
>> images (450x450) provided by Thomas Fischer is about one degree or better
>> less.
>>
>> My present interpolation strategy for the sample images is:
>>
>> //
>> run( "Create Selection" );
>> run( "Interpolate", "interval=4 smooth" );
>> run( "Fit Spline" );
>> run( "Interpolate", "interval=2 adjust" );
>> //
>>
>> Finally I decided not to use polar coordinates but parametrized
>> coordinates:
>> <
>> https://en.wikipedia.org/wiki/Curvature#In_terms_of_a_general_parametrization
>>>
>>
>> For the sample image "0453.tif" I get 390 values.
>> Attached please find the results table as a text file.
>> Results_0453.txt
>> <http://imagej.1557.x6.nabble.com/file/t380516/Results_0453.txt>
>>
>> For comparison, I really should like to see the corresponding results of
>> your approach.
>>
>> Regards
>>
>> Herbie
>> :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
>>
>> Robert Dougherty wrote
>>> Herbie,I have a post hoc processing step in my code. I smooth the
>>> reciprocal of the radius of curvature. I actually use a weighted power
>>> mean for that, as it seemed like the right thing to do, without much
>>> evidence.Bob
>>>
>>>
>>> Thomas,Thanks for the feedback and context.  There are several things I
>>> want to do with this, but I need to focus on my day job for a while.Bob
>>>
>>>
>>> Sent from Smallbiz Yahoo Mail for iPhone
>>>
>>>
>>> On Sunday, July 5, 2020, 10:14 AM, Thomas Fischer &lt;
>>
>>> thmfischer@
>>
>>> &gt; wrote:
>>>
>>> Dear Bob,
>>>
>>> My reply is late because I had computer problems. The result of the
>> plugin
>>> looks nice. In order to use it I would need two features
>>> 1) A parameter to tune the sensitivity. Right now it is not sensitive
>>> enough for my purpose. I am aware that an increase in sensitivity would
>>> make the result more noisy. But as with the plugin of Thomas I would do
>>> the
>>> smoothing afterwards.
>>> 2) A list of the curvature values along the circumference. Just looking
>> at
>>> the nice result is not enough in my case. I have to extract numbers from
>>> this list.
>>>
>>> I am content with the plugin of Thomas. But as we say in German: the
>>> better
>>> is the enemy of the good.
>>>
>>> Best regards, Thomas
>>>
>>>
>>>
>>>
>>>
>>> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty &lt;
>>
>>> rpd@
>>
>>> &gt;:
>>>
>>>>   Gabriel,
>>>> Thanks.  In case it matters, there is a new version with smoother
>>>> calculation and a black background.
>>>> Bob
>>>>
>>>>     On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
>>>>
>>
>>> g.landini@.ac
>>
>>>> wrote:
>>>>
>>>>   Thanks Bob, I can confirm that it works fine.
>>>> I think colourblind observers (red-green type) would see the green as
>>>> some
>>>> shades of yellow and blue as blue. At lease that is what the Dichromacy
>>>> plugin
>>>> shows.
>>>> Regards
>>>>
>>>> Gabriel
>>>>
>>>>
>>>> On Saturday, 4 July 2020 18:05:09 BST you wrote:
>>>>>   Gabriel,
>>>>> In the meantime, I tried and failed to track down how ImageJ is
>>>> supposed
>>>> to
>>>>> load the Phase LUT. Giving up, I changed the code to use another
>>>>> sign-friendly LUT that I coded explicitly.  Now Curvature displays the
>>>>> results in green-blue. Going forward, it may be a question of which
>>>> color
>>>>> scheme is better.  One could experiment by running the new version of
>>>>> Curvature and then manually changing the LUT to Phase to simulate the
>>>> old
>>>>> version.  Perhaps green-blue is better for colorblindness than the
>>>> red-blue
>>>>> scheme of Phase?
>>>>>
>>>>> Bob
>>>>
>>>> --
>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>
>>>>
>>>> --
>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>
>>>
>>>
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>>
>>
>>
>>
>> --
>> Sent from: http://imagej.1557.x6.nabble.com/
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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Re: curvature along the outline of a thresholded object

Kenneth R Sloan-2
This may be irrelevant and ignorant, but I'll ask anyway: is the "interpolation" being done over  a cyclic  domain?  If not, that would explain a glitch at the transition from end to start of the contour.

--
Kenneth Sloan
[hidden email]
Vision is the art of seeing what is invisible to others.

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Re: curvature along the outline of a thresholded object

Herbie
Kenneth,

your remark is to the point and was also made by Michael Schmid offlist.

The problem is, that the spline is applied to a selection by a macro and
therefore I see no easy way to avoid it. What I did and what allows me
to reduce the glitch, is to also compute local curvatures from the same
but rotated contour (180deg). From both results I can detect the
problematic values and try to compensate them...

Thanks for chiming in

Herbie

:::::::::::::::::::::::::::::::::::::::::::
Am 07.07.20 um 22:30 schrieb Kenneth Sloan:

> This may be irrelevant and ignorant, but I'll ask anyway: is the "interpolation" being done over  a cyclic  domain?  If not, that would explain a glitch at the transition from end to start of the contour.
>
> --
> Kenneth Sloan
> [hidden email]
> Vision is the art of seeing what is invisible to others.
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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Re: curvature along the outline of a thresholded object

Herbie
In reply to this post by foxtango
Dear Thomas and all listers who are still interested in this topic,

attached please find my results (of sample image "0453.tif") without the
previously discussed glitch.
For the time being they represent the best I could achieve.

"curvature2", "curvature3", and "curvature4" are results obtained with
increasing smoothing of the underlying contour selection.
As mentioned before, I have no idea what interpolation scheme is
formally adequate and I'm still not sure if there exists such an scheme.
(The graphs are now rotated about 180deg along the object circumference,
in order to conform with the graphs provided earlier.)

Best

Herbie

::::::::::::::::::::::::::::::::::::::::::::
Am 07.07.20 um 11:48 schrieb Thomas Fischer:

> Dear Herbie,
>
> enclosed are two plots one with Thomas' the other one with your code. The
> circles are the data. The line is a spline. With one little exception both
> codes find the same number of locations with negative curvatures. Your code
> produces much smoother data but does not run smoothly across the junction
> between begin and end of the data file. Please note that this junction is
> in the middle of the plot.
>
> Best, Thomas
>
> Am Mo., 6. Juli 2020 um 18:30 Uhr schrieb Herbie <[hidden email]>:
>
>> Dear Bob and all others interested in this topic,
>>
>> meanwhile I've coded a little macro that appears working reasonably well.
>>
>> As expected, the interpolation is crucial and it turns out that a
>> reasonable
>> angle increment, i.e. number of local curvature values, for the sample
>> images (450x450) provided by Thomas Fischer is about one degree or better
>> less.
>>
>> My present interpolation strategy for the sample images is:
>>
>> //
>> run( "Create Selection" );
>> run( "Interpolate", "interval=4 smooth" );
>> run( "Fit Spline" );
>> run( "Interpolate", "interval=2 adjust" );
>> //
>>
>> Finally I decided not to use polar coordinates but parametrized
>> coordinates:
>> <
>> https://en.wikipedia.org/wiki/Curvature#In_terms_of_a_general_parametrization
>>>
>>
>> For the sample image "0453.tif" I get 390 values.
>> Attached please find the results table as a text file.
>> Results_0453.txt
>> <http://imagej.1557.x6.nabble.com/file/t380516/Results_0453.txt>
>>
>> For comparison, I really should like to see the corresponding results of
>> your approach.
>>
>> Regards
>>
>> Herbie
>> :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
>>
>> Robert Dougherty wrote
>>> Herbie,I have a post hoc processing step in my code. I smooth the
>>> reciprocal of the radius of curvature. I actually use a weighted power
>>> mean for that, as it seemed like the right thing to do, without much
>>> evidence.Bob
>>>
>>>
>>> Thomas,Thanks for the feedback and context.  There are several things I
>>> want to do with this, but I need to focus on my day job for a while.Bob
>>>
>>>
>>> Sent from Smallbiz Yahoo Mail for iPhone
>>>
>>>
>>> On Sunday, July 5, 2020, 10:14 AM, Thomas Fischer &lt;
>>
>>> thmfischer@
>>
>>> &gt; wrote:
>>>
>>> Dear Bob,
>>>
>>> My reply is late because I had computer problems. The result of the
>> plugin
>>> looks nice. In order to use it I would need two features
>>> 1) A parameter to tune the sensitivity. Right now it is not sensitive
>>> enough for my purpose. I am aware that an increase in sensitivity would
>>> make the result more noisy. But as with the plugin of Thomas I would do
>>> the
>>> smoothing afterwards.
>>> 2) A list of the curvature values along the circumference. Just looking
>> at
>>> the nice result is not enough in my case. I have to extract numbers from
>>> this list.
>>>
>>> I am content with the plugin of Thomas. But as we say in German: the
>>> better
>>> is the enemy of the good.
>>>
>>> Best regards, Thomas
>>>
>>>
>>>
>>>
>>>
>>> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty &lt;
>>
>>> rpd@
>>
>>> &gt;:
>>>
>>>>   Gabriel,
>>>> Thanks.  In case it matters, there is a new version with smoother
>>>> calculation and a black background.
>>>> Bob
>>>>
>>>>     On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
>>>>
>>
>>> g.landini@.ac
>>
>>>> wrote:
>>>>
>>>>   Thanks Bob, I can confirm that it works fine.
>>>> I think colourblind observers (red-green type) would see the green as
>>>> some
>>>> shades of yellow and blue as blue. At lease that is what the Dichromacy
>>>> plugin
>>>> shows.
>>>> Regards
>>>>
>>>> Gabriel
>>>>
>>>>
>>>> On Saturday, 4 July 2020 18:05:09 BST you wrote:
>>>>>   Gabriel,
>>>>> In the meantime, I tried and failed to track down how ImageJ is
>>>> supposed
>>>> to
>>>>> load the Phase LUT. Giving up, I changed the code to use another
>>>>> sign-friendly LUT that I coded explicitly.  Now Curvature displays the
>>>>> results in green-blue. Going forward, it may be a question of which
>>>> color
>>>>> scheme is better.  One could experiment by running the new version of
>>>>> Curvature and then manually changing the LUT to Phase to simulate the
>>>> old
>>>>> version.  Perhaps green-blue is better for colorblindness than the
>>>> red-blue
>>>>> scheme of Phase?
>>>>>
>>>>> Bob
>>>>
>>>> --
>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>
>>>>
>>>> --
>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>
>>>
>>>
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>>
>>
>>
>>
>> --
>> Sent from: http://imagej.1557.x6.nabble.com/
>>
>> --
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>>
>
> --
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>

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Re: curvature along the outline of a thresholded object

Robert Dougherty
In reply to this post by foxtango
 Thomas,
I have updated the plugin at http://www.optinav.info/Curvature.htm.  Version 5 shows tabular output and is probably more accurate than my earlier version.

Bob




    On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <[hidden email]> wrote:  
 
 Dear Bob,

My reply is late because I had computer problems. The result of the plugin
looks nice. In order to use it I would need two features
1) A parameter to tune the sensitivity. Right now it is not sensitive
enough for my purpose. I am aware that an increase in sensitivity would
make the result more noisy. But as with the plugin of Thomas I would do the
smoothing afterwards.
2) A list of the curvature values along the circumference. Just looking at
the nice result is not enough in my case. I have to extract numbers from
this list.

I am content with the plugin of Thomas. But as we say in German: the better
is the enemy of the good.

Best regards, Thomas





Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <[hidden email]
>:

>  Gabriel,
> Thanks.  In case it matters, there is a new version with smoother
> calculation and a black background.
> Bob
>
>    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> [hidden email]> wrote:
>
>  Thanks Bob, I can confirm that it works fine.
> I think colourblind observers (red-green type) would see the green as some
> shades of yellow and blue as blue. At lease that is what the Dichromacy
> plugin
> shows.
> Regards
>
> Gabriel
>
>
> On Saturday, 4 July 2020 18:05:09 BST you wrote:
> >  Gabriel,
> > In the meantime, I tried and failed to track down how ImageJ is supposed
> to
> > load the Phase LUT. Giving up, I changed the code to use another
> > sign-friendly LUT that I coded explicitly.  Now Curvature displays the
> > results in green-blue. Going forward, it may be a question of which color
> > scheme is better.  One could experiment by running the new version of
> > Curvature and then manually changing the LUT to Phase to simulate the old
> > version.  Perhaps green-blue is better for colorblindness than the
> red-blue
> > scheme of Phase?
> >
> > Bob
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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Re: curvature along the outline of a thresholded object

fabrice senger-2
Dear all,
I really enjoyed this thread. I'm right in the assumption that in the end
to get the curvature you're sampling the contour with a number of points
and use 3 consecutive points to retrieve the radius of curvature? If, so,
how do you set the distance between those points, as for small values you
will run into noise...

Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a écrit :

>  Thomas,
> I have updated the plugin at http://www.optinav.info/Curvature.htm.
> Version 5 shows tabular output and is probably more accurate than my
> earlier version.
>
> Bob
>
>
>
>
>     On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
> [hidden email]> wrote:
>
>  Dear Bob,
>
> My reply is late because I had computer problems. The result of the plugin
> looks nice. In order to use it I would need two features
> 1) A parameter to tune the sensitivity. Right now it is not sensitive
> enough for my purpose. I am aware that an increase in sensitivity would
> make the result more noisy. But as with the plugin of Thomas I would do the
> smoothing afterwards.
> 2) A list of the curvature values along the circumference. Just looking at
> the nice result is not enough in my case. I have to extract numbers from
> this list.
>
> I am content with the plugin of Thomas. But as we say in German: the better
> is the enemy of the good.
>
> Best regards, Thomas
>
>
>
>
>
> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
> [hidden email]
> >:
>
> >  Gabriel,
> > Thanks.  In case it matters, there is a new version with smoother
> > calculation and a black background.
> > Bob
> >
> >    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> > [hidden email]> wrote:
> >
> >  Thanks Bob, I can confirm that it works fine.
> > I think colourblind observers (red-green type) would see the green as
> some
> > shades of yellow and blue as blue. At lease that is what the Dichromacy
> > plugin
> > shows.
> > Regards
> >
> > Gabriel
> >
> >
> > On Saturday, 4 July 2020 18:05:09 BST you wrote:
> > >  Gabriel,
> > > In the meantime, I tried and failed to track down how ImageJ is
> supposed
> > to
> > > load the Phase LUT. Giving up, I changed the code to use another
> > > sign-friendly LUT that I coded explicitly.  Now Curvature displays the
> > > results in green-blue. Going forward, it may be a question of which
> color
> > > scheme is better.  One could experiment by running the new version of
> > > Curvature and then manually changing the LUT to Phase to simulate the
> old
> > > version.  Perhaps green-blue is better for colorblindness than the
> > red-blue
> > > scheme of Phase?
> > >
> > > Bob
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
> --
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>

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Re: curvature along the outline of a thresholded object

Herbie
Bonjour Fabrice,

as stated earlier already, the main problem, given a binary-valued
object, is to obtain a suitable description of the object contour. This
description requires interpolation and perhaps smoothing of the sampled
object's border points.
I'm not aware of a unique mathematically exact approach for this task.
Consequently, this first step or pre-processing is based on heuristics.

To obtain local curvatures from a contour description, exact numeric
methods can be applied. Numeric, not analytic, because differentials are
approximated by quotients of differences. However, I would not denote
the approximation effects as noise.

With ImageJ it is possible to obtain selections or RoIs, i.e. contour
descriptions, that show near to evenly spaced sample points having, of
course, real-valued coordinates. From contour descriptions showing such
parametrized coordinates, local curvatures can be obtained according to
<https://en.wikipedia.org/wiki/Curvature#In_terms_of_a_general_parametrization>

The many investigations of mine since the beginning of this thread show
that the main problem really is in the pre-processing stage:
Curvatures strongly depend on how the contour description is computed.
Even minor parameter changes in the pre-processing can have dramatic
effects on the local curvatures.

That said, I've not yet decided about an adequate ImageJ-based heuristic
for the pre-processing.

Thanks for your interest

Herbie

:::::::::::::::::::::::::::::::::::::::::::
Am 11.07.20 um 13:26 schrieb Fabrice Senger:

> Dear all,
> I really enjoyed this thread. I'm right in the assumption that in the end
> to get the curvature you're sampling the contour with a number of points
> and use 3 consecutive points to retrieve the radius of curvature? If, so,
> how do you set the distance between those points, as for small values you
> will run into noise...
>
> Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a écrit :
>
>>   Thomas,
>> I have updated the plugin at http://www.optinav.info/Curvature.htm.
>> Version 5 shows tabular output and is probably more accurate than my
>> earlier version.
>>
>> Bob
>>
>>
>>
>>
>>      On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
>> [hidden email]> wrote:
>>
>>   Dear Bob,
>>
>> My reply is late because I had computer problems. The result of the plugin
>> looks nice. In order to use it I would need two features
>> 1) A parameter to tune the sensitivity. Right now it is not sensitive
>> enough for my purpose. I am aware that an increase in sensitivity would
>> make the result more noisy. But as with the plugin of Thomas I would do the
>> smoothing afterwards.
>> 2) A list of the curvature values along the circumference. Just looking at
>> the nice result is not enough in my case. I have to extract numbers from
>> this list.
>>
>> I am content with the plugin of Thomas. But as we say in German: the better
>> is the enemy of the good.
>>
>> Best regards, Thomas
>>
>>
>>
>>
>>
>> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
>> [hidden email]
>>> :
>>
>>>   Gabriel,
>>> Thanks.  In case it matters, there is a new version with smoother
>>> calculation and a black background.
>>> Bob
>>>
>>>     On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
>>> [hidden email]> wrote:
>>>
>>>   Thanks Bob, I can confirm that it works fine.
>>> I think colourblind observers (red-green type) would see the green as
>> some
>>> shades of yellow and blue as blue. At lease that is what the Dichromacy
>>> plugin
>>> shows.
>>> Regards
>>>
>>> Gabriel
>>>
>>>
>>> On Saturday, 4 July 2020 18:05:09 BST you wrote:
>>>>   Gabriel,
>>>> In the meantime, I tried and failed to track down how ImageJ is
>> supposed
>>> to
>>>> load the Phase LUT. Giving up, I changed the code to use another
>>>> sign-friendly LUT that I coded explicitly.  Now Curvature displays the
>>>> results in green-blue. Going forward, it may be a question of which
>> color
>>>> scheme is better.  One could experiment by running the new version of
>>>> Curvature and then manually changing the LUT to Phase to simulate the
>> old
>>>> version.  Perhaps green-blue is better for colorblindness than the
>>> red-blue
>>>> scheme of Phase?
>>>>
>>>> Bob
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>
>>>
>>> --
>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>>
>> --
>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>
>
> --
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>

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Re: curvature along the outline of a thresholded object

Robert Dougherty
In reply to this post by fabrice senger-2
Fabrice,I’m taking a different approach from Herbie and Thomas. For each point, I define the radius of curvature using a circle containing that point and two other points in the polygon. (Actually I apply 3-point smoothing to the pixel polygon from "Wand" to produce the source data.) The trick is to choose which other two points.  If the object is supposed to be a circle, then the best points for accuracy are far away, not close!  If the shape is more complicated than a circle, then the points have to be closer together, but if they are too close, then the result is noisy.  I'm still working on the selection algorithm.  I just had an aha moment that the points must not bridge inflection points. This is not yet implemented in my posted code, version 5. I expect it will be in version 6.
Bob


Sent from Smallbiz Yahoo Mail for iPhonet


On Saturday, July 11, 2020, 4:27 AM, Fabrice Senger <[hidden email]> wrote:

Dear all,
I really enjoyed this thread. I'm right in the assumption that in the end
to get the curvature you're sampling the contour with a number of points
and use 3 consecutive points to retrieve the radius of curvature? If, so,
how do you set the distance between those points, as for small values you
will run into noise...

Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a écrit :

>  Thomas,
> I have updated the plugin at http://www.optinav.info/Curvature.htm.
> Version 5 shows tabular output and is probably more accurate than my
> earlier version.
>
> Bob
>
>
>
>
>    On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
> [hidden email]> wrote:
>
>  Dear Bob,
>
> My reply is late because I had computer problems. The result of the plugin
> looks nice. In order to use it I would need two features
> 1) A parameter to tune the sensitivity. Right now it is not sensitive
> enough for my purpose. I am aware that an increase in sensitivity would
> make the result more noisy. But as with the plugin of Thomas I would do the
> smoothing afterwards.
> 2) A list of the curvature values along the circumference. Just looking at
> the nice result is not enough in my case. I have to extract numbers from
> this list.
>
> I am content with the plugin of Thomas. But as we say in German: the better
> is the enemy of the good.
>
> Best regards, Thomas
>
>
>
>
>
> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
> [hidden email]
> >:
>
> >  Gabriel,
> > Thanks.  In case it matters, there is a new version with smoother
> > calculation and a black background.
> > Bob
> >
> >    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> > [hidden email]> wrote:
> >
> >  Thanks Bob, I can confirm that it works fine.
> > I think colourblind observers (red-green type) would see the green as
> some
> > shades of yellow and blue as blue. At lease that is what the Dichromacy
> > plugin
> > shows.
> > Regards
> >
> > Gabriel
> >
> >
> > On Saturday, 4 July 2020 18:05:09 BST you wrote:
> > >  Gabriel,
> > > In the meantime, I tried and failed to track down how ImageJ is
> supposed
> > to
> > > load the Phase LUT. Giving up, I changed the code to use another
> > > sign-friendly LUT that I coded explicitly.  Now Curvature displays the
> > > results in green-blue. Going forward, it may be a question of which
> color
> > > scheme is better.  One could experiment by running the new version of
> > > Curvature and then manually changing the LUT to Phase to simulate the
> old
> > > version.  Perhaps green-blue is better for colorblindness than the
> > red-blue
> > > scheme of Phase?
> > >
> > > Bob
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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Re: curvature along the outline of a thresholded object

fabrice senger-2
Ha ha yes if you don't want to run into infinity

Le sam. 11 juil. 2020 à 19:12, Robert Dougherty <[hidden email]> a écrit :

> Fabrice,I’m taking a different approach from Herbie and Thomas. For each
> point, I define the radius of curvature using a circle containing that
> point and two other points in the polygon. (Actually I apply 3-point
> smoothing to the pixel polygon from "Wand" to produce the source data.) The
> trick is to choose which other two points.  If the object is supposed to be
> a circle, then the best points for accuracy are far away, not close!  If
> the shape is more complicated than a circle, then the points have to be
> closer together, but if they are too close, then the result is noisy.  I'm
> still working on the selection algorithm.  I just had an aha moment that
> the points must not bridge inflection points. This is not yet implemented
> in my posted code, version 5. I expect it will be in version 6.
> Bob
>
>
> Sent from Smallbiz Yahoo Mail for iPhonet
>
>
> On Saturday, July 11, 2020, 4:27 AM, Fabrice Senger <
> [hidden email]> wrote:
>
> Dear all,
> I really enjoyed this thread. I'm right in the assumption that in the end
> to get the curvature you're sampling the contour with a number of points
> and use 3 consecutive points to retrieve the radius of curvature? If, so,
> how do you set the distance between those points, as for small values you
> will run into noise...
>
> Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a écrit
> :
>
> >  Thomas,
> > I have updated the plugin at http://www.optinav.info/Curvature.htm.
> > Version 5 shows tabular output and is probably more accurate than my
> > earlier version.
> >
> > Bob
> >
> >
> >
> >
> >    On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
> > [hidden email]> wrote:
> >
> >  Dear Bob,
> >
> > My reply is late because I had computer problems. The result of the
> plugin
> > looks nice. In order to use it I would need two features
> > 1) A parameter to tune the sensitivity. Right now it is not sensitive
> > enough for my purpose. I am aware that an increase in sensitivity would
> > make the result more noisy. But as with the plugin of Thomas I would do
> the
> > smoothing afterwards.
> > 2) A list of the curvature values along the circumference. Just looking
> at
> > the nice result is not enough in my case. I have to extract numbers from
> > this list.
> >
> > I am content with the plugin of Thomas. But as we say in German: the
> better
> > is the enemy of the good.
> >
> > Best regards, Thomas
> >
> >
> >
> >
> >
> > Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
> > [hidden email]
> > >:
> >
> > >  Gabriel,
> > > Thanks.  In case it matters, there is a new version with smoother
> > > calculation and a black background.
> > > Bob
> > >
> > >    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> > > [hidden email]> wrote:
> > >
> > >  Thanks Bob, I can confirm that it works fine.
> > > I think colourblind observers (red-green type) would see the green as
> > some
> > > shades of yellow and blue as blue. At lease that is what the Dichromacy
> > > plugin
> > > shows.
> > > Regards
> > >
> > > Gabriel
> > >
> > >
> > > On Saturday, 4 July 2020 18:05:09 BST you wrote:
> > > >  Gabriel,
> > > > In the meantime, I tried and failed to track down how ImageJ is
> > supposed
> > > to
> > > > load the Phase LUT. Giving up, I changed the code to use another
> > > > sign-friendly LUT that I coded explicitly.  Now Curvature displays
> the
> > > > results in green-blue. Going forward, it may be a question of which
> > color
> > > > scheme is better.  One could experiment by running the new version of
> > > > Curvature and then manually changing the LUT to Phase to simulate the
> > old
> > > > version.  Perhaps green-blue is better for colorblindness than the
> > > red-blue
> > > > scheme of Phase?
> > > >
> > > > Bob
> > >
> > > --
> > > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> > >
> > >
> > > --
> > > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> > >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>
>
>
> --
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>

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Re: curvature along the outline of a thresholded object

foxtango
Hi herbie,

I understand your wish to tackle a rigorously posed mathematical problem.
Here are two suggestions.
1) find the curvatures along the outline of a binary object in a wavelength
range given in fractions of the length of the outline.
The second goes back to what you may have meant in your first answer in
this thread.
2) calculate the minimum number of Fourier Descriptors necessary to match
the shape in such a way that the sum of the pixels outside the Fourier
outline plus the white pixels inside the Fourier outline is below a
threshold given in fractions of the area of the object.

Of course, heuristic or experience however named enters in the choice of
the Parameters and where the thresholds are set.

Best, Thomas

Am Sa., 11. Juli 2020 um 19:24 Uhr schrieb Fabrice Senger <
[hidden email]>:

> Ha ha yes if you don't want to run into infinity
>
> Le sam. 11 juil. 2020 à 19:12, Robert Dougherty <[hidden email]> a écrit
> :
>
> > Fabrice,I’m taking a different approach from Herbie and Thomas. For each
> > point, I define the radius of curvature using a circle containing that
> > point and two other points in the polygon. (Actually I apply 3-point
> > smoothing to the pixel polygon from "Wand" to produce the source data.)
> The
> > trick is to choose which other two points.  If the object is supposed to
> be
> > a circle, then the best points for accuracy are far away, not close!  If
> > the shape is more complicated than a circle, then the points have to be
> > closer together, but if they are too close, then the result is noisy.
> I'm
> > still working on the selection algorithm.  I just had an aha moment that
> > the points must not bridge inflection points. This is not yet implemented
> > in my posted code, version 5. I expect it will be in version 6.
> > Bob
> >
> >
> > Sent from Smallbiz Yahoo Mail for iPhonet
> >
> >
> > On Saturday, July 11, 2020, 4:27 AM, Fabrice Senger <
> > [hidden email]> wrote:
> >
> > Dear all,
> > I really enjoyed this thread. I'm right in the assumption that in the end
> > to get the curvature you're sampling the contour with a number of points
> > and use 3 consecutive points to retrieve the radius of curvature? If, so,
> > how do you set the distance between those points, as for small values you
> > will run into noise...
> >
> > Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a
> écrit
> > :
> >
> > >  Thomas,
> > > I have updated the plugin at http://www.optinav.info/Curvature.htm.
> > > Version 5 shows tabular output and is probably more accurate than my
> > > earlier version.
> > >
> > > Bob
> > >
> > >
> > >
> > >
> > >    On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
> > > [hidden email]> wrote:
> > >
> > >  Dear Bob,
> > >
> > > My reply is late because I had computer problems. The result of the
> > plugin
> > > looks nice. In order to use it I would need two features
> > > 1) A parameter to tune the sensitivity. Right now it is not sensitive
> > > enough for my purpose. I am aware that an increase in sensitivity would
> > > make the result more noisy. But as with the plugin of Thomas I would do
> > the
> > > smoothing afterwards.
> > > 2) A list of the curvature values along the circumference. Just looking
> > at
> > > the nice result is not enough in my case. I have to extract numbers
> from
> > > this list.
> > >
> > > I am content with the plugin of Thomas. But as we say in German: the
> > better
> > > is the enemy of the good.
> > >
> > > Best regards, Thomas
> > >
> > >
> > >
> > >
> > >
> > > Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
> > > [hidden email]
> > > >:
> > >
> > > >  Gabriel,
> > > > Thanks.  In case it matters, there is a new version with smoother
> > > > calculation and a black background.
> > > > Bob
> > > >
> > > >    On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
> > > > [hidden email]> wrote:
> > > >
> > > >  Thanks Bob, I can confirm that it works fine.
> > > > I think colourblind observers (red-green type) would see the green as
> > > some
> > > > shades of yellow and blue as blue. At lease that is what the
> Dichromacy
> > > > plugin
> > > > shows.
> > > > Regards
> > > >
> > > > Gabriel
> > > >
> > > >
> > > > On Saturday, 4 July 2020 18:05:09 BST you wrote:
> > > > >  Gabriel,
> > > > > In the meantime, I tried and failed to track down how ImageJ is
> > > supposed
> > > > to
> > > > > load the Phase LUT. Giving up, I changed the code to use another
> > > > > sign-friendly LUT that I coded explicitly.  Now Curvature displays
> > the
> > > > > results in green-blue. Going forward, it may be a question of which
> > > color
> > > > > scheme is better.  One could experiment by running the new version
> of
> > > > > Curvature and then manually changing the LUT to Phase to simulate
> the
> > > old
> > > > > version.  Perhaps green-blue is better for colorblindness than the
> > > > red-blue
> > > > > scheme of Phase?
> > > > >
> > > > > Bob
> > > >
> > > > --
> > > > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> > > >
> > > >
> > > > --
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> > > >
> > >
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> > >
> > >
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> > > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> > >
> >
> > --
> > ImageJ mailing list: http://imagej.nih.gov/ij/list.html
> >
> >
> >
> > --
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> >
>
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Re: curvature along the outline of a thresholded object

Herbie
Dear Thomas!

re 1:
As far as I understand, the problem of contour finding isn't solved by
this approach.
But I must admit that I don't understand what "wavelength" means in this
context.

re 2:
Although a bit heuristic, this approach appears worth being considered.

Presently, I try to convert my approach to an IJ-plugin.
However, I can't really get rid of the "start end"-glitch...

Regards

Herbie

::::::::::::::::::::::::::::::::::::::::::::
Am 12.07.20 um 18:20 schrieb Thomas Fischer:

> Hi herbie,
>
> I understand your wish to tackle a rigorously posed mathematical problem.
> Here are two suggestions.
> 1) find the curvatures along the outline of a binary object in a wavelength
> range given in fractions of the length of the outline.
> The second goes back to what you may have meant in your first answer in
> this thread.
> 2) calculate the minimum number of Fourier Descriptors necessary to match
> the shape in such a way that the sum of the pixels outside the Fourier
> outline plus the white pixels inside the Fourier outline is below a
> threshold given in fractions of the area of the object.
>
> Of course, heuristic or experience however named enters in the choice of
> the Parameters and where the thresholds are set.
>
> Best, Thomas
>
> Am Sa., 11. Juli 2020 um 19:24 Uhr schrieb Fabrice Senger <
> [hidden email]>:
>
>> Ha ha yes if you don't want to run into infinity
>>
>> Le sam. 11 juil. 2020 à 19:12, Robert Dougherty <[hidden email]> a écrit
>> :
>>
>>> Fabrice,I’m taking a different approach from Herbie and Thomas. For each
>>> point, I define the radius of curvature using a circle containing that
>>> point and two other points in the polygon. (Actually I apply 3-point
>>> smoothing to the pixel polygon from "Wand" to produce the source data.)
>> The
>>> trick is to choose which other two points.  If the object is supposed to
>> be
>>> a circle, then the best points for accuracy are far away, not close!  If
>>> the shape is more complicated than a circle, then the points have to be
>>> closer together, but if they are too close, then the result is noisy.
>> I'm
>>> still working on the selection algorithm.  I just had an aha moment that
>>> the points must not bridge inflection points. This is not yet implemented
>>> in my posted code, version 5. I expect it will be in version 6.
>>> Bob
>>>
>>>
>>> Sent from Smallbiz Yahoo Mail for iPhonet
>>>
>>>
>>> On Saturday, July 11, 2020, 4:27 AM, Fabrice Senger <
>>> [hidden email]> wrote:
>>>
>>> Dear all,
>>> I really enjoyed this thread. I'm right in the assumption that in the end
>>> to get the curvature you're sampling the contour with a number of points
>>> and use 3 consecutive points to retrieve the radius of curvature? If, so,
>>> how do you set the distance between those points, as for small values you
>>> will run into noise...
>>>
>>> Le sam. 11 juil. 2020 à 08:02, Robert Dougherty <[hidden email]> a
>> écrit
>>> :
>>>
>>>>   Thomas,
>>>> I have updated the plugin at http://www.optinav.info/Curvature.htm.
>>>> Version 5 shows tabular output and is probably more accurate than my
>>>> earlier version.
>>>>
>>>> Bob
>>>>
>>>>
>>>>
>>>>
>>>>     On Sunday, July 5, 2020, 10:14:07 AM PDT, Thomas Fischer <
>>>> [hidden email]> wrote:
>>>>
>>>>   Dear Bob,
>>>>
>>>> My reply is late because I had computer problems. The result of the
>>> plugin
>>>> looks nice. In order to use it I would need two features
>>>> 1) A parameter to tune the sensitivity. Right now it is not sensitive
>>>> enough for my purpose. I am aware that an increase in sensitivity would
>>>> make the result more noisy. But as with the plugin of Thomas I would do
>>> the
>>>> smoothing afterwards.
>>>> 2) A list of the curvature values along the circumference. Just looking
>>> at
>>>> the nice result is not enough in my case. I have to extract numbers
>> from
>>>> this list.
>>>>
>>>> I am content with the plugin of Thomas. But as we say in German: the
>>> better
>>>> is the enemy of the good.
>>>>
>>>> Best regards, Thomas
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Am So., 5. Juli 2020 um 07:33 Uhr schrieb Robert Dougherty <
>>>> [hidden email]
>>>>> :
>>>>
>>>>>   Gabriel,
>>>>> Thanks.  In case it matters, there is a new version with smoother
>>>>> calculation and a black background.
>>>>> Bob
>>>>>
>>>>>     On Saturday, July 4, 2020, 11:33:56 AM PDT, Gabriel Landini <
>>>>> [hidden email]> wrote:
>>>>>
>>>>>   Thanks Bob, I can confirm that it works fine.
>>>>> I think colourblind observers (red-green type) would see the green as
>>>> some
>>>>> shades of yellow and blue as blue. At lease that is what the
>> Dichromacy
>>>>> plugin
>>>>> shows.
>>>>> Regards
>>>>>
>>>>> Gabriel
>>>>>
>>>>>
>>>>> On Saturday, 4 July 2020 18:05:09 BST you wrote:
>>>>>>   Gabriel,
>>>>>> In the meantime, I tried and failed to track down how ImageJ is
>>>> supposed
>>>>> to
>>>>>> load the Phase LUT. Giving up, I changed the code to use another
>>>>>> sign-friendly LUT that I coded explicitly.  Now Curvature displays
>>> the
>>>>>> results in green-blue. Going forward, it may be a question of which
>>>> color
>>>>>> scheme is better.  One could experiment by running the new version
>> of
>>>>>> Curvature and then manually changing the LUT to Phase to simulate
>> the
>>>> old
>>>>>> version.  Perhaps green-blue is better for colorblindness than the
>>>>> red-blue
>>>>>> scheme of Phase?
>>>>>>
>>>>>> Bob
>>>>>
>>>>> --
>>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>>
>>>>>
>>>>> --
>>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>>
>>>>
>>>> --
>>>> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>>>>
>>>>
>>>> --
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>>>>
>>>
>>> --
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>>>
>>>
>>>
>>> --
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>>>
>>
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>>
>
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Re: curvature along the outline of a thresholded object

Robert Dougherty
In reply to this post by Robert Dougherty
 Fabrice, Thomas, Thomas, Herbie, Gabriel, and others who might be following this,

I just posted Version 6 of my curvature plugin at http://www.optinav.info/Curvature.htm I hope it is finished.
My ulterior motive in writing this was that the curvature subject reminded me of the Kelvin effect in evaporating respiratory droplets that are trying to propagate COVID-19.  I realize that this is probably not the OP application.  Also, [1] suggests the Kelvin effect becomes important for droplets smaller than 0.5 microns, and this is pretty small for this case. Even (dried) talking droplets are 0.9 microns or so. Anyway, it is what it is. An introduction to this subject can be found under "Interesting Video" on the top of http://www.optinav.info/ I'd like feedback from biologists.

Bob
1. Marr, L. C., Tang, J. W., Van Mullekom, J., & Lakdawala, S. S. (2019). Mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence. Journal of the Royal Society Interface, 16(150), 20180298.





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Re: curvature along the outline of a thresholded object

Aryeh Weiss
Hi Bob, and thanks for the plugin.

I tried to compile and run it in the Fiji script editor (in part to
learn how to do it, mostly I use python). After installing openjdk-8
,when I run it
I get the following error:
java.lang.ArrayIndexOutOfBoundsException.

So I decided to try to see where this happens. First thing I did was to
make the pixels not square, and I indeed get the warning message about
that. So I knew that it is running at least that far.

Then I added another showMessage right after that one (actually I
started lower down and worked my way up), like so:

         if(pw != ph){
             IJ.showMessage("Warning: pixel height and width in the
image calibration differ.\n"+
                     "This plugin is not designed for that.  The pixel
width \n"+
                     "will be used and the pixel height will be ignored.");
             IJ.showMessage("does this print");   // line that I added
         }

And in this case, the first warning pops up, but the second one that I
added does not, and I get the java.lang.ArrayIndexOutOfBoundsException

I dont know Java, but this seems very strange to me

Thanks in advance for any assistance
--aryeh

On 13/07/2020 06:36, Robert Dougherty wrote:
>   Fabrice, Thomas, Thomas, Herbie, Gabriel, and others who might be following this,
>
> I just posted Version 6 of my curvature plugin at http://www.optinav.info/Curvature.htm I hope it is finished.
> My ulterior motive in writing this was that the curvature subject reminded me of the Kelvin effect in evaporating respiratory droplets that are trying to propagate COVID-19.  I realize that this is probably not the OP application.  Also, [1] suggests the Kelvin effect becomes important for droplets smaller than 0.5 microns, and this is pretty small for this case. Even (dried) talking droplets are 0.9 microns or so. Anyway, it is what it is. An introduction to this subject can be found under "Interesting Video" on the top of http://www.optinav.info/ I'd like feedback from biologists.
>
> Bob
> 1. Marr, L. C., Tang, J. W., Van Mullekom, J., & Lakdawala, S. S. (2019). Mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence. Journal of the Royal Society Interface, 16(150), 20180298.
>
--
Aryeh Weiss
Faculty of Engineering
Bar Ilan University
Ramat Gan 52900 Israel

Ph:  972-3-5317638
FAX: 972-3-7384051

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Re: curvature along the outline of a thresholded object

Kenneth R Sloan-2
My first suspicion is that the code you show is not the code actually running (for whatever reason).

Can you please add a new IJ.showMessage() *before* the one that does print - just to rule out this possibility?
--
Kenneth Sloan
[hidden email]
Vision is the art of seeing what is invisible to others.

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Re: curvature along the outline of a thresholded object

Robert Dougherty
 Kenneth,
Here is a reply that I sent to Aryeh about the out of bounds bug:

That bug is fixed in  Version 7, just posted.  It could happen when particles touched the edges of the image.
The plugin should have no issues for images where the height in pixels, h, differs from the width in pixels, w.  There is a problem when the "pixel width",  pw, differs from the "pixel height", ph. This situation can be created by setting a "Pixel aspect ratio" different from 1.0 in "Analyze/Set Scale" or by setting unequal values for pw and ph in "Image/Properties..." The plugin refuses to run in that case, issuing an error dialog containing "This plugin is not designed for that." because the curvature calculation assumes that the horizontal and vertical scales match.


Aryeh then replied that it is not fixed yet, but I think it should be....
Bob


    On Monday, July 13, 2020, 10:32:36 AM PDT, Kenneth Sloan <[hidden email]> wrote:  
 
 My first suspicion is that the code you show is not the code actually running (for whatever reason).

Can you please add a new IJ.showMessage() *before* the one that does print - just to rule out this possibility?
--
Kenneth Sloan
[hidden email]
Vision is the art of seeing what is invisible to others.

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Re: curvature along the outline of a thresholded object

Aryeh Weiss
Update - Bob's plug-in works (at least on my system).

There is an issue with how I was trying to debug it, in that my
showmessage calls were not doing anything even though the call in the
code worked fine (and the output was exactly as written in the code).

I will need to see why that happened, but it is a separate issue, and
mot likely related to how  I was trying to run it.
When I have a chance I will play with it some more.

--aryeh

On 13/07/2020 20:48, Robert Dougherty wrote:

>   Kenneth,
> Here is a reply that I sent to Aryeh about the out of bounds bug:
>
> That bug is fixed in  Version 7, just posted.  It could happen when particles touched the edges of the image.
> The plugin should have no issues for images where the height in pixels, h, differs from the width in pixels, w.  There is a problem when the "pixel width",  pw, differs from the "pixel height", ph. This situation can be created by setting a "Pixel aspect ratio" different from 1.0 in "Analyze/Set Scale" or by setting unequal values for pw and ph in "Image/Properties..." The plugin refuses to run in that case, issuing an error dialog containing "This plugin is not designed for that." because the curvature calculation assumes that the horizontal and vertical scales match.
>
>
> Aryeh then replied that it is not fixed yet, but I think it should be....
> Bob
>
>
>      On Monday, July 13, 2020, 10:32:36 AM PDT, Kenneth Sloan <[hidden email]> wrote:
>  
>   My first suspicion is that the code you show is not the code actually running (for whatever reason).
I think you are correct about this.

>
> Can you please add a new IJ.showMessage() *before* the one that does print - just to rule out this possibility?
> --
> Kenneth Sloan
> [hidden email]
> Vision is the art of seeing what is invisible to others.
>
> --
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>
> --
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> .


--
Aryeh Weiss
Faculty of Engineering
Bar Ilan University
Ramat Gan 52900 Israel

Ph:  972-3-5317638
FAX: 972-3-7384051

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123